544 distinct sources across 365 days and 52 start-here pages. Each day also shows its own sources on the last slide of its Learn tab. Where a figure is a physical constant or plain arithmetic, that is said rather than dressed up as a study.
Week 1 · Home energy
The unit, the kettle, the geyser, the shower, and the five things that decide your electricity bill.
Start here · How electricity is measured- South African standard low-voltage supply: 230 V single phase (SANS 10142-1 / NRS 048).
- Definitions: watt = volt × amp; kilowatt-hour = 1,000 watt-hours (SI derived units).
- Eskom Distribution, Tariffs and Charges Booklet 2026/27 (Homelight prepaid 271 c/kWh from 1 April 2026).
Day 1 · What a unit is- Eskom Distribution, Tariffs and Charges Booklet 2026/27 (Homelight prepaid 271 c/kWh from 1 April 2026).
- Definition of the kilowatt-hour: SI derived unit, 1 kWh = 3.6 MJ.
Day 2 · The kettle- Specific heat capacity of water, 4.186 kJ per kg per kelvin (standard physical constant).
- Eskom Distribution, Tariffs and Charges Booklet 2026/27 (Homelight prepaid 271 c/kWh).
Day 3 · The geyser- Specific heat capacity of water, 4.186 kJ per kg per kelvin.
- Eskom Distribution, Residential calculator assumptions page (water heating share of household use).
- Lawrence Berkeley National Laboratory, Residential Water Heating Demand Side Management, South Africa, 2024.
Day 4 · The shower- CLASP, South African Shower Heads Testing Report, October 2022 (measured flow rates; low-flow under 10 L/min).
- Specific heat capacity of water, 4.186 kJ per kg per kelvin; mixing by energy balance.
- Eskom Distribution, Tariffs and Charges Booklet 2026/27.
Day 5 · The little red lights- Arithmetic: 24 h × 365 d = 8,760 h; 1 W × 8,760 h = 8.76 kWh.
- Eskom Distribution, Tariffs and Charges Booklet 2026/27.
Day 6 · The LED swap- US Federal Trade Commission, Shopping for Light Bulbs (60 W incandescent ≈ 800 lumens; LED equivalents).
- Eskom Distribution, Tariffs and Charges Booklet 2026/27.
Day 7 · Your big five- Arithmetic: kWh per day = W × h ÷ 1000.
- Eskom Distribution, Residential calculator assumptions page (water heating leads household use).
- Eskom Distribution, Tariffs and Charges Booklet 2026/27.
Week 2 · Water at home
Litres you use, the leak test, rain on your roof, the dripping tap, and how big a tank needs to be.
Start here · How water is measured- Definitions: 1 L = 1 dm³; 1 kL = 1 m³; density of water about 1 kg per litre (SI units).
- CLASP, South African Shower Heads Testing Report, 2022 (typical and low-flow rates).
- City of Cape Town, DIY Guide to Finding and Fixing Water Leaks (reading the meter); Cape Town water and sanitation tariffs 2025/26 (stepped tariffs, fixed connection charge).
Day 8 · Reading the water meter- City of Cape Town, water and sanitation tariffs 2025/26 (domestic steps R24.32, R33.42, R49.96, R96.37 per kilolitre; 15 mm connection R87.29 a month), as reported by IOL, 30 July 2025.
- Definition: 1 kilolitre = 1,000 litres = 1 cubic metre.
- City of Cape Town, DIY Guide to Finding and Fixing Water Leaks (how to read the meter).
Day 9 · Litres a person- Water Research Commission, du Plessis et al. (2020), per capita consumption by service level: family of four, full connection with outdoor use, about 221 litres per person per day (via Water SA, 2022).
- Water Research Commission (2012) national benchmark 235 litres per person per day; Africa Check (2023) finds the 'almost double the world average' claim unproven.
- City of Cape Town Level 6B restrictions, 2018: 50 litres per person per day.
Day 10 · The toilet- GreenCape, Domestic Water Saving Fixtures Report (older syphon cisterns 9 to 15 litres; modern about 6; efficient dual flush 4 and 2.6 litres).
- Geberit Southern Africa, water usage per toilet flush (dual flush 6/3 litres).
- City of Cape Town, water tariff step 1, 2025/26: R24.32 per kilolitre.
Day 11 · The dripping tap- United States Geological Survey, Drip calculator: one drip = 0.25 mL, 4,000 drips per litre.
- City of Cape Town, DIY Guide to Finding and Fixing Water Leaks (the toilet-paper test for a trickling cistern).
- City of Cape Town, water tariff step 1, 2025/26: R24.32 per kilolitre.
Day 12 · The leak test- City of Cape Town, DIY Guide to Finding and Fixing Water Leaks (meter test with no water use).
- City of Tshwane, Check and repair leaks in your home (overnight meter test).
- City of Cape Town, water tariff step 1, 2025/26: R24.32 per kilolitre.
Day 13 · Rain on your roof- Definition: 1 mm of rain over 1 m² = 1 litre.
- Rain Harvest South Africa, rainwater harvesting calculator: runoff coefficients (metal 0.85 to 0.90, tile 0.75 to 0.80, thatch 0.50 to 0.60).
- South African Weather Service, long-term climate statistics: Cape Town about 500 mm a year, Johannesburg about 700 mm (rounded).
Day 14 · The tank- Rain Harvest South Africa, rainwater harvesting calculator (yield = area × rainfall × runoff; runoff coefficients by roof type).
- Definition: 1 mm of rain over 1 m² = 1 litre.
- Arithmetic throughout; household daily allowance is the reader's own input.
Week 3 · Percentages you meet every day
VAT, discounts, markups, per cent versus percentage points, and the percentage that lies.
Day 15 · VAT- South African Revenue Service, Value-Added Tax: standard rate 15 percent; the 2025 increases to 15.5 and 16 percent were withdrawn by the Bill of 24 April 2025.
- South African Revenue Service, VAT 404 Guide for Vendors, Schedule 2 Part B: zero-rated foodstuffs (brown bread, maize meal, samp, rice, dried beans, lentils, eggs, milk, fruit, vegetables, vegetable oil, pilchards, and others).
- Arithmetic: a price × 1.15 is undone by ÷ 1.15.
Day 17 · Markup and margin- Standard definitions: markup = profit ÷ cost; gross margin = profit ÷ selling price; margin = markup ÷ (1 + markup).
Day 18 · Points and percent- Statistics South Africa, Quarterly Labour Force Survey releases: changes in the unemployment rate are reported in percentage points.
- Arithmetic: points = new − old; percent change = (new − old) ÷ old.
Day 21 · Percent of what?- Arithmetic: a combined rate is the sum of counts over the sum of bases (the weighted mean), not the mean of the rates.
Week 4 · Interest and time
The rule of 72, compound versus simple interest, the loan statement, the minimum payment, and a savings goal.
Day 22 · The rule of 72- The rule of 72 approximates ln 2 ÷ ln(1 + r) ≈ 0.72 ÷ r for rates in the usual range; the exact figure is the compound-interest sum shown beside it.
Day 24 · The bond statement- Standard amortising-loan formula: instalment = P·i ÷ (1 − (1 + i)^−n), with i the monthly rate and n the months. South African home loans charge interest monthly on the outstanding balance.
Day 26 · The minimum payment- Months to clear at payment M: n = −ln(1 − B·i ÷ M) ÷ ln(1 + i); a payment at or below the month's interest never clears (the page shows a dash). Card rates and minimums are on your own statement.
Day 27 · The savings goal- Annuity formulas: payment to reach a future value PMT = FV·i ÷ ((1 + i)^n − 1); future value of a monthly amount FV = PMT·((1 + i)^n − 1) ÷ i.
Day 28 · Inflation- Statistics South Africa, Consumer Price Index (monthly statistical release P0141).
- Fisher relation: real return = (1 + nominal) ÷ (1 + inflation) − 1; purchasing power = amount ÷ (1 + inflation)^years.
Week 5 · The till slip
Price per kilogram, bulk versus small, specials that are not, rounding, and the loyalty card.
Start here · How to read a till slip- Consumer Protection Act 68 of 2008, section 23: displayed price prevails.
- South African Revenue Service, VAT 404 Guide for Vendors: tax invoices and zero-rated foodstuffs.
- South African Revenue Service, 2023 clarification on the VAT treatment of cash rounding differences.
Day 32 · The rounding line- South African Revenue Service, October 2023: VAT treatment of cash rounding differences (rounding to the nearest circulating coin).
- South African Reserve Bank, as reported by EWN: coins remain legal tender and consumers may insist on exact change.
- Arithmetic: uniform rounding down over 0 to 9 cents averages 4.5 cents.
Day 33 · The cost per use- Arithmetic: cost per use = pack price ÷ (pack size ÷ dose). The dose is the reader's own, from the pack.
Day 34 · The loyalty card- Arithmetic: reward as a percentage of spend, compared on the same spend. Individual scheme rates are on each scheme's own terms.
Day 35 · Your basket- Arithmetic: per-unit price × weekly use, summed; a month is 52 ÷ 12 = 4.33 weeks.
Week 6 · The kitchen: measuring
Cups, grams and millilitres, the scale, oven temperatures, doubling a recipe, and ratios.
Start here · How the kitchen measures- Metric kitchen measures as used in South Africa: cup 250 ml, tablespoon 15 ml, teaspoon 5 ml (US customary cup 236.6 ml, tablespoon 14.8 ml).
- Celsius to Fahrenheit: F = 1.8 × C + 32.
Day 36 · Cups to grams- Standard recipe conversion tables for the 250 ml cup: water 250 g, sugar about 200 g, cake flour about 125 g, butter about 225 g, oats about 90 g, cocoa about 100 g (approximate; packing changes flour by 20 percent or more).
Day 37 · The baker's percentages- Baker's percentage: each ingredient expressed as a percentage of total flour weight (flour = 100 percent); standard professional baking practice.
Day 38 · Oven temperatures- F = 1.8 × C + 32. Fan (convection) ovens: reduce the set temperature by about 20 °C or the time by about 10 to 15 percent, the common manufacturer guidance.
Day 39 · Doubling a recipe- Area of a circle = π r²; area scales with the square of the diameter, so diameter scales with the square root of the factor.
Day 40 · Ratios- Arithmetic of ratios: one share = amount ÷ its parts; part of a total = total × parts ÷ sum of parts. Rice by absorption: about 1 part rice to 1.5 parts water by volume (packet guidance).
Day 41 · Portions- Packet serving guidance: dry pasta and rice about 75 to 100 g per person; WHO: at least 400 g of fruit and vegetables a day, about five 80 g servings.
Week 7 · The kitchen: heat and cooking
Why oil smokes, boiling on the Highveld, the pressure cooker, the microwave, and fridge temperatures.
Start here · How heat cooks- Specific heat of water 4.186 kJ per kg per kelvin; heat transfer by conduction, convection and radiation; WHO Five Keys to Safer Food temperatures (5 °C, 60 °C, 70 °C); Maillard browning from roughly 140 °C.
Day 43 · Why oil smokes- Published smoke-point tables (approximate): butter 150 to 177 °C, extra virgin olive oil 190 to 215 °C, refined canola about 204 °C, refined sunflower about 227 °C, ghee about 250 °C. Values vary by refinement and freshness.
Day 44 · Boiling on the Highveld- Boiling point of water falls about 1 °C per 285 to 300 m of altitude (standard tables); Johannesburg about 94 °C. Vapour pressure equals atmospheric pressure at boiling.
Day 45 · The pressure cooker- At about 1 bar (15 psi) above atmospheric pressure water boils at about 120 to 121 °C; manufacturers commonly claim up to 70 percent time saving. The saving is the reader's input.
Day 46 · The microwave- Energy = power × time; time scales inversely with wattage for the same energy. Eskom Homelight prepaid 271 c/kWh from 1 April 2026.
Day 47 · The fridge and the danger zone- WHO, Five Keys to Safer Food: keep food below 5 °C or above 60 °C; cook to 70 °C. USDA FSIS: bacteria can double in as little as 20 minutes in the danger zone; freezer at −18 °C.
Day 48 · The braai- Heating value of barbecue charcoal: lump about 28 to 33 MJ/kg, briquettes about 24 MJ/kg (Heliyon, 2022). 1 kWh = 3.6 MJ. Hand test seconds as taught by Ultimate Braai Master and Weber.
Day 49 · What the kitchen costs- kWh = W × minutes ÷ 60 ÷ 1000; Eskom Homelight prepaid 271 c/kWh from 1 April 2026; wattages and minutes are the reader's own from the labels.
Week 8 · Food and energy
Kilojoules, the label, sugar in teaspoons, salt, and what a portion really is.
Start here · How food energy is measured- 1 kcal = 4.184 kJ. Energy factors: carbohydrate and protein 17 kJ/g, fat 37 kJ/g, alcohol 29 kJ/g (Codex / South African labelling convention). Regulation R146 requires energy in kJ per 100 g and per serving.
Day 50 · Reading the label- Regulation R146 (Foodstuffs, Cosmetics and Disinfectants Act): nutrition table per 100 g/ml and per serving, energy in kJ. Reference adult day about 8,400 kJ (2,000 kcal) is a common comparison base, not a target.
Day 51 · The four fuels- Energy conversion factors used on South African labels: carbohydrate 17 kJ/g, protein 17 kJ/g, fat 37 kJ/g, alcohol 29 kJ/g.
Day 52 · Sugar in teaspoons- WHO Guideline: Sugars intake for adults and children (2015): free sugars below 10 percent of energy, further benefit below 5 percent. A level teaspoon of sugar is about 4 g.
Day 53 · Salt and sodium- WHO: less than 5 g of salt (2 g sodium) a day; salt = sodium × 2.5. South Africa's sodium regulations (R214 of 2013, under the Foodstuffs, Cosmetics and Disinfectants Act) set limits for bread and other categories.
Day 54 · The sugar tax- South African Revenue Service, Health Promotion Levy on sugary beverages: 2.31 c per gram of sugar above 4 g per 100 ml (rate from 1 April 2022, unchanged since).
Day 55 · Energy density- Approximate label values from food composition tables: fried potato chips about 1,300 kJ/100 g, apple about 220 kJ/100 g (SAFOODS / USDA FoodData Central); hand-portion guide as commonly taught by dietitians.
