Mathematics

Science 6 min A cantilever uses up its deflection limit by the square of its length A beam fixed at one end bends eight times as far under a tip load when its length doubles, but because deflect... KE Kenji Tanaka 3 Nov Science 6 min A head wind costs a cyclist far more power than warm air gives back Cycling power goes to the tyres, the air and any gradient, and the split changes sharply with speed and slope.... NA Nadia Rahim 3 Nov Science 6 min Euler's buckling formula stays above Hong Kong's steel column curves Euler's formula gives the buckling load of an ideal column, and Hong Kong's steel code uses it as an input to... KE Kenji Tanaka 2 Nov Science 6 min How the degree of kinship between two parents sets their child's inbreeding coefficient The inbreeding coefficient, F, is the chance that a child inherits two copies of the same gene from one ancest... NA Nadia Rahim 27 Oct Science 6 min The 2% rule overstates true airspeed at lower levels and understates it near the tropopause True airspeed is calibrated airspeed corrected for the thinner air at altitude and for temperature. The FAA's... KE Kenji Tanaka 27 Oct Statistics 6 min Roman numerals on Roman stones fail today's strict standard form Roman numerals today follow a strict standard form that allows six subtractive pairs, no letter more than thre... NA Nadia Rahim 19 Oct Science 6 min Hazen-Williams C values and how far the published tables disagree Hazen-Williams estimates friction loss in a water pipe from one roughness number, C, and published tables give... NA Nadia Rahim 19 Oct Science 6 min Horsepower, PS and kilowatts, and where the torque and power curves cross Car power is printed in mechanical horsepower, metric horsepower (PS) or kilowatts, three units that differ by... KE Kenji Tanaka 18 Oct Finance 6 min Doubling times from the rule of 72 fit interest compounded once a year The rule of 72 estimates the years money takes to double by dividing 72 by the yearly interest rate. It works... SA Sarah Chew 16 Oct Science 6 min The clock rule taught for crosswind reads high, most of all at sixty degrees The crosswind on a runway is the wind speed times the sine of the angle between wind and runway, and flight tr... KE Kenji Tanaka 16 Oct Science 6 min Warm water shifts a pipe's Reynolds number more than the laminar limits differ Physics texts put the end of laminar pipe flow at a Reynolds number of 2,000 or 2,300, depending on the source... KE Kenji Tanaka 15 Oct Science 6 min Rebar weight by the d²/162 rule runs a fraction heavy against the standards Rebar mass per metre is usually worked out as the bar's diameter in millimetres, squared, divided by 162. We c... KE Kenji Tanaka 15 Oct Statistics 6 min Singapore's golf tees turn one handicap index into very different stroke counts A Course Handicap rescales a golfer's Handicap Index by the Slope Rating of the tee being played. Across the 8... NA Nadia Rahim 15 Oct Statistics 6 min Net run rate tables from the ICC add up only when overs are counted in balls Net run rate is a cricket side's runs per over minus the runs per over scored against it, across every match w... NA Nadia Rahim 14 Oct Developer Tools 5 min What CSS ease and ease-in-out actually do The default CSS easing, ease, is 80% of the way there at half the time, and it does not start from rest. We ev... KE Kenji Tanaka 27 Sep Statistics 7 min How to count fan in Hong Kong mahjong, and why every table scores differently In Hong Kong mahjong every table agrees that all chows is 1 fan and a full flush 7, but the rarer hands and th... NA Nadia Rahim 23 Sep Science 5 min Finding the years your lunar and solar birthdays fall on the same day Your lunar birthday and your solar birthday meet