Day 56 · Your plate- Approximate per-100 g values from food composition tables (SAFOODS / USDA), illustrative only; the reader replaces them from labels. Reference day 8,400 kJ is a comparison base.
Week 9 · The body: numbers you meet
Blood pressure, pulse, temperature, waist, sleep hours, and what each number is measuring.
Day 57 · Blood pressure- WHO Guideline for the pharmacological treatment of hypertension in adults (2021): hypertension at ≥140/90 mmHg on repeated measurement. American Heart Association: normal below 120/80, high at 130/80 and above. Mean arterial pressure ≈ diastolic + (systolic − diastolic) ÷ 3.
Day 58 · The pulse- American Heart Association: normal adult resting heart rate 60 to 100 beats per minute. Maximum heart rate estimate 220 − age (Fox formula), an approximation with wide individual variation.
Day 59 · Temperature- NHS: a fever is usually a temperature of 38 °C or above. Normal range about 36.5 to 37.5 °C with daily variation. F = 1.8 × C + 32.
Day 60 · Waist and body mass index- WHO: BMI categories, healthy range 18.5 to 24.9. NICE guideline NG246 (2022): waist-to-height ratio, aim for a waist less than half of height.
Day 61 · Sleep in cycles- American Academy of Sleep Medicine / Sleep Research Society: adults should sleep 7 or more hours a night; sleep cycles average about 90 minutes. Sleep onset latency of 10 to 20 minutes is typical.
Day 62 · Steps and distance- Stride length ≈ 0.415 × height for walking (common pedometer rule of thumb). Lancet Public Health meta-analysis (Paluch et al., 2022): mortality benefit rises with steps and plateaus around 6,000 to 10,000 depending on age.
Day 63 · Your numbers in their ranges- Ranges as quoted on days 57 to 62: AHA resting pulse 60 to 100; AASM sleep 7+ hours; NICE waist-to-height below 0.5; AHA normal systolic below 120; WHO BMI 18.5 to 24.9. Position = (value − low) ÷ (high − low).
Week 10 · The medicine cabinet
Milligrams per kilogram, millilitres and syringes, dosing intervals, expiry dates, and the 24-hour clock.
Start here · How doses are written- Units on South African medicine labels (SAHPRA-approved package inserts): mg per tablet, mg per 5 ml for liquids, mg per kg for paediatric dosing, with interval and 24-hour maximum. Millilitres = dose ÷ strength × 5.
Day 64 · Milligrams per kilogram- National Department of Health, Paediatric Standard Treatment Guidelines and EML, paracetamol dosing reference (January 2024): 15 mg/kg per dose, maximum 4 doses in 24 hours, at least 4 hours apart. Paediatric syrups in South Africa are commonly 120 mg per 5 ml (product labels).
Day 66 · Every six hours- Adult paracetamol package inserts (South Africa): 500 mg to 1 g every 4 to 6 hours, not more than 4 g in 24 hours, counting all paracetamol-containing products. 24-hour clock arithmetic.
Day 67 · The half-life- Caffeine half-life about 5 hours in healthy adults (StatPearls, NIH), longer in pregnancy and with some medicines. Remaining = amount × 0.5^(hours ÷ half-life).
Day 68 · The pack and the date- Expiry printed as month and year means the last day of that month (regulatory convention, e.g. FDA and EU guidance; the same convention applies on South African packs). Typical storage instruction on South African inserts: store below 25 °C, protected from light and moisture.
Day 69 · Percent on a tube- Percentage strength w/w or w/v = grams per 100 g or 100 ml (pharmacopoeial convention). WHO / Rehydration Project home ORS: half a level teaspoon of salt and six level teaspoons of sugar in one litre of clean water; pharmacy ORS sachets are preferred where available.
Day 70 · The dose sheet- Arithmetic: mg a day = mg per dose × doses; mg/kg/day = mg a day ÷ body weight. Example rows are illustrative strengths from common South African products, not recommendations.
Week 11 · Chance and risk
Dice, the lottery, relative versus absolute risk, base rates, and what 1 in 100 means.
Start here · How chance is counted- Elementary probability: P = favourable ÷ total; independent events multiply; P(at least once) = 1 − (1 − p)^n; the law of large numbers.
Day 71 · Dice and coins- Elementary probability: P(no six in 4 rolls) = (5/6)^4; totals with two dice from 36 equally likely pairs; ten heads = (1/2)^10 = 1/1,024.
Day 72 · The Lotto- Ithuba National Lottery game rules: Lotto draws 6 from 52 (jackpot odds 1 in 20,358,520); PowerBall 5 from 50 plus 1 from 20 (1 in 42,375,200). Combinations C(52,6) = 52·51·50·49·48·47 ÷ 720.
Day 73 · Relative and absolute risk- Absolute risk difference = |new − baseline|; number needed to treat (or harm) = 1 ÷ absolute risk difference. Gigerenzer, Reckoning with Risk (2002): report risks as natural frequencies.
Day 74 · Base rates and tests- Bayes' rule expressed as natural frequencies (Gigerenzer & Hoffrage, 1995); positive predictive value = true positives ÷ all positives. Screening practice: a positive screen is confirmed by a second test.
Day 77 · Chances in your year- P(at least once) = 1 − (1 − p)^occasions. Row chances are the reader's own estimates; the Lotto row uses Ithuba's published jackpot odds.
Week 12 · Reading the news
Averages and medians, per capita, graphs that mislead, sample sizes, and what up 50 percent means.
Start here · How to read a number in the news- Statistics South Africa, Mid-year population estimates 2026 (P0302): 63.5 million. https://www.statssa.gov.za/publications/P0302/P03022026.pdf
- Margin of error for a simple random sample at 95 percent confidence ≈ 1 ÷ √n (standard result).
Day 78 · The average that misleads- Statistics South Africa reports median monthly earnings in the Quarterly Labour Force Survey (P0211). https://www.statssa.gov.za/?page_id=1854&PPN=P0211
- Definitions: arithmetic mean and median.
Day 79 · Per capita- Statistics South Africa, Mid-year population estimates 2026 (P0302): 63.5 million. https://www.statssa.gov.za/publications/P0302/P03022026.pdf
- Rate per 100,000 = count ÷ population × 100,000.
Day 80 · Up fifty percent- Percentage change = (after − before) ÷ before; absolute change = after − before. Huff, How to Lie with Statistics (1954), on percentages without bases.
Day 82 · The graph that lies- Huff, How to Lie with Statistics (1954), the 'gee-whiz graph'; Tufte, The Visual Display of Quantitative Information (1983), the lie factor = size of effect in the graphic ÷ size of effect in the data.
Day 83 · Records and runs- For independent, identically distributed years the expected number of records in n years is the harmonic number H(n) ≈ ln n + 0.5772 (Arnold, Balakrishnan & Nagaraja, Records, 1998); the chance a given year is the maximum of n is 1/n.
Week 13 · Weather
The chance of rain, wind chill and heat index, the UV index, humidity, and cold fronts.
Start here · How weather is measured- World Health Organization, Global Solar UV Index: a practical guide (2002), exposure categories. https://www.who.int/publications/i/item/9241590076
- World Meteorological Organization, Guide to Instruments and Methods of Observation (WMO-No. 8): screen temperature at 1.25 to 2 m. https://library.wmo.int/idurl/4/41650
- 1 m/s = 3.6 km/h; 1 mm of rain over 1 m² = 1 litre.
Day 85 · The chance of rain- US National Weather Service, Probability of Precipitation: the chance that measurable precipitation occurs at a point in the forecast period. https://www.weather.gov/ffc/pop
- Thresholds for 'measurable' differ by service (0.2 to 0.25 mm in the US, Canada and Australia); the South African Weather Service forecasts use the same idea. https://www.weathersa.co.za/
Day 86 · Wind chill- Environment and Climate Change Canada, wind chill index: T_wc = 13.12 + 0.6215T − 11.37V^0.16 + 0.3965T·V^0.16 (T in °C, V in km/h), valid for T ≤ 10 °C and V ≥ 4.8 km/h. https://www.canada.ca/en/environment-climate-change/services/weather-health/wind-chill-cold-weather/wind-chill-index.html
- US National Weather Service wind chill chart (same 2001 formula). https://www.weather.gov/safety/cold-wind-chill-chart
Day 87 · Humidity and the feel of heat- Dew point by the Magnus formula with the Alduchov and Eskridge (1996) constants 17.625 and 243.04 °C. https://doi.org/10.1175/1520-0450(1996)035<0601:IMFAOS>2.0.CO;2
- Environment and Climate Change Canada, humidex: T + 0.5555 × (e − 10), with e the vapour pressure in hPa from the dew point. https://www.canada.ca/en/environment-climate-change/services/seasonal-weather-hazards/warm-season-weather-hazards.html
Day 88 · The UV index and sunscreen- World Health Organization, Global Solar UV Index: a practical guide (2002): categories low 0–2, moderate 3–5, high 6–7, very high 8–10, extreme 11+. https://www.who.int/publications/i/item/9241590076
- SPF definition: the ratio of UV dose producing erythema with and without the product; fraction transmitted ≈ 1 ÷ SPF (ISO 24444).
Day 89 · Pressure and the barometer- International Standard Atmosphere (ISO 2533 / US Standard Atmosphere 1976): p = 1013.25 × (1 − 2.25577×10⁻⁵ h)^5.25588. https://ntrs.nasa.gov/citations/19770009539
- South African Weather Service, synoptic charts and cold-front sequence for the south-western Cape. https://www.weathersa.co.za/
Day 90 · Temperature with height- International Standard Atmosphere: temperature lapse rate 6.5 °C per km in the troposphere. https://ntrs.nasa.gov/citations/19770009539
- Table Mountain 1,085 m; Sani Pass summit 2,876 m (topographic survey heights).
Week 14 · The sky
Day length, seasons, moon phases, why the midday sun is in the north, and finding south by the stars.
Start here · How the sky works- NASA, Earth fact sheet: obliquity 23.44°, perihelion 147.1 million km (early January), aphelion 152.1 million km (early July). https://nssdc.gsfc.nasa.gov/planetary/factsheet/earthfact.html
- US Naval Observatory, seasons and the Earth's orbit. https://aa.usno.navy.mil/faq/seasons_orbit
- Solar declination approximation δ = 23.44° × sin(360° × (N − 81) ÷ 365); noon altitude = 90° − |latitude − δ|.
Day 92 · The length of the day- Sunrise equation: cos(hour angle) = −tan(φ)·tan(δ); day length = 2 × hour angle ÷ 15° per hour. https://aa.usno.navy.mil/faq/RST_defs
- Declination approximation as on the start-here page; refraction adds roughly 4 minutes at each end (USNO defines sunrise at −50 arcminutes).
Day 93 · The noon Sun and your shadow- Noon altitude = 90° − |φ − δ|; shadow = height ÷ tan(altitude). Eratosthenes' measurement of the Earth (c. 240 BC) used the same geometry. https://aa.usno.navy.mil/faq/RST_defs
Day 94 · Seasons by tilt and by distance- NASA Earth fact sheet: perihelion 147.1 million km, aphelion 152.1 million km. https://nssdc.gsfc.nasa.gov/planetary/factsheet/earthfact.html
- Inverse-square law for irradiance; Lambert's cosine law for the spread of light on a surface (irradiance ∝ sin of the Sun's altitude).
Day 95 · The phases of the Moon- NASA, the Moon's orbit: synodic month 29.53 days; the Moon rises on average about 50 minutes later each day. https://eclipse.gsfc.nasa.gov/SEhelp/moonorbit.html
- Illuminated fraction k = (1 − cos(phase angle)) ÷ 2 with the phase angle proportional to the Moon's age (circular-orbit approximation).
Day 96 · Finding south by the stars- Astronomical Society of Southern Africa, finding south with the Southern Cross: extend the long axis about 4.5 times to the south celestial pole; the Pointers' perpendicular bisector crosses there. https://assa.saao.ac.za/
- The altitude of the celestial pole equals the observer's latitude (spherical astronomy). A finger at arm's length spans about 1.5°.
Day 97 · The tropic in Limpopo- Tropic of Capricorn at 23.44° S (obliquity of the ecliptic), crossing Limpopo north of Polokwane. https://nssdc.gsfc.nasa.gov/planetary/factsheet/earthfact.html
- Days with the noon Sun south of overhead, for a place just north of the tropic, from the rate at which the declination changes near the solstice (linearised: about 4 days per degree of declination near the turning point).
Week 15 · Time and calendars
Time zones, leap years, days between dates, the average month, and week numbers.
Start here · How time is counted- US Naval Observatory: the tropical year is 365.2422 days; the synodic month 29.53 days. https://aa.usno.navy.mil/faq/calendars
- South African Standard Time is UTC+2 throughout the year (no daylight saving). https://www.timeanddate.com/time/zone/south-africa/johannesburg
Day 99 · Time zones- Time zone offsets and daylight-saving rules by country. https://www.timeanddate.com/time/map/
- South African Standard Time UTC+2, no daylight saving. https://www.timeanddate.com/time/zone/south-africa/johannesburg
Day 100 · Sun time and clock time- The Earth rotates 15° per hour, 1° per 4 minutes; South African Standard Time is based on the 30° E meridian. https://www.timeanddate.com/time/zone/south-africa/johannesburg
- US Naval Observatory, the equation of time (the seasonal wobble of up to about 16 minutes). https://aa.usno.navy.mil/faq/eqtime
Day 101 · Leap years- US Naval Observatory, calendars: the Gregorian leap-year rule and the tropical year of 365.2422 days. https://aa.usno.navy.mil/faq/calendars
- Leap seconds are added by the International Earth Rotation and Reference Systems Service. https://www.iers.org/
Day 102 · Days between dates- Julian Day Number from a Gregorian date (Richards, in the Explanatory Supplement to the Astronomical Almanac, 2013); JDN mod 7 gives the weekday with Monday = 0. https://aa.usno.navy.mil/data/JulianDate
Day 104 · Week numbers- ISO 8601 week dates: weeks begin on Monday; week 1 contains the first Thursday (equivalently 4 January). https://www.iso.org/iso-8601-date-and-time-format.html
- Week = floor((ordinal day − weekday + 10) ÷ 7), with the 0 and 53 edge cases belonging to the adjacent year.
Day 105 · The year's dates- Public Holidays Act 36 of 1994 (South Africa): fixed-date holidays and the Sunday-to-Monday rule. https://www.gov.za/about-sa/public-holidays
- Day of the year for a non-leap year: N = floor(275M ÷ 9) − 2 × floor((M + 9) ÷ 12) + D − 30.
Week 16 · Travel by car
Litres per 100 km, the cost of a trip, tyre pressure, braking distance, and speed versus time.
Start here · How a car's numbers work- 1 km/h = 1/3.6 m/s; 1 bar = 100 kPa = 14.504 psi (SI and customary unit definitions).
- Kinetic energy = ½mv², so stopping energy and aerodynamic drag both scale with the square of speed (classical mechanics).
Day 106 · Litres per hundred- Fuel consumption = litres ÷ kilometres × 100 (the metric convention used in South Africa); the tank-to-tank method as recommended by the Automobile Association of South Africa. https://www.aa.co.za/
Day 107 · The cost of a trip- Department of Mineral Resources and Energy, monthly fuel price adjustments (the reader enters the current pump price). https://www.dmre.gov.za/energy-resources/fuel-prices
- Automobile Association of South Africa route distances: Cape Town to Johannesburg via the N1 about 1,400 km. https://www.aa.co.za/
Day 108 · Tyre pressure- US Department of Energy, fueleconomy.gov: about 0.2 percent fuel economy loss for every 1 psi drop in the average pressure of all tyres. https://www.fueleconomy.gov/feg/maintain.jsp
- 1 bar = 100 kPa = 14.504 psi.
Day 109 · Braking distance- Braking distance = v² ÷ (2μg) from kinetic energy against friction; typical dry-tar friction coefficient about 0.7, wet about 0.4. Arrive Alive, stopping distances. https://www.arrivealive.co.za/Stopping-Distances
- Driver reaction time about 1.5 s under normal conditions (AA and road-safety authorities).
Day 110 · Speed against time- Time = distance ÷ speed; aerodynamic drag force ∝ v² (fluid dynamics), so drag rises 44 percent from 100 to 120 km/h.
- US Department of Energy: fuel economy typically falls sharply above about 80 km/h as drag dominates. https://www.fueleconomy.gov/feg/driveHabits.jsp
Day 111 · The two-second rule- Following distance = speed × time; the two-second rule and the three-second wet-weather extension as taught by Arrive Alive and the AA. https://www.arrivealive.co.za/Following-Distances
Day 112 · What the car costs per kilometre- Cost per km = rand ÷ kilometres covered, summed across cost lines; the Automobile Association of South Africa publishes vehicle running-cost schedules on the same principle. https://www.aa.co.za/ Starting rows are illustrative.
Week 17 · Taxi, bus and plane
Fares per kilometre, luggage weight, altitude and your ears, jet lag, and the airline seat.
Start here · How travel is priced and measured- Fare ÷ distance ÷ people, the unit-price principle from week 5 applied to transport.
- US Federal Aviation Regulations 14 CFR 25.841: cabin pressure altitude not above 8,000 ft (2,438 m) in normal operation. https://www.ecfr.gov/current/title-14/part-25/section-25.841
Day 113 · Fares per kilometre- Unit price per kilometre and per person, as on the start-here page; fares are the reader's own from the trip. Own-car cost per kilometre from week 16, day 112.
Day 114 · Luggage weight- Allowances and excess-baggage fees are set by each airline and printed on the fare rules; the sum is (weight − allowance) × fee per kilogram. Example: FlySafair baggage policy. https://www.flysafair.co.za/
- 1 litre of water = 1 kg.
Day 115 · Altitude and your ears- US Federal Aviation Regulations 14 CFR 25.841: cabin pressure altitude not above 8,000 ft (2,438 m) in normal operation. https://www.ecfr.gov/current/title-14/part-25/section-25.841
- Boyle's law: at constant temperature, volume × pressure is constant; standard-atmosphere pressures as on week 13, day 89.
Day 116 · Jet lag- US Centers for Disease Control, CDC Yellow Book, Jet Lag: symptoms are unusual with fewer than three zones crossed; recovery about one day per time zone, eastward travel generally harder; timed light exposure is the evidence-based countermeasure. https://wwwnc.cdc.gov/travel/yellowbook/2024/environmental-hazards-risks/jet-lag
Day 117 · The flight time- Great-circle distance Cape Town (CPT) to Johannesburg (JNB) about 1,270 km. https://www.greatcirclemap.com/
- Typical airliner cruise speed about 850 km/h (Mach 0.78 to 0.8); ground speed = true airspeed ± wind component.
Day 118 · The airline seat and the weight budget- European Union Air Operations regulation (EU) 965/2012, CAT.POL.MAB.100: standard adult passenger mass 84 kg including hand baggage (for aircraft of 20 seats or more). https://www.easa.europa.eu/en/document-library/regulations
- Seat pitch ranges as published in airline seat maps and specifications (about 28 to 32 inches, 71 to 81 cm).
Day 119 · Your trip, mode by mode- Rand per km = fare ÷ km; per person = fare ÷ people; speed = km ÷ minutes × 60. Starting fares are illustrative; the reader enters current fares.
Week 18 · Maps and distance
Scale, GPS, walking pace, contour lines, and as the crow flies.
Start here · How a map measures- National Geo-spatial Information (South Africa), 1:50,000 topographic map series with 20 m contour interval. https://ngi.dalrrd.gov.za/
- WGS84: one degree of latitude ≈ 111.32 km; one degree of longitude ≈ 111.32 km × cos(latitude). https://www.movable-type.co.uk/scripts/latlong.html
Day 120 · Scale- National Geo-spatial Information, South African topographic series at 1:50,000 and 1:250,000. https://ngi.dalrrd.gov.za/
- Ground distance = map distance × scale factor.
Day 121 · Contour lines- National Geo-spatial Information 1:50,000 series: 20 m contour interval. https://ngi.dalrrd.gov.za/
- Gradient = rise ÷ run; angle = arctan(rise ÷ run).
Day 122 · The mountaineers' rule- Naismith's rule (1892): allow one hour for every 3 miles (5 km) of distance plus one hour for every 2,000 ft (600 m) of ascent; widely used by mountaineering clubs. https://www.mountaineering.scot/safety-and-skills/essential-skills/navigation/naismiths-rule
Day 123 · A degree of latitude and longitude- WGS84 ellipsoid: a degree of latitude ≈ 111.32 km; a degree of longitude ≈ 111.32 km × cos(latitude). https://www.movable-type.co.uk/scripts/latlong.html
- GPS.gov: civilian GPS accuracy typically within a few metres in open sky. https://www.gps.gov/systems/gps/performance/accuracy/
Day 124 · As the crow flies- Haversine formula for great-circle distance on a sphere of radius 6,371 km. https://www.movable-type.co.uk/scripts/latlong.html
- Airport coordinates from published aeronautical data (CPT −33.97, 18.60; JNB −26.14, 28.24).
Day 126 · The hike, leg by leg- Naismith's rule applied per leg: hours = km ÷ pace + ascent ÷ 600. https://www.mountaineering.scot/safety-and-skills/essential-skills/navigation/naismiths-rule
Week 19 · Building and DIY
Area and paint, tiles, a concrete mix, level and plumb, loads, and which drill bit.
Start here · How a building is measured- Area and volume of rectangles and boxes; the 3-4-5 right triangle (Pythagoras). Concrete density about 2,400 kg/m³ (Cement & Concrete SA). https://www.cemcon-sa.org.za/
Day 127 · Area and paint- Spreading rates printed on paint tins; typical interior emulsions cover about 8 to 12 m² per litre per coat (e.g. Dulux South Africa product data). https://www.dulux.co.za/
- Area arithmetic as on the start-here page.
Day 128 · Tiles and waste- Tiles = area ÷ tile area, plus a waste allowance of about 10 percent for straight layouts and 15 for diagonal (trade practice, e.g. tile retailers' calculators).
Day 129 · The concrete mix- Cement & Concrete SA, concrete mixes for small jobs by volume (1:2:3 general purpose; roughly 7 bags of 50 kg cement per m³; density about 2,400 kg/m³). https://www.cemcon-sa.org.za/
- Volume = length × width × thickness in metres.
Day 130 · Square, level and fall- Pythagoras: diagonal² = a² + b²; the 3-4-5 triangle. Fall = run ÷ ratio.
- SANS 10252-2 (drainage) sets minimum gradients by pipe size; paving typically falls about 1 in 80 away from buildings (trade practice). https://www.sabs.co.za/
Day 131 · What a floor can carry- SANS 10160-2 (basis of structural design, imposed loads): domestic floors 1.5 kN/m². https://www.sabs.co.za/
- 1 kPa = 1 kN/m² ≈ 102 kg/m²; 1 litre of water = 1 kg.
Day 132 · Which drill bit- Wall-plug and drill-bit pairing from plug manufacturers' tables (e.g. fischer: 6 mm plug, 6 mm bit, 4 to 5 mm screw). https://www.fischer.co.za/
- Pilot-hole rule of thumb: about 70 percent of screw diameter in softwood, 90 percent in hardwood (trade practice).
Day 133 · The room, priced- Quantity × unit price, summed, plus a contingency; prices in the starting rows are illustrative and the reader enters the shop's.
Week 20 · Fabrics and laundry
Metres of fabric, wash temperatures, why stains lift, ironing, and drying.
Start here · How cloth and washing are measured- ISO 3758 / GINETEX care labelling symbols: wash tub, bleach triangle, drying square, iron dots (110, 150, 200 °C), dry-clean circle. https://www.ginetex.net/
- Specific heat of water 4.186 kJ per kg per kelvin; 1 inch = 2.54 cm.
Day 134 · Metres of fabric- Curtain-making practice: fullness of 2 to 2.5 times the track width; standard roll widths 115 and 150 cm (fabric trade convention).
Day 135 · Wash temperatures- Wash-water heating from the specific heat of water; Eskom Homelight prepaid 271 c/kWh. Detergent enzymes are most active at 30 to 40 °C and denature above about 60 °C (detergent manufacturers' technical guidance, e.g. AISE). https://www.aise.eu/
Day 136 · Detergent and why stains lift- Dosing instructions on detergent packs scale by load and water hardness (manufacturers' labels; AISE dosing guidance). https://www.aise.eu/
- Surfactant action, enzyme (protease, amylase) stain removal and oxygen-bleach decolouring: standard detergent chemistry.
Day 137 · Ironing- ISO 3758 ironing symbols: one dot up to 110 °C, two up to 150 °C, three up to 200 °C. https://www.ginetex.net/
- Energy = watts × hours; Eskom Homelight prepaid 271 c/kWh.
Day 138 · Drying- Latent heat of vaporisation of water about 2,260 kJ per kg.
- EU energy labelling for washing machines (Regulation (EU) 2019/2014): remaining moisture content after spinning, typically around 50 percent at 1,400 rpm and higher at lower speeds. https://eur-lex.europa.eu/eli/reg_del/2019/2014/oj
- Heat-pump dryers use roughly half the energy of vented dryers (EU energy label classes).
Day 139 · Shrinkage and sizes- 1 inch = 2.54 cm (exact). Shrinkage stated on fabric and garment labels as a percentage of dimension (textile trade practice).
Day 140 · The laundry week- Heating energy from the specific heat of water, incoming water assumed 20 °C; a month is 4.33 weeks; Eskom Homelight prepaid 271 c/kWh.
Week 21 · The garden
Soil volume, compost, millimetres of rain to litres, plant spacing, watering, and pH.
Start here · How a garden is measured- Volume and area arithmetic; 1 mm of rain over 1 m² = 1 litre. Royal Horticultural Society, soil pH and its logarithmic scale. https://www.rhs.org.uk/soil-composts-mulches/soil-ph
Day 141 · Soil volume- Royal Horticultural Society, raised beds: fill with a topsoil and compost mix; volume = length × width × depth. https://www.rhs.org.uk/garden-features/raised-beds
- Nursery bag sizes of 30 litres are the common South African retail unit.
Day 142 · Compost by the ratio- Royal Horticultural Society, composting: aim for roughly 25 to 50 percent greens by volume, the rest browns; the heap shrinks substantially as it decomposes. https://www.rhs.org.uk/soil-composts-mulches/composting
- Carbon-to-nitrogen ratio of about 30:1 for active composting (Cornell Waste Management Institute). https://compost.css.cornell.edu/
Day 143 · Rain into the bed- Royal Horticultural Society, watering: vegetables need roughly 25 mm a week in the growing season; water deeply rather than little and often. https://www.rhs.org.uk/garden-jobs/watering
- 1 mm of rain over 1 m² = 1 litre.
Day 144 · Plant spacing- Seed-packet spacings for common vegetables (e.g. lettuce 30 cm, tomato 60 cm, carrot 5 to 8 cm); Department of Agriculture vegetable production guidelines. https://www.dalrrd.gov.za/
Day 145 · Watering- Royal Horticultural Society, watering: about 25 mm a week for vegetables; water in the morning; mulch reduces evaporation. https://www.rhs.org.uk/garden-jobs/watering
- Flow rate by the bucket test, as in week 1.
Day 146 · pH- Royal Horticultural Society, soil pH: the scale is logarithmic; most vegetables grow best at pH 6 to 7; lime raises pH, sulphur lowers it. https://www.rhs.org.uk/soil-composts-mulches/soil-ph
- pH = −log₁₀[H⁺], so a difference of 1 is a factor of 10.
Day 147 · The bed, planted- Plants = area ÷ spacing², with the packet's spacing; a 10 percent allowance for failed seedlings is common nursery advice.
Week 22 · Sport numbers
Pace per kilometre, heart-rate zones, the scoreboard, handicaps, and averages.
Start here · How sport is counted- American Heart Association, target heart rates: maximum about 220 − age, training range 50 to 85 percent of it. https://www.heart.org/en/healthy-living/fitness/fitness-basics/target-heart-rates
- Pace = minutes ÷ km; speed = 60 ÷ pace.
Day 149 · Heart-rate zones- Karvonen, M. J. et al. (1957): target heart rate = resting + (maximum − resting) × intensity; the heart-rate reserve method. American College of Sports Medicine guidelines use the same method. https://www.acsm.org/
- Maximum heart rate estimate 220 − age with a standard deviation of about 10 to 12 beats (Tanaka et al., 2001).
Day 150 · The scoreboard- Laws of Cricket (MCC) and ICC playing conditions: an over is six legal balls; run rate = runs ÷ overs. https://www.lords.org/mcc/the-laws-of-cricket
Day 151 · The golf handicap- World Handicap System, Rules of Handicapping, Rule 6.1: Course Handicap = Handicap Index × (Slope Rating ÷ 113) + (Course Rating − Par). https://www.usga.org/handicapping/roh/Content/rules/6%201%20Course%20Handicap%20Calculation.htm
- GolfRSA administers the WHS in South Africa. https://www.golfrsa.com/
Day 152 · Cricket's averages- Cricket statistics conventions: batting average = runs ÷ (innings − not outs); strike rate = runs per 100 balls; bowling average = runs conceded ÷ wickets; economy = runs per over (ICC / ESPNcricinfo statistical definitions). https://www.espncricinfo.com/
Day 153 · Predicting the longer race- Riegel, P. S. (1981). Athletic records and human endurance. American Scientist, 69(3): T₂ = T₁ × (D₂ ÷ D₁)^1.06. https://www.jstor.org/stable/27850427
Week 23 · Electricity and safety
Amps, volts and watts, the plug fuse, extension cords, and why the trip switch trips.
Start here · How electricity is kept safe- SANS 10142-1, the wiring of premises: 230 V single-phase supply; earth-leakage protection (30 mA) required for domestic installations. https://www.sabs.co.za/
- SANS 164-1 (16 A three-pin plug) and the 2.5 A two-pin Europlug (SANS 164-5 / CEE 7/16).
Day 155 · Amps from watts- Ohm's law and power: I = P ÷ V; heating in a conductor ∝ I²R. Typical South African socket circuits are protected at 20 A (SANS 10142-1). https://www.sabs.co.za/
Day 156 · The plug's rating- SANS 164-1: 16 A three-pin plug; SANS 164-2: the 16 A compact three-pin plug; SANS 164-5 / CEE 7/16 Europlug rated 2.5 A. https://www.sabs.co.za/
- Adaptor ratings are printed on the adaptor and shared across its outlets.
Day 157 · The extension cord- Copper resistivity about 0.0175 Ω·mm²/m; voltage drop = I × R over the go-and-return length. Flexible-cord current ratings by cross-section (IEC 60227 / SANS 1574): 0.75 mm² about 6 A, 1.0 mm² about 10 A, 1.5 mm² about 16 A. https://www.sabs.co.za/
Day 158 · Why the trip switch trips- Circuit breakers open on sustained overcurrent with an inverse time characteristic (IEC 60898); typical domestic socket circuit rating 20 A (SANS 10142-1). https://www.sabs.co.za/
Day 159 · Thirty milliamps- IEC 60479-1, effects of current on human beings: let-go threshold about 10 mA; ventricular fibrillation risk rises above about 30 to 50 mA depending on duration. https://webstore.iec.ch/
- SANS 10142-1: 30 mA earth-leakage protection required in domestic installations; residual-current devices compare outgoing and returning current. https://www.sabs.co.za/
Day 160 · Sizing a generator or inverter- Apparent power (kVA) × power factor = real power (kW); a power factor of about 0.8 is the usual rating basis for small generators. Compressor motors draw a starting current of several times their running current (manufacturers' data).
Day 161 · The circuit's load- Amps = watts ÷ 230, summed; compared with the breaker or cord rating (SANS 10142-1 socket circuits typically 20 A). https://www.sabs.co.za/
Week 24 · Solar and batteries
Panel watts, kilowatt-hours a day, battery amp-hours, the inverter, and payback.
Start here · How solar power is measured- Global Solar Atlas (World Bank / Solargis): specific photovoltaic power output for South Africa, roughly 4.5 to 5.5 kWh per kWp per day. https://globalsolaratlas.info/
- NREL PVWatts: typical system losses about 14 percent plus inverter and temperature effects; performance ratios of 0.75 to 0.8 are usual. https://pvwatts.nrel.gov/
Day 162 · Panel watts to kilowatt-hours- Global Solar Atlas: photovoltaic output in South Africa about 4.5 to 5.5 kWh per installed kWp per day. https://globalsolaratlas.info/
- Performance ratio 0.75 to 0.8 (NREL PVWatts loss defaults). https://pvwatts.nrel.gov/
Day 163 · Peak sun hours and the panel- Standard test conditions for photovoltaic modules: 1,000 W/m², 25 °C (IEC 61215). Global Solar Atlas gives daily global horizontal and tilted irradiation by location. https://globalsolaratlas.info/
- Commercial silicon module efficiencies about 18 to 23 percent (manufacturers' datasheets).
Day 164 · Battery amp-hours- Watt-hours = amp-hours × volts. Depth of discharge: lithium iron phosphate typically 80 to 90 percent, flooded lead-acid about 50 percent for cycle life (Battery University). https://batteryuniversity.com/article/bu-808-how-to-prolong-lithium-based-batteries
Day 165 · The inverter's draw- Power = volts × amps; inverter efficiency typically 90 to 95 percent (manufacturers' datasheets). Conductor sizing for DC currents per SANS 10142-1. https://www.sabs.co.za/
Day 166 · The geyser on solar- Geyser energy from week 1, day 3 (150 L heated 45 °C ≈ 7.85 kWh). Heat-pump water heaters use about a third of the electricity of a resistive element (coefficient of performance about 3; Eskom and manufacturers' data).
Day 167 · Payback- Simple payback = cost ÷ yearly saving; with a saving growing at rate e, years = ln(1 + cost·e ÷ saving) ÷ ln(1 + e) (geometric series). Panel degradation about 0.5 percent a year (NREL). https://www.nrel.gov/
Day 168 · The night's loads- Watt-hours = watts × hours; amp-hours = watt-hours ÷ volts ÷ usable share. Appliance draws are the reader's own from labels and week 1.
Week 25 · The car and its physics
Why an engine warms up, oil, brakes and friction, aquaplaning, and seatbelts.
Day 169 · Why an engine warms up- US Department of Energy, fueleconomy.gov: fuel economy falls about 12 percent in cold conditions in city driving and up to about 20 percent on short trips of a few kilometres; idling to warm up is not recommended. https://www.fueleconomy.gov/feg/coldweather.shtml
Day 170 · Oil- SAE J300 engine oil viscosity classification: the W grade is the low-temperature rating, the second number the high-temperature rating. https://www.sae.org/standards/content/j300_202104/
- Service intervals as specified by the vehicle manufacturer, by distance or time.
Day 171 · Brakes and friction- Kinetic energy ½mv²; potential energy mgh; specific heat of water 4.186 kJ per kg per kelvin. Brake fade from overheating: vehicle engineering texts and Arrive Alive guidance on descents. https://www.arrivealive.co.za/
Day 172 · Aquaplaning- Horne, W. B. and Dreher, R. C. (1963), Phenomena of pneumatic tire hydroplaning, NASA TN D-2056: hydroplaning speed (knots) ≈ 9 √(tyre pressure in psi). https://ntrs.nasa.gov/citations/19640000612
- 1 knot = 1.852 km/h; 1 bar = 14.504 psi.
Day 173 · Seatbelts and the crumple zone- Deceleration a = v² ÷ 2d; force = mass × a (classical mechanics). Seatbelt effectiveness: WHO, Road traffic injuries; Arrive Alive on seatbelts. https://www.who.int/news-room/fact-sheets/detail/road-traffic-injuries
Day 174 · Cornering- Centripetal acceleration v² ÷ r; maximum cornering speed v = √(μ g r) for a flat bend (classical mechanics); friction coefficients as in week 16.
Week 26 · Phones and data
Megabytes and gigabytes, what a video costs in data, battery milliamp-hours, and charging.
Start here · How data and batteries are counted- IEC 80000-13: decimal prefixes kilo, mega, giga in steps of 1,000; binary prefixes (kibi, mebi, gibi) for 1,024 steps. https://www.iso.org/standard/31898.html
- Typical smartphone battery nominal voltage 3.85 V (manufacturers' specifications).
Day 176 · Megabytes and gigabytes- IEC 80000-13 decimal prefixes. Typical sizes: smartphone photo 3 to 5 MB, WhatsApp text message a few KB, audio streaming about 1 MB per minute at 128 kbps (service documentation).
Day 177 · What a video costs in data- Netflix Help Center, How to control how much data Netflix uses: about 1 GB per hour standard definition, up to 3 GB per hour high definition, up to 7 GB per hour ultra-high definition. https://help.netflix.com/en/node/87
Day 178 · The battery- Energy = charge × voltage; smartphone cells are nominally about 3.85 V (manufacturers' specifications). Battery capacity fade of roughly 20 percent after several hundred cycles (Battery University). https://batteryuniversity.com/
Day 179 · Charging- Energy = power × time; charging efficiency of roughly 80 to 90 percent; lithium-ion charging slows above about 80 percent (constant-voltage phase) and heat accelerates ageing (Battery University). https://batteryuniversity.com/article/bu-409-charging-lithium-ion
Day 181 · The cost of a gigabyte- Unit price = rand ÷ gigabytes; effective price = rand ÷ gigabytes used. ICASA End-User and Subscriber Service Charter Regulations (2019): data rollover and transfer rights before expiry. https://www.icasa.org.za/
Day 182 · Your month in data- Per-unit sizes are typical service figures (Netflix about 3 GB per HD hour, about 50 MB a minute; audio about 1 MB a minute; video calls roughly 5 MB a minute); the reader replaces them from the network's usage report.
Week 27 · The internet in numbers
Megabits versus megabytes, download times, passwords and combinations, and the QR code.
Start here · How the internet counts- 1 byte = 8 bits; data rates in bits per second, sizes in bytes (IEC 80000-13). Speed of light in optical fibre about 2 × 10⁸ m/s (refractive index about 1.47).
Day 184 · Streaming and the line- Netflix Help Center, internet connection speed recommendations: 3 Mbps SD, 5 Mbps HD, 15 Mbps 4K. https://help.netflix.com/en/node/306
- Video-calling services recommend about 1.5 to 3 Mbps for HD calls (e.g. Zoom system requirements). https://support.zoom.com/
Day 185 · Passwords and combinations- NIST Special Publication 800-63B, Digital Identity Guidelines: favour length, allow long passphrases, screen against breached-password lists. https://pages.nist.gov/800-63-3/sp800-63b.html
- Combinations = alphabet^length; entropy in bits = length × log₂(alphabet).
Day 186 · The QR code- ISO/IEC 18004 QR Code specification: symbol size 21 × 21 modules at version 1, increasing by 4 per version to 177 × 177 at version 40; error-correction levels L 7 %, M 15 %, Q 25 %, H 30 %. Denso Wave, About the QR code. https://www.qrcode.com/en/about/version.html
- Scanning distance of about ten times the symbol width is the usual design rule.
Day 187 · Addresses by the power of two- IETF RFC 791 (IPv4, 32-bit addresses) and RFC 8200 (IPv6, 128-bit addresses). https://www.rfc-editor.org/rfc/rfc8200
- World population about 8.1 billion (United Nations World Population Prospects 2024). https://population.un.org/wpp/
Day 188 · Latency and the speed of light- Speed of light 299,792 km/s; in silica fibre about 0.67 of that (refractive index about 1.47). Geostationary orbit altitude about 35,786 km. Cable route lengths exceed great-circle distances (e.g. SAT-3/WASC, about 14,000 km Cape Town to Portugal). https://www.submarinecablemap.com/
Day 189 · The household's line- Per-activity rates from service recommendations (Netflix 3/5/15 Mbps; video calls about 3 Mbps; online games typically under 5 Mbps but latency-sensitive).
Week 28 · AI and algorithms in daily life
What a recommendation is doing, spotting a fake, coincidence, and asking a chatbot well.
Start here · How a machine learns- NIST AI Risk Management Framework (AI RMF 1.0): characteristics of trustworthy AI, including accuracy and reliability limits. https://www.nist.gov/itl/ai-risk-management-framework
- Tokenisation: roughly 0.75 English words per token (OpenAI tokenizer documentation). https://platform.openai.com/tokenizer
Day 190 · What a recommendation is doing- Association rules and lift: lift = P(Y | X) ÷ P(Y) (Agrawal et al., 1993; recommender-systems texts such as Ricci, Rokach and Shapira, Recommender Systems Handbook). https://doi.org/10.1007/978-1-4899-7637-6
Day 191 · Next-word probability and tokens- Autoregressive language models sample each token from a probability distribution over the vocabulary (Vaswani et al., 2017, Attention Is All You Need). https://arxiv.org/abs/1706.03762
- Tokenisation: about 0.75 English words per token (OpenAI tokenizer documentation). https://platform.openai.com/tokenizer
Day 192 · Spotting a fake- Bayes' rule as natural frequencies (Gigerenzer & Hoffrage, 1995), as on week 11 day 74.
- OpenAI, July 2023: its AI-text classifier was withdrawn because of its low rate of accuracy. https://openai.com/blog/new-ai-classifier-for-indicating-ai-written-text
Day 193 · Coincidence- The birthday problem: with n people the probability of a shared birthday is 1 − ∏(365 − i)/365, closely approximated by 1 − exp(−n(n − 1)/730); 23 people give 50.7 percent. https://mathworld.wolfram.com/BirthdayProblem.html
- Littlewood's law of miracles (J. E. Littlewood, A Mathematician's Miscellany, 1953).
Day 194 · Asking a chatbot well- Probability of independent events all occurring = product of their probabilities. NIST AI RMF on accuracy, reliability and human oversight. https://www.nist.gov/itl/ai-risk-management-framework
- Prompting guidance from model providers converges on role, task, context, format and verification (e.g. OpenAI prompt engineering guide; Anthropic prompt engineering documentation). https://platform.openai.com/docs/guides/prompt-engineering
Day 195 · How things spread in a feed- Branching processes and the basic reproduction number R₀: growth when R₀ > 1, extinction when R₀ < 1 (Kermack & McKendrick; standard epidemiology and network-diffusion texts). Geometric series sum (rⁿ⁺¹ − 1)/(r − 1).
Week 29 · Household chemistry
Bleach dilution, vinegar and bicarbonate, soap, rust, and why silver tarnishes.
Start here · How the cupboard's chemistry works- Dilution: C₁V₁ = C₂V₂. Household chlorine bleach in South Africa is commonly 3.5 percent sodium hypochlorite (product labels). WHO: chlorine solutions of 0.05 percent for surfaces and 0.5 percent for body-fluid spills; never mix bleach with acids or ammonia. https://www.who.int/publications/i/item/9789240011045
Day 197 · Bleach dilution- WHO, Cleaning and disinfection of environmental surfaces in the context of COVID-19 (2020): 0.1 percent (1,000 ppm) sodium hypochlorite for surfaces, 0.5 percent for body-fluid spills; contact time of at least one minute; prepare fresh. https://www.who.int/publications/i/item/cleaning-and-disinfection-of-environmental-surfaces-inthe-context-of-covid-19
- Dilution C₁V₁ = C₂V₂; household bleach strength from the product label.
Day 198 · Vinegar and bicarbonate- NaHCO₃ (84 g/mol) + CH₃COOH (60 g/mol) → CH₃COONa + H₂O + CO₂; one mole of gas occupies about 24 litres at room temperature. Table vinegar is about 5 percent acetic acid (product labels).
Day 199 · Descaling the kettle- CaCO₃ (100 g/mol) + 2 CH₃COOH (2 × 60 g/mol) → Ca(CH₃COO)₂ + H₂O + CO₂; citric acid (192 g/mol, triprotic) needs about 128 g per 100 g of scale. Water hardness classes per WHO (soft below 60 mg/L CaCO₃, hard above 120).
Day 200 · The cupboard's pH- pH = −log₁₀[H⁺]. Typical values: vinegar about 2.4 to 2.9, bicarbonate solution about 8.3, household ammonia about 11, chlorine bleach about 12.5 (chemistry reference tables). Bleach with acids releases chlorine; with ammonia, chloramines (CDC/NIOSH). https://www.cdc.gov/niosh/
Day 201 · Rust and the zinc that stops it- ISO 9223 corrosivity categories: zinc corrosion rates from about 0.1 µm/year (C1) to over 4 µm/year (C5 coastal/industrial); ISO 1461 hot-dip galvanising thickness about 70 to 85 µm on structural steel. https://www.iso.org/standard/53499.html
- Rust (hydrated iron oxides) occupies several times the volume of the parent iron, causing spalling of concrete (corrosion engineering texts).
Day 202 · Why silver tarnishes- Tarnish is silver sulphide, Ag₂S, from hydrogen sulphide in air; the aluminium-foil electrochemical method reduces it back to silver (3 Ag₂S + 2 Al → 6 Ag + Al₂S₃) in a warm electrolyte of bicarbonate and salt (standard chemistry demonstration, e.g. Royal Society of Chemistry). https://edu.rsc.org/
- Sterling silver is 92.5 percent silver (hallmark 925).
Day 203 · The cupboard, diluted- C₁V₁ = C₂V₂ per row; label strengths are typical retail products (bleach 3.5 percent, vinegar 5, peroxide 6, pool chlorine 12.5) and target strengths per WHO surface guidance; the reader enters their own labels.
Week 30 · Cleaning and germs
Soap and 20 seconds, temperatures that matter, dilution ratios, and the zones of the fridge.
Start here · How germs are counted- Log reduction: 1-log = 90 percent, 3-log = 99.9 percent (US EPA disinfectant efficacy definitions). https://www.epa.gov/pesticide-registration/antimicrobial-pesticide-registration
- Pasteurisation equivalents: 72 °C for 15 s (HTST) or 63 °C for 30 min (LTLT), Codex Alimentarius / dairy standards.
Day 204 · Soap and twenty seconds- US CDC, Handwashing: clean hands save lives; scrub for at least 20 seconds; soap lifts microbes from skin, rinsing removes them. https://www.cdc.gov/clean-hands/about/index.html
- WHO Guidelines on Hand Hygiene in Health Care (2009): log reductions of about 2 for handwashing with plain soap in laboratory tests. https://www.who.int/publications/i/item/9789241597906
Day 205 · The temperatures that matter- WHO Five Keys to Safer Food: cook to 70 °C; keep food below 5 °C or above 60 °C. Pasteurisation 72 °C/15 s or 63 °C/30 min (Codex). Mixing by energy balance as in week 1.
Day 206 · Dilution ratios on labels- Dilution notations: 1:N (one part product to N parts diluent), percent v/v (ml per 100 ml), and per-container doses; cleaning-product labelling practice.
Day 207 · The zones of the fridge- WHO Five Keys: refrigerate below 5 °C. Freezer star ratings (ISO 15502 / EN 62552): one star −6 °C, two stars −12 °C, three stars −18 °C, four stars freezes fresh food at −18 °C or below. https://www.iso.org/standard/
- USDA FSIS: store raw meat on the lowest shelf to prevent drips. https://www.fsis.usda.gov/
Day 208 · Fresh air and air changes- US CDC, Ventilation in buildings: air changes per hour and clearance times (about 2.3 ACH-hours for 90 percent, 4.6 for 99 percent removal under well-mixed conditions). https://www.cdc.gov/niosh/ventilation/
- CO₂ below about 800 ppm as an indicator of adequate ventilation (REHVA / ASHRAE guidance).
Day 209 · Sanitiser strength- US CDC: use an alcohol-based hand sanitiser with at least 60 percent alcohol; wash with soap and water when hands are visibly dirty. https://www.cdc.gov/clean-hands/about/hand-sanitizer.html
- WHO-recommended handrub formulations: 80 percent ethanol or 75 percent isopropanol. https://www.who.int/publications/i/item/WHO-IER-PSP-2010.5
Day 210 · The fridge audit- USDA FSIS, Cold food storage chart: raw poultry and ground meats 1 to 2 days; cooked leftovers 3 to 4 days; eggs 3 to 5 weeks; at 4 °C or below. https://www.fsis.usda.gov/food-safety/safe-food-handling-and-preparation/food-safety-basics/cold-food-storage-charts
Week 31 · Tests and screening
False positives, what a normal range means, cholesterol units, and HbA1c.
Start here · How a test result is read- Clinical and Laboratory Standards Institute EP28-A3c: reference intervals as the central 95 percent of a healthy reference population. https://clsi.org/standards/products/method-evaluation/documents/ep28/
- Unit conversions: cholesterol mg/dL = mmol/L × 38.67; glucose mg/dL = mmol/L × 18.02 (molar masses 386.7 and 180.2 g/mol).
Day 211 · False positives in screening- Gigerenzer, G. (2002), Reckoning with Risk: the mammography example in natural frequencies (about 8 in 1,000, sensitivity about 90 percent, false-positive rate about 9 percent, positive predictive value under 10 percent). https://doi.org/10.1136/bmj.327.7417.741
- Bayes' rule as natural frequencies (Gigerenzer & Hoffrage, 1995).
Day 212 · What a normal range means- CLSI EP28-A3c: reference intervals defined as the central 95 percent of a healthy population; the multiple-testing consequence (1 − 0.95ⁿ) is standard in clinical chemistry teaching. https://clsi.org/standards/products/method-evaluation/documents/ep28/
Day 213 · The units on the lipid and glucose lines- Unit conversions from molar masses: cholesterol 386.7 g/mol (× 38.67), triglycerides about 885.7 g/mol (× 88.57), glucose 180.2 g/mol (× 18.02).
- South African Dyslipidaemia Guideline Consensus Statement (2018, SA Heart Association and LASSA): LDL targets by risk category; total cholesterol below 5 and LDL below 3 mmol/L commonly cited for low-risk adults. https://www.samj.org.za/index.php/samj/article/view/12489
Day 214 · HbA1c- NGSP / IFCC master equation: IFCC (mmol/mol) = 10.929 × (NGSP % − 2.15). http://www.ngsp.org/ifcc.asp
- ADAG study (Nathan et al., 2008): estimated average glucose (mmol/L) = 1.59 × HbA1c (%) − 2.59. https://doi.org/10.2337/dc08-0545
- WHO (2011): HbA1c of 48 mmol/mol (6.5 %) as the diagnostic cut-point for diabetes. https://www.who.int/publications/i/item/use-of-glycated-haemoglobin-(-hba1c)-in-diagnosis-of-diabetes-mellitus
Day 215 · The second test- Sequential (serial) testing: the post-test probability of the first test is the pre-test probability of the second (Bayes' rule applied twice); standard in evidence-based medicine (Sackett et al., Clinical Epidemiology). https://doi.org/10.1136/bmj.329.7458.168
Day 216 · Screening's own arithmetic- Cochrane Review, Screening for breast cancer with mammography (Gøtzsche & Jørgensen, 2013): for 2,000 women screened over 10 years, one fewer breast-cancer death and about 10 healthy women overdiagnosed and treated; false-positive recalls are common over repeated rounds. https://doi.org/10.1002/14651858.CD001877.pub5
- Number needed to screen = 1 ÷ absolute risk reduction.
Day 217 · Your report in its ranges- Position = (value − low) ÷ (high − low). Example ranges are of the kind printed on South African lab reports (lipids per the SA dyslipidaemia guideline; fasting glucose and HbA1c per WHO diagnostic criteria); the reader uses the ranges on their own report.
Week 32 · Ageing well in numbers
Muscle, bone, steps, hearing, eyesight and diopters, and what changes with age.
Start here · How the body's numbers change- Volpi, Nazemi and Fujita (2004): muscle mass declines about 3 to 8 percent per decade after age 30, faster after 60. https://doi.org/10.1097/01.mco.0000134362.76653.b2
- American College of Sports Medicine: VO₂max declines roughly 10 percent per decade in sedentary adults, about half that in trained adults. https://www.acsm.org/
Day 218 · Muscle- Volpi, Nazemi and Fujita (2004), Muscle tissue changes with aging: 3 to 8 percent per decade after 30. https://doi.org/10.1097/01.mco.0000134362.76653.b2
- Cruz-Jentoft et al. (2019), Sarcopenia: revised European consensus (EWGSOP2): grip strength as the primary measure; resistance training as the intervention with the best evidence. https://doi.org/10.1093/ageing/afy169
Day 219 · Bone and the T-score- WHO Study Group (1994): osteoporosis defined as bone mineral density 2.5 standard deviations or more below the young-adult mean (T-score ≤ −2.5); osteopenia between −1 and −2.5. https://iris.who.int/handle/10665/39142
- International Osteoporosis Foundation: bone loss about 1 percent a year after 40, accelerating around menopause. https://www.osteoporosis.foundation/
Day 220 · Steps by age- Paluch et al. (2022), Daily steps and all-cause mortality: a meta-analysis of 15 cohorts, Lancet Public Health: risk plateaued at about 6,000 to 8,000 steps a day in adults 60 and over and about 8,000 to 10,000 in younger adults. https://doi.org/10.1016/S2468-2667(21)00302-9
Day 221 · Hearing in decibels- Decibel: 10 × log₁₀ of the power ratio; a 10 dB increase is perceived as about twice as loud (Stevens' power law).
- WHO World Report on Hearing (2021): grades of hearing loss by better-ear threshold: normal below 20 dB, mild 20–34, moderate 35–49, moderately severe 50–64, severe 65–79, profound 80–94. https://www.who.int/publications/i/item/9789240020481
Day 222 · Reading glasses in diopters- Hofstetter's formulae for amplitude of accommodation: average = 18.5 − 0.3 × age, minimum = 15 − 0.25 × age (Hofstetter, 1950). https://doi.org/10.1097/00006324-195010000-00003
- Lens power in diopters = 1 ÷ focal length in metres.
Day 223 · The twelve-minute test- Cooper, K. H. (1968), A means of assessing maximal oxygen intake, JAMA: VO₂max ≈ (distance in metres − 504.9) ÷ 44.73. https://doi.org/10.1001/jama.1968.03140030033008
- ACSM: VO₂max declines about 10 percent per decade in sedentary adults, about 5 percent in those who train.
Day 224 · Your numbers a decade on- Rates as cited on days 218 to 223 (Volpi 2004; ACSM; IOF); grip-strength norms decline with age from midlife (Dodds et al., 2014, PLoS ONE). https://doi.org/10.1371/journal.pone.0113637
- Projection = now × (1 + rate)^decades; rates are population averages and inputs.
Week 33 · School maths at home
Fractions, times-table tricks, estimating, helping with homework, and why show your working.
Start here · How to help with maths at home- Rowe, M. B. (1986), Wait time: slowing down may be a way of speeding up, Journal of Teacher Education: pauses of 3 seconds or more improve the quality of student responses. https://doi.org/10.1177/002248718603700110
- Estimation by rounding to one significant figure; Department of Basic Education CAPS mathematics emphasises estimation and checking. https://www.education.gov.za/
Day 225 · Fractions- Addition of fractions: a/b + c/d = (ad + cb)/bd, then simplify; CAPS Intermediate Phase mathematics. https://www.education.gov.za/
Day 227 · Estimating- Rounding to one significant figure and front-end estimation are core CAPS mental-mathematics skills. https://www.education.gov.za/
Day 228 · The year mark- Weighted average: year = Σ(mark × weight); required exam = (target − banked) ÷ exam weight. Weights per the school's assessment policy under the CAPS National Protocol for Assessment. https://www.education.gov.za/
Day 229 · The order of operations- Order of operations (BODMAS / PEMDAS): brackets, orders, division and multiplication, addition and subtraction, left to right within a level; CAPS Senior Phase mathematics. https://www.education.gov.za/
Day 230 · Method marks- Marking guidelines for mathematics allocate method (M) and accuracy (A) marks; the Department of Basic Education's examination marking guidelines follow this convention. https://www.education.gov.za/
Day 231 · The term's marks- Weighted term mark = Σ(mark ÷ total × weight); weights per the school's assessment programme under CAPS. https://www.education.gov.za/
Week 34 · Measuring the world
The metric system, prefixes, the litre and the kilogram, temperature scales, and conversions.
Start here · How the metric system fits together- BIPM, The International System of Units (SI), 9th edition (2019): base units and SI prefixes. https://www.bipm.org/en/publications/si-brochure
- Density of water about 1.00 kg per litre at room temperature.
Day 232 · The prefixes- SI prefixes (BIPM SI Brochure, 9th ed.): kilo 10³, mega 10⁶, giga 10⁹, milli 10⁻³, micro 10⁻⁶, nano 10⁻⁹. https://www.bipm.org/en/measurement-units/si-prefixes
Day 233 · The litre and the kilogram- Densities at room temperature (approximate): water 1.00, milk 1.03, vegetable oil 0.92, petrol 0.72 to 0.78, honey 1.42 kg/L (engineering reference tables). The 2019 SI redefinition fixes the kilogram via the Planck constant (BIPM). https://www.bipm.org/en/si-base-units/kilogram
Day 234 · Temperature scales- Kelvin defined via the Boltzmann constant (SI 2019); absolute zero = −273.15 °C; F = 1.8 × C + 32 (BIPM SI Brochure). https://www.bipm.org/en/si-base-units/kelvin
Day 235 · Squares and cubes- Dimensional analysis: area scales with the square of length, volume with the cube (Galileo's square–cube law, 1638).
Day 236 · Imperial to metric- Exact definitions (international yard and pound agreement, 1959): 1 in = 2.54 cm, 1 lb = 0.45359237 kg; 1 mile = 1.609344 km; US gallon 3.78541 L, imperial gallon 4.54609 L (NIST SP 811). https://www.nist.gov/pml/special-publication-811
- South Africa's metrication was completed in the 1970s (SABS).
Day 237 · Precision and the digits- Measurement uncertainty and significant figures: absolute uncertainties add for sums, relative (percent) uncertainties add for products (JCGM 100:2008, Guide to the Expression of Uncertainty in Measurement). https://www.bipm.org/en/committees/jc/jcgm/publications
Week 35 · Estimation
How many taxis in the city, how much water a household uses, and rounding well.
Start here · How to estimate- Fermi estimation (Enrico Fermi's order-of-magnitude problems); Weinstein & Adam, Guesstimation (Princeton, 2008): geometric mean of bounds for wide uncertainty. https://press.princeton.edu/books/paperback/9780691129495/guesstimation
Day 239 · How many taxis- Statistics South Africa, National Household Travel Survey 2020 (P0320): minibus taxis are the dominant public-transport mode, carrying the majority of public-transport trips. https://www.statssa.gov.za/publications/P0320/P03202020.pdf
- Fermi estimation: product of one-figure factors.
Day 240 · The city's water- 1 ML = 1,000 m³ = 1,000,000 L. City of Cape Town weekly dam levels and the 2018 water-restriction arithmetic (50 L per person). https://www.capetown.gov.za/
Day 242 · Rounding well- Significant figures and rounding conventions (NIST SP 811, section on rounding). https://www.nist.gov/pml/special-publication-811
- Statistics South Africa reports mid-year population estimates to the nearest hundred thousand.
Day 243 · Orders of magnitude- Earth's mean diameter about 12,742 km (NASA); a human hair about 0.05 to 0.1 mm; resting heart rate about 72 beats per minute (week 9). Order of magnitude = log₁₀ of the ratio.
Week 36 · Shapes and space
Area, volume, packing the boot, why tanks are round, and angles.
Day 246 · The circle- Circumference = πd, area = πr²; π ≈ 3.14159. NIST Handbook 44 Appendix C, general tables of units and formulas. https://www.nist.gov/pml/weights-and-measures/publications/nist-handbooks/handbook-44
Day 247 · Why tanks are round- Isoperimetric inequality: of all closed curves of a given length the circle encloses the most area; hoop stress in thin-walled cylinders σ = pr/t (Barlow's formula). Timoshenko, Strength of Materials; overview: https://en.wikipedia.org/wiki/Isoperimetric_inequality
Day 248 · The tank's litres- Cylinder volume V = πr²h; 1 m³ = 1,000 L. Typical 5,000 L vertical tank dimensions from South African tank makers' product pages, e.g. https://www.jojo.co.za/
Day 249 · Packing the boot- VDA 700 boot-volume method: 200×100×50 mm litre blocks counted into the boot (Verband der Automobilindustrie). Packing efficiency of mixed rigid items 60–70% is a planning assumption, in line with random close packing of about 64% (Bernal & Mason, Nature 1960). https://www.nature.com/articles/188910a0
Day 250 · Angles and the roof- Right-triangle trigonometry: tan = rise/run, cos = run/hypotenuse; road grade as percent = 100 × tan. SANS 10400-L (roofs) uses pitch in degrees. https://www.sabs.co.za/
Day 251 · Doubling the size- Area ∝ diameter²; volume ∝ diameter³ (square-cube law). Screen and pizza comparisons follow directly from πr². https://en.wikipedia.org/wiki/Square%E2%80%93cube_law
Day 252 · Your rooms measured- Rectangle area = l × w; box volume = l × w × h. Typical South African ceiling height 2.4–2.7 m (SANS 10400-C minimum 2.4 m for habitable rooms). https://www.sabs.co.za/
Week 37 · Sound and music
Decibels, why twice the sound is not twice as loud, pitch, and hearing protection.
Start here · How sound is measured- Decibel: L = 10 log10(I/I₀); Stevens' power law and the sone scale: +10 dB ≈ doubling of perceived loudness (Stevens, 1957). ISO 226:2023 equal-loudness contours. https://www.iso.org/standard/83117.html
Day 253 · The decibel ladder- Typical sound levels (quiet room 30, conversation 60, traffic 85, lawnmower 90, club 100, pain 120 dB): US CDC/NIOSH noise and hearing loss pages; WHO Environmental Noise Guidelines 2018. https://www.cdc.gov/niosh/noise/about/noise.html
Day 254 · Two of everything- Adding incoherent sound sources: L = L₁ + 10 log10(n); unequal sources L = 10 log10(Σ 10^(Lᵢ/10)). Engineering acoustics standard result; e.g. https://www.engineeringtoolbox.com/adding-decibel-d_63.html
Day 255 · Sound over distance- Inverse-square law for a point source in free field: ΔL = 20 log10(d₂/d₁), 6 dB per doubling of distance. ISO 9613-2 (outdoor sound propagation). https://www.iso.org/standard/20649.html
Day 256 · The three-decibel rule- South Africa: Noise-Induced Hearing Loss Regulations, 2003 (OHS Act 85 of 1993), noise-rating limit 85 dB(A); SANS 10083 equal-energy (3 dB) exchange rate. NIOSH Criteria for a Recommended Standard, 1998: 85 dBA 8-h TWA, 3-dB exchange rate. https://www.cdc.gov/niosh/docs/98-126/
Day 257 · Pitch and the octave- ISO 16:1975, standard tuning frequency A4 = 440 Hz; twelve-tone equal temperament, semitone ratio 2^(1/12); string frequency ∝ 1/length (Mersenne's laws). https://www.iso.org/standard/3601.html
Day 258 · Thunder and the speed of sound- Speed of sound in dry air c ≈ 331.3 + 0.606 T (°C) m/s, linear approximation valid near ordinary temperatures; 343 m/s at 20 °C. NPL and physics references, e.g. https://www.engineeringtoolbox.com/air-speed-sound-d_603.html
Day 259 · Your day in decibels- Noise dose D = Σ (Cᵢ/Tᵢ) × 100 with Tᵢ = 8/2^((Lᵢ−85)/3) (3-dB exchange, 85 dB(A) criterion): NIOSH 1998; SA Noise-Induced Hearing Loss Regulations 2003. https://www.cdc.gov/niosh/docs/98-126/
Week 38 · Light and colour
Why the sky is blue, sunsets, rainbows, sunglasses and UV, and warm versus cool LEDs.
Start here · How light is measured- Visible spectrum ~380–700 nm; luminous efficacy: incandescent ~14 lm/W, LED 80–150 lm/W (US DOE); correlated colour temperature (CIE); WHO Global Solar UV Index (1 unit = 25 mW/m² erythemally weighted). https://www.who.int/publications/i/item/9241590076
Day 260 · Why the sky is blue- Rayleigh scattering ∝ 1/λ⁴ (Lord Rayleigh, 1871); Mie scattering for droplets and dust. HyperPhysics, Blue sky. http://hyperphysics.phy-astr.gsu.edu/hbase/atmos/blsky.html
Day 261 · Sunsets- Air mass ≈ sec(zenith angle), valid to about 80°; ~38 at the horizon (Kasten & Young, Applied Optics 1989); atmospheric scale height ~8.4 km. https://doi.org/10.1364/AO.28.004735
Day 262 · The rainbow- Primary rainbow at ~42° from the antisolar point, secondary at ~51° (Descartes, 1637; Nussenzveig, Scientific American 1977). https://www.atoptics.co.uk/rainbows/primrays.htm
Day 263 · Sunglasses and UV- WHO Global Solar UV Index: A Practical Guide (2002), 1 index unit = 25 mW/m² erythemally weighted; minimal erythema dose ~250 J/m² for Fitzpatrick skin type II (ISO/CIE 17166:2019). SPF as a multiplier of time at 2 mg/cm². https://www.who.int/publications/i/item/9241590076
Day 264 · Warm and cool LEDs- Correlated colour temperature: 2700 K warm, 4000 K neutral, 6500 K daylight (CIE); recommended illuminance: living rooms 100–300 lx, kitchens 300–500 lx (SANS 10114-1 / CIBSE Code for Lighting); utilisation factor ~0.5 for ordinary rooms. https://www.cibse.org/
Day 265 · The half-height mirror- Law of reflection (angle of incidence = angle of reflection); the half-height plane-mirror result, e.g. HyperPhysics, Plane mirror. http://hyperphysics.phy-astr.gsu.edu/hbase/geoopt/mirror.html
Day 266 · Your home relit- Illuminance = lumens × utilisation / area; recommended lux by room (SANS 10114-1; CIBSE Code for Lighting); utilisation ~0.5 for typical rooms. https://www.cibse.org/
Week 39 · Heat and cold
Insulation, why wind feels colder, the thermos, why ice floats, and the geyser blanket.
Start here · How heat is measured- Specific heat of water 4.18 kJ/(kg·K); 1 kWh = 3.6 MJ; U-value = W/(m²·K), typical values from SANS 10400-XA and CIBSE Guide A. https://www.cibse.org/
Day 267 · Insulation and the U-value- Heat flow Q = U·A·ΔT; typical U-values: uninsulated pitched roof with ceiling ~2.5, with 100 mm mineral wool ~0.4 W/m²K (CIBSE Guide A); SANS 10400-XA roof insulation requirements by climate zone. https://www.sabs.co.za/
Day 268 · Why wind feels colder- Wind chill temperature index (Osczevski & Bluestein, 2001; adopted by Environment Canada and the US National Weather Service, 2001): Twc = 13.12 + 0.6215T − 11.37V^0.16 + 0.3965TV^0.16, T in °C, V in km/h; valid for T ≤ 10 °C and V ≥ 4.8 km/h. https://www.weather.gov/safety/cold-wind-chill-chart
Day 269 · The thermos- Newton's law of cooling, T(t) = Tₐ + (T₀ − Tₐ)e^(−kt); Dewar flask (1892). Flask ratings (e.g. ≥ 70 °C after 6 h from boiling) imply k ≈ 0.02–0.04 h⁻¹. https://en.wikipedia.org/wiki/Newton%27s_law_of_cooling
Day 270 · Why ice floats- Density of ice Ih at 0 °C 916.7 kg/m³, water at 0 °C 999.8, seawater ~1,025 (CRC Handbook of Chemistry and Physics); Archimedes' principle: submerged fraction = ρ_object/ρ_fluid. https://hbcp.chemnetbase.com/
Day 271 · The geyser blanket- Series thermal resistance: U = 1/(1/U₀ + R_added); SANS 151 standing-loss rating on South African geysers (class A–D, kWh/24 h); Eskom geyser-blanket guidance. Tariff R2.71/kWh as in week 1. https://www.eskom.co.za/
Day 272 · Why the roof creaks- Linear thermal expansion ΔL = α·L·ΔT; α: steel ~12, concrete ~12, aluminium ~23, PVC ~70, borosilicate glass ~3.3 ×10⁻⁶/K (Engineering Toolbox, CRC Handbook). https://www.engineeringtoolbox.com/linear-expansion-coefficients-d_95.html
Day 273 · Your home's heat losses- Q = U·A·ΔT summed over the envelope (steady-state heat-loss method, CIBSE Guide A); typical U-values: uninsulated ceiling 2.5, 220 mm brick wall 2.0, single glazing 5.8, ground floor 0.7, timber door 3.0 W/m²K. https://www.cibse.org/
Week 40 · Air and breathing
Air pressure, altitude, why a ball bounces, carbon dioxide in a room, and ventilation.
Start here · How air is measured- Air density 1.204 kg/m³ at 20 °C and 101.325 kPa; composition 78.08% N₂, 20.95% O₂, 0.042% CO₂ by volume (oxygen 23.1% by mass); standard atmosphere ISO 2533:1975. NOAA Global Monitoring Laboratory for CO₂. https://gml.noaa.gov/ccgg/trends/
Day 274 · The weight of the air- Standard atmosphere 101.325 kPa = 101,325 N/m²; hydrostatic pressure ρgh with water 1,000 kg/m³, g 9.81 m/s²; Torricelli's barometer (1643) and the ~10.3 m suction limit. http://hyperphysics.phy-astr.gsu.edu/hbase/pflu.html
Day 275 · Pressure with altitude- International Standard Atmosphere (ISO 2533:1975): p = 101.325(1 − 2.25577×10⁻⁵h)^5.25588 kPa in the troposphere. Johannesburg 1,753 m; Sani Pass 2,876 m. https://www.iso.org/standard/7472.html
Day 276 · Why a ball bounces- ITF Rules of Tennis, Appendix I: a ball dropped 254 cm onto concrete must rebound 135–147 cm (e ≈ 0.73–0.76); coefficient of restitution h₂/h₁ = e²; Gay-Lussac's law p ∝ T at constant volume. https://www.itftennis.com/en/about-us/tennis-tech/rules-of-tennis/
Day 277 · Carbon dioxide in a room- Steady-state CO₂: C = C_out + G/Q; adult at rest generates ~0.004–0.005 L/s CO₂ (Persily & de Jonge, Indoor Air 2017); ASHRAE 62.1 guidance of ~700 ppm above outdoors (~1,000 ppm); infiltration of closed rooms ~0.3–0.7 ACH. https://doi.org/10.1111/ina.12383
Day 278 · The breath- Tidal volume ~500 mL, respiratory rate 12–20/min, minute ventilation 6–8 L at rest; exhaled air ~16% O₂; resting oxygen consumption ~250–350 mL/min (Guyton & Hall, Textbook of Medical Physiology). Air density 1.2 kg/m³. https://www.ncbi.nlm.nih.gov/books/NBK482502/
Day 279 · Flushing a room- Exponential decay of a well-mixed contaminant: C(t) − C_out = (C₀ − C_out)e^(−ACH·t); 95% removal after 3 air changes (CDC/NIOSH clearance-time tables); natural cross-ventilation typically 4–10 ACH (CIBSE AM10). https://www.cdc.gov/infection-control/hcp/environmental-control/appendix-b-air.html
Day 280 · Your rooms' air- Steady-state CO₂ per room, C = 420 + G/Q with G = 0.005 L/s per person (Persily & de Jonge 2017) and Q = volume × ACH; air density 1.2 kg/m³. https://doi.org/10.1111/ina.12383
Week 41 · Water science
Why water boils, evaporation and drying, humidity, salt, freezing, and floating.
Start here · How water behaves- Latent heat of fusion 334 kJ/kg, of vaporisation 2,257 kJ/kg at 100 °C; specific heat 4.18 kJ/(kg·K) (CRC Handbook). https://hbcp.chemnetbase.com/
Day 281 · Why water boils, and where- Clausius–Clapeyron relation with the enthalpy of vaporisation of water 40.65 kJ/mol; boiling point ~94 °C at 82 kPa, ~120 °C at 200 kPa; rule of thumb ~10 °C doubles reaction rate (Arrhenius). https://en.wikipedia.org/wiki/Clausius%E2%80%93Clapeyron_relation
Day 282 · Evaporation and cooling- Latent heat of vaporisation ~2,430 kJ/kg at 30–35 °C (CRC Handbook); resting metabolic heat ~100 W; sweat rates of 1–2 L/h in hard exercise (ACSM position stand on exercise and fluid replacement, 2007). https://doi.org/10.1249/mss.0b013e31802ca597
Day 283 · Humidity and the dew point- Magnus formula with Alduchov & Eskridge (1996) coefficients a = 17.625, b = 243.04 °C; absolute humidity from saturation vapour pressure (Bolton 1980). Dew-point comfort bands per US NWS. https://doi.org/10.1175/1520-0450(1996)035<0601:IMFAOS>2.0.CO;2
Day 284 · Salt- Colligative properties: K_f(water) = 1.86 K·kg/mol, K_b = 0.512 K·kg/mol; NaCl molar mass 58.44 g/mol, van 't Hoff factor ≈ 1.8 at these concentrations; seawater salinity 35 g/kg, freezing ≈ −1.9 °C. https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)/Physical_Properties_of_Matter/Solutions_and_Mixtures/Colligative_Properties
Day 285 · Freezing- Latent heat of fusion of water 334 kJ/kg; specific heat 4.18 kJ/(kg·K); freezing capacity rating in kg/24 h under IEC 62552 (water from 25 °C to −18 °C, taken here as ≈ 417.6 kJ/kg for the fresh-load sum). https://webstore.iec.ch/publication/23811
Day 286 · The boat and its load- Archimedes' principle; tonnes per centimetre immersion = waterplane area × ρ / 100 (naval architecture); SAMSA small-vessel capacity plates. Seawater 1,025 kg/m³. https://en.wikipedia.org/wiki/Archimedes%27_principle
Day 287 · The kitchen's water heat- Q = m·c·ΔT + m·L: c = 4.18 kJ/(kg·K), L_vap = 2,260 kJ/kg, L_fus = 334 kJ/kg; 1 kWh = 3,600 kJ; tariff R2.71/kWh as in week 1. https://hbcp.chemnetbase.com/
Week 42 · Materials
Why steel rusts and aluminium does not, plastic codes, glass, and recycling.
Start here · How materials are measured- Densities and mechanical properties: Ashby, Materials Selection in Mechanical Design (4th ed., 2011); embodied energy from the Inventory of Carbon and Energy (ICE) v2.0, Hammond & Jones, University of Bath, 2011. https://circularecology.com/embodied-carbon-footprint-database.html
Day 288 · Why steel rusts and aluminium does not- ISO 9223:2012 corrosivity categories: carbon steel first-year loss C2 1.3–25 µm, C3 25–50, C4 50–80, C5 80–200 µm; Pilling–Bedworth ratio Fe₂O₃ 2.1 (hydrated rusts higher), Al₂O₃ 1.28 (protective). https://www.iso.org/standard/53499.html
Day 289 · The plastic codes- Resin identification codes, ASTM D7611; polymer densities PET 1.38, PVC 1.40, HDPE 0.95, LDPE 0.92, PP 0.90 g/cm³; PETCO South Africa annual reports on PET bottle collection rates. https://petco.co.za/
Day 290 · Glass and the bottle- Soda-lime glass composition and density 2,500 kg/m³ (Ashby 2011); toughened glass surface compression (BS EN 12150); cullet saves ~2.5–3% furnace energy per 10% (Glass Packaging Institute / FEVE). https://feve.org/
Day 291 · What a recycled can saves- Primary aluminium ~14–15 kWh/kg of electricity (International Aluminium Institute); recycling uses ~5% of primary energy (IAI, The Aluminium Story); can mass ~13–15 g. https://international-aluminium.org/
Day 292 · The door that sticks in winter- USDA Forest Products Laboratory, Wood Handbook (2010), ch. 4: dimensional change ≈ 0.2% per 1% moisture content tangentially for many species, ~0.1% radially, ~0.01% longitudinally. https://www.fpl.fs.usda.gov/documnts/fplgtr/fpl_gtr190.pdf
Day 293 · Paper by the gram- ISO 216 paper sizes (A0 = 1 m², A4 = 210 × 297 mm); grammage ISO 536; typical 80 g/m² office paper caliper ~0.1 mm. https://www.iso.org/standard/36631.html
Day 294 · Your packaging week- Embodied energy (cradle to gate): PET ~84 MJ/kg, aluminium (general) 155, glass 15, steel (general) 20.1, cardboard ~7 MJ/kg — Inventory of Carbon and Energy (ICE) v2.0, Hammond & Jones, University of Bath, 2011; 1 kWh = 3.6 MJ. https://circularecology.com/embodied-carbon-footprint-database.html
Week 43 · Movement and forces
Friction, gravity, leaning into corners, levers and wheelbarrows, and pulleys.
Start here · How forces are measured- SI: newton, joule, watt; standard gravity 9.80665 m/s²; coefficients of friction from engineering tables (Engineering Toolbox). https://www.bipm.org/en/measurement-units
Day 295 · Pushing the fridge- Coulomb friction F = μN; typical kinetic coefficients: rubber on dry concrete 0.6–0.85, rubber on wet tile ~0.2–0.4, PTFE/plastic sliders 0.05–0.2 (Engineering Toolbox). https://www.engineeringtoolbox.com/friction-coefficients-d_778.html
Day 296 · The dropped phone- Free fall: h = ½gt², v = √(2gh), g = 9.81 m/s²; air resistance negligible for dense objects over a few metres. http://hyperphysics.phy-astr.gsu.edu/hbase/traj.html
Day 297 · Leaning into corners- Centripetal acceleration a = v²/r; lean angle tan θ = v²/(gr); maximum cornering speed v = √(μgr); tyre–road friction dry ~0.7, wet ~0.4 (Gillespie, Fundamentals of Vehicle Dynamics, SAE 1992). http://hyperphysics.phy-astr.gsu.edu/hbase/mechanics/carbank.html
Day 298 · The wheelbarrow- Law of the lever (Archimedes): F₁d₁ = F₂d₂; second-class lever (wheelbarrow) mechanical advantage = effort arm / load arm. http://hyperphysics.phy-astr.gsu.edu/hbase/Mechanics/lever.html
Day 299 · The pulley- Block and tackle: ideal mechanical advantage = number of supporting rope segments; efficiency losses ~5–10% per sheave. http://hyperphysics.phy-astr.gsu.edu/hbase/Mechanics/pulley.html
Day 300 · The seatbelt- Impulse–momentum theorem F·Δt = m·Δv; vehicle crash pulse durations ~0.07–0.15 s (NHTSA); belt loads and crumple zones. http://hyperphysics.phy-astr.gsu.edu/hbase/impulse.html
Day 301 · Your day's lifting- Work W = mgh; 1 kcal = 4.184 kJ; gross mechanical efficiency of human muscle ~20–25% (Åstrand & Rodahl, Textbook of Work Physiology). https://hbcp.chemnetbase.com/
Week 44 · Electricity and magnetism
Magnets, motors, static shocks, the induction stove, and the fridge magnet.
Day 302 · The fridge magnet- Magnet pull ratings and pull-versus-distance curves (K&J Magnetics calculator); friction coefficient painted steel/coated magnet ~0.2–0.4; flexible ferrite magnets use multipole (Halbach-like) striping. https://www.kjmagnetics.com/calculator.asp
Day 303 · The motor- P = τω, ω = 2π·rpm/60; DC motor back-EMF and stall current (Hughes & Drury, Electric Motors and Drives, 5th ed. 2019). http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/motdc.html
Day 304 · Static shocks- Human body model 100 pF (ANSI/ESDA/JEDEC JS-001); walking on carpet in dry air generates 10–35 kV (ESD Association); air breakdown ~3 kV/mm. https://www.esda.org/esd-overview/esd-fundamentals/
Day 305 · The induction stove- US Department of Energy cooking-product test data (2014): induction ~84%, electric coil ~74%, gas ~40% energy to the water; eddy-current heating in ferromagnetic cookware. https://www.energy.gov/eere/buildings/articles/induction-cooking-technology-design-and-assessment
Day 306 · The compass- World Magnetic Model 2025 (NOAA NCEI): declination ~25° W at Cape Town, ~20° W at Johannesburg; South Atlantic Anomaly field intensity ~23–25 µT over southern Africa. https://www.ncei.noaa.gov/products/world-magnetic-model
Day 307 · The charger- Ideal transformer V₁/V₂ = N₁/N₂, I₁/I₂ = N₂/N₁; switch-mode chargers 80–90% efficient (IEC 62684 / USB-PD); Eskom distribution voltages 132 kV → 11 kV → 230 V. http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/transf.html
Day 308 · Your motors- Typical motor ratings: domestic fridge compressor 100–150 W with ~30% duty; pool pumps 0.75 kW; motor efficiencies 70–85% for fractional-horsepower motors (IEC 60034-30-1). Tariff R2.71/kWh as in week 1. https://www.iec.ch/
Week 45 · The earth
Tides, earthquakes, winter rain in the Cape, dam levels in percent, and soil.
Start here · How the earth is measured- Earth mean radius 6,371 km, equatorial rotation speed 1,670 km/h; African plate motion ~2.15 cm/yr NE (NASA/JPL GPS time series; DeMets et al. 2010, MORVEL). https://geodesy.unr.edu/
Day 309 · Tides- Lunar day 24 h 50 min; semidiurnal tides; rule of twelfths (sinusoidal approximation); South African tide tables, SA Navy Hydrographic Office. Cape Town spring range ~1.8 m. https://www.sanho.co.za/
Day 310 · Earthquakes- Energy–magnitude relation log₁₀E = 1.5M + 4.8 (Gutenberg–Richter); Ceres–Tulbagh earthquake 29 Sep 1969 M6.3 and Orkney 5 Aug 2014 M5.5 (Council for Geoscience, South Africa); Tōhoku 2011 M9.0 (USGS). https://www.geoscience.org.za/
Day 311 · Winter rain in the Cape- Cape Town International Airport 1991–2020 normals ~515 mm/yr, ~70% May–September (South African Weather Service); Mediterranean climate and the seasonal shift of the westerlies (Tyson & Preston-Whyte, The Weather and Climate of Southern Africa, 2000). https://www.weathersa.co.za/
Day 312 · Dam levels in percent- Western Cape Water Supply System: six major dams, 898 million m³ total (City of Cape Town weekly dam levels); Day Zero threshold 13.5% (2018); dead storage ~10% (Department of Water and Sanitation). https://www.capetown.gov.za/Family%20and%20home/residential-utility-services/residential-water-and-sanitation-services/this-weeks-dam-levels
Day 313 · The soil in a jar- USDA soil texture triangle and the jar (sedimentation) test; available water capacity by texture: sand 0.06–0.09, loam 0.15–0.18, clay 0.13–0.16 cm/cm (USDA NRCS Soil Quality Indicators). https://www.nrcs.usda.gov/sites/default/files/2022-10/Available-Water-Capacity.pdf
Day 314 · The horizon- Distance to the geometric horizon d ≈ 3.57√h km (h in metres), from Earth's radius 6,371 km; atmospheric refraction adds ~8% (Bowditch, The American Practical Navigator). Table Mountain 1,085 m. https://msi.nga.mil/Publications/APN
Day 315 · Your garden's water- Available water = area × root depth × AWC (USDA NRCS); reference evapotranspiration 3–6 mm/day in South African summer (FAO Irrigation and Drainage Paper 56, Allen et al. 1998). https://www.fao.org/4/x0490e/x0490e00.htm
Week 46 · Plants and food science
Photosynthesis, why bread rises, fermentation, ripening, and why onions make you cry.
Start here · How plants and food science are measured- Photosynthesis and respiration stoichiometry; temperature coefficient Q₁₀ ≈ 2 for biological reactions (van 't Hoff rule); ethylene as the ripening hormone. Campbell Biology (12th ed.). https://www.ncbi.nlm.nih.gov/books/NBK9861/
Day 316 · The tree made of air- Dry wood ~50% carbon by mass (IPCC 2006 Guidelines, Vol. 4, Table 4.3); molar masses C 12, O₂ 32, CO₂ 44; human exhaled CO₂ ~0.9–1 kg/day. https://www.ipcc-nggip.iges.or.jp/public/2006gl/vol4.html
Day 317 · Why bread rises- Alcoholic fermentation C₆H₁₂O₆ → 2 C₂H₅OH + 2 CO₂ (Gay-Lussac 1815); molar volume of a gas 24.5 L/mol at 25 °C; oven spring. McGee, On Food and Cooking (2004). https://www.ncbi.nlm.nih.gov/books/NBK22591/
Day 318 · The beer's alcohol- ABV ≈ (OG − FG) × 131.25 (standard homebrewing approximation); ethanol density 0.789 g/mL; South African standard drink = 12 g of pure alcohol (Department of Health; SAB Foundation). https://www.who.int/publications/i/item/9789240087934
Day 319 · Ripening- Ethylene as the ripening hormone; climacteric fruit (banana, avocado, apple, tomato); banana chilling injury below ~13 °C; Q₁₀ ≈ 2. Kader (ed.), Postharvest Technology of Horticultural Crops, UC Davis. https://postharvest.ucdavis.edu/
Day 320 · Why onions make you cry- Lachrymatory factor synthase and propanethial S-oxide (Imai et al., Nature 2002); inverse-square dilution of a point source; Q₁₀ ≈ 2. https://doi.org/10.1038/419685a
Day 321 · Jam and the sugar that keeps- Water activity and preservation: jams ≥ 65% soluble solids (Codex Standard 296-2009); osmosis; brine and dry-salting concentrations. McGee, On Food and Cooking (2004). https://www.fao.org/fao-who-codexalimentarius/
Day 322 · Your fruit bowl- Typical ripening times at room temperature for climacteric fruit (UC Davis Postharvest Technology Center); Q₁₀ ≈ 2 for ripening rate. https://postharvest.ucdavis.edu/
Week 47 · Animals and pets
Dog years, pet doses by weight, why cats land on their feet, migration, and ticks.
Start here · How animals are measured- Kleiber's law (1932), metabolic rate ∝ M^0.75; resting energy requirement RER = 70 × BW(kg)^0.75 kcal/day and life-stage factors (WSAVA Global Nutrition Guidelines, 2011). https://wsava.org/global-guidelines/global-nutrition-guidelines/
Day 323 · Dog years- Wang, T. et al., 'Quantitative translation of dog-to-human aging by conserved remodeling of the DNA methylome', Cell Systems 11 (2020): human age = 16 ln(dog age) + 31. https://doi.org/10.1016/j.cels.2020.06.006
Day 324 · The vet's dose- Body-weight dosing in veterinary practice (BSAVA Small Animal Formulary); paracetamol toxicity in cats due to deficient glucuronidation (Merck Veterinary Manual). https://www.merckvetmanual.com/toxicology/toxicities-from-human-drugs/acetaminophen-toxicosis-in-dogs-and-cats
Day 325 · Why cats land on their feet- Cat righting reflex, conservation of angular momentum (Kane & Scher, 'A dynamical explanation of the falling cat phenomenon', 1969); reflex time ~0.3 s; Marey's chronophotographs (1894). https://doi.org/10.1016/0020-7683(69)90086-9
Day 326 · The swallows' journey- Barn swallow migration ~300 km/day, Europe to southern Africa (BTO; Turner, The Barn Swallow, 2006); humpback whale migration 5,000–8,000 km (Whale and Dolphin Conservation). https://www.bto.org/understanding-birds/species-focus/swallow
Day 327 · Ticks by the thousand- Rhipicephalus and Amblyomma tick fecundity 2,000–5,000 eggs per female, three-host life cycle (Walker et al., Ticks of Domestic Animals in Africa, 2003); tick removal guidance and African tick-bite fever (NICD South Africa). https://www.nicd.ac.za/
Day 328 · The food bill by the bag- Metabolisable energy of dry dog food typically 3,200–4,000 kcal/kg (AAFCO / FEDIAF labelling); WSAVA feeding guidance by MER. https://europeanpetfood.org/self-regulation/nutritional-guidelines/
Day 329 · Your animals' day- RER = 70 × BW^0.75; life-stage factors (neutered adult 1.6, growth up to 3.0, indoor cat 1.2) from WSAVA Global Nutrition Guidelines 2011; rabbit maintenance energy ~ 1.5 × RER (BSAVA Manual of Rabbit Medicine). https://wsava.org/global-guidelines/global-nutrition-guidelines/
Week 48 · Budgets and tax
Tax brackets, PAYE, the emergency fund, inflation on a salary, and pension growth.
Start here · How a salary is taxed and stretched- SARS individual tax table 2025/26 (unchanged from 2024/25; Budget 2025 gave no bracket relief): 18% to R237,100; 26% to R370,500; 31% to R512,800; 36% to R673,000; 39% to R857,900; 41% to R1,817,000; 45% above; primary rebate R17,235; UIF 1% capped at R177.12 a month. Check SARS for the current year's table. https://www.sars.gov.za/tax-rates/income-tax/rates-of-tax-for-individuals/
Day 330 · The brackets and a raise- SARS individual tax table 2025/26 (unchanged from 2024/25; Budget 2025 gave no bracket relief): 18% to R237,100; 26% to R370,500; 31% to R512,800; 36% to R673,000; 39% to R857,900; 41% to R1,817,000; 45% above; primary rebate R17,235; UIF 1% capped at R177.12 a month. Check SARS for the current year's table. https://www.sars.gov.za/tax-rates/income-tax/rates-of-tax-for-individuals/
Day 331 · The payslip- SARS individual tax table 2025/26 (unchanged from 2024/25; Budget 2025 gave no bracket relief): 18% to R237,100; 26% to R370,500; 31% to R512,800; 36% to R673,000; 39% to R857,900; 41% to R1,817,000; 45% above; primary rebate R17,235; UIF 1% capped at R177.12 a month. Check SARS for the current year's table. https://www.sars.gov.za/tax-rates/income-tax/rates-of-tax-for-individuals/
- Medical scheme fees tax credit 2025/26: R364 a month for each of the first two beneficiaries, R246 for each additional (SARS). https://www.sars.gov.za/tax-rates/medical-tax-credit-rates/
Day 332 · The emergency fund- Emergency fund of 3–6 months of essential expenses (standard personal-finance guidance, e.g. Old Mutual Savings Monitor); future value of an annuity n = ln(1 + FV·r/PMT)/ln(1+r). https://www.oldmutual.co.za/
Day 333 · Inflation on a salary- Fisher relation (1+n) = (1+r)(1+i); Stats SA CPI and the SARB 3–6% target band with a 4.5% midpoint; bracket creep when tables are not inflation-adjusted (National Treasury Budget Review 2025). https://www.statssa.gov.za/?page_id=1854&PPN=P0141
Day 334 · The pension- Future value of an annuity FV = PMT·((1+r)^n − 1)/r; 4% safe-withdrawal rule (Bengen 1994; Trinity study 1998); long-run real returns of balanced funds ~4–6% (ASISA); fee drag (National Treasury retirement reform papers). https://www.asisa.org.za/
Day 335 · Capital gains- Capital gains tax for individuals 2025/26: annual exclusion R40,000, inclusion rate 40%, primary residence exclusion R2 million (SARS Comprehensive Guide to CGT). https://www.sars.gov.za/types-of-tax/capital-gains-tax/
Day 336 · Your household's tax year- SARS individual tax table 2025/26 (unchanged from 2024/25; Budget 2025 gave no bracket relief): 18% to R237,100; 26% to R370,500; 31% to R512,800; 36% to R673,000; 39% to R857,900; 41% to R1,817,000; 45% above; primary rebate R17,235; UIF 1% capped at R177.12 a month. Check SARS for the current year's table. https://www.sars.gov.za/tax-rates/income-tax/rates-of-tax-for-individuals/
Week 49 · Buying and selling
Depreciation, resale, second-hand prices, cost per use, and warranties.
Start here · How a thing loses value- Declining-balance depreciation V = P(1 − r)^t; typical passenger-car depreciation 15–20% a year after a first-year drop of 20–25% (TransUnion SA Vehicle Pricing Index; AA of South Africa). https://www.transunion.co.za/
Day 338 · The asking price- Straight-line depreciation V = P(1 − t/L); pricing from completed sales rather than listings (standard resale guidance). https://en.wikipedia.org/wiki/Depreciation#Straight-line_depreciation
Day 339 · Second-hand per year of life- Cost-per-year comparison of new and used durables; appliance service lives 8–13 years (NAHB/Bank of America Study of Life Expectancy of Home Components, 2007). https://www.nahb.org/
Day 341 · The extended warranty- Expected value of a warranty = P(claim) × cost; Consumer Protection Act 68 of 2008 s56 implied six-month warranty; consumer research on extended-warranty pricing (Consumer Reports). https://www.gov.za/documents/consumer-protection-act
Day 342 · Trade-in or private sale- Trade-in (wholesale) versus retail values (TransUnion SA Auto Dealers' Guide); VAT on second-hand goods sold by dealers (SARS VAT 404 Guide). https://www.sars.gov.za/types-of-tax/value-added-tax/
Day 343 · Your things per year- Total cost of ownership = depreciation + opportunity cost of capital (+ running costs); AA of SA vehicle operating-cost tables. https://aa.co.za/
Week 50 · Insurance and probability
Premiums, the excess, expected value, and how an insurer stays in business.
Start here · How insurance is priced- Pure premium = expected loss; expense and profit loading typically 25–40% of gross premium (short-term insurance loss ratios ~60–70%, Prudential Authority/FSCA industry statistics). https://www.fsca.co.za/
Day 344 · How the insurer stays in business- Binomial claim counts: mean np, standard deviation √(np(1−p)); law of large numbers; solvency capital under the Insurance Act 18 of 2017 (Prudential Authority). https://www.resbank.co.za/en/home/what-we-do/Prudential-regulation
Day 345 · The excess- Deductible economics: expected cost of a higher deductible = P(claim) × Δdeductible against the premium saving (standard insurance economics; Rees & Wambach, The Microeconomics of Insurance, 2008). https://www.nowpublishers.com/article/Details/MIC-023
Day 346 · Underinsurance- Average (pro-rata) condition in South African short-term policies; Ombudsman for Short-Term Insurance guidance on underinsurance and replacement value. https://www.osti.co.za/
Day 347 · Life cover: how much- Human-life-value / needs approach: PV of an annuity = A·(1 − (1+r)^−n)/r; term versus whole-life cover (ASISA consumer guides; FSCA). https://www.asisa.org.za/
Day 348 · The small claim- No-claim bonus mechanics and post-claim loading (South African short-term insurers' policy wordings; Ombudsman for Short-Term Insurance). https://www.osti.co.za/
Day 349 · Insure or self-insure- Expected value of cover = P(claim) × (value − excess); device-insurance pricing and loss ratios (consumer research, e.g. Which? on gadget insurance). https://www.which.co.uk/
Day 350 · Your policies- Expected payout = P(claim) × average claim; premium-to-expected-loss ratios by product line (FSCA short-term insurance statistics; ASISA life statistics). https://www.fsca.co.za/
Week 51 · Data about you
Steps, sleep, screen time, reading your own trends, and finding your baseline.
Start here · How to read your own numbers- Mean, population standard deviation, and the two-standard-deviation rule; standard error of a mean = σ/√n. Any introductory statistics text, e.g. OpenStax Introductory Statistics. https://openstax.org/details/books/introductory-statistics-2e
Day 351 · The unusual morning- z-score = (x − μ)/σ; resting heart rate elevation as an early illness signal in wearable data (Mishra et al., Nature Biomedical Engineering 2020). https://doi.org/10.1038/s41551-020-00640-6
Day 352 · Steps by the week- Step-count and mortality dose-response levelling near 7,000–8,000 steps/day (Paluch et al., Lancet Public Health 2022); origin of 10,000 steps in the 1965 manpo-kei pedometer. https://doi.org/10.1016/S2468-2667(21)00302-9
Day 353 · Sleep regularity- Social jetlag = difference in mid-sleep between free and work days (Wittmann et al., Chronobiology International 2006); sleep regularity and health (Windred et al., Sleep 2024). https://doi.org/10.1080/07420520500545979
Day 354 · Screen time- Device-reported screen time (Apple Screen Time / Android Digital Wellbeing); adult smartphone use averages 3–5 h/day (Data.ai State of Mobile 2024). https://www.data.ai/en/insights/market-data/state-of-mobile-2024/
Day 355 · Trend or noise- Standard error of the mean σ/√n; standard deviation of a difference of two independent means σ√(2/n); daily body-weight fluctuation ~0.5–1 kg (Vivanti 2012, Clinical Nutrition). https://doi.org/10.1016/j.clnu.2011.09.008
Day 356 · The day after the best day- Regression to the mean (Galton 1886); expected value of the next observation E[X₂|X₁] = μ + ρ(X₁ − μ); Kahneman, Thinking, Fast and Slow (2011), ch. 17. https://en.wikipedia.org/wiki/Regression_toward_the_mean
Day 357 · Your week in numbers- Weekly averaging as baseline; deviation from baseline; the two-standard-deviation rule (OpenStax Introductory Statistics). https://openstax.org/details/books/introductory-statistics-2e
Week 52 · The year in numbers
Your rate, your big five, your doubling time, your pace: a year of knowhow and what to keep.
Day 358 · Your rate- Opportunity cost of time; 173 hours = 40 h × 52 / 12 (standard monthly hours in South African payroll practice). Basic Conditions of Employment Act 75 of 1997 (45-hour maximum week). https://www.gov.za/documents/basic-conditions-employment-act
Day 359 · Your big five- Unit prices as met during the year: Eskom Homelight R2.71/kWh; petrol ~R21.50/L (Department of Mineral Resources and Energy monthly adjustment); municipal water ~R35/kL; SARB inflation target midpoint 4.5%. https://www.dmre.gov.za/
Day 360 · Your doubling times- Doubling time t = ln 2 / ln(1 + r); rule of 72 as its approximation (week 4). Eskom tariff increases 2019–2025 averaged above 10% a year (NERSA decisions). https://www.nersa.org.za/
Day 362 · One percent, tested- Compound growth (1+r)^n; the '1% better every day' claim (Clear, Atomic Habits, 2018) and its limits as a model of skill or fitness. https://jamesclear.com/continuous-improvement
Day 363 · Your year's card- The year's own weeks: 1 (electricity), 2 (water, 150 L per person a day), 16 (fuel), 48 (savings rate). Average month = 365/12 days.
Day 364 · Your year of units- Seasonal household electricity profile for a South African home with an electric geyser (Eskom residential load research); tariff R2.71/kWh as on Day 1. https://www.eskom.co.za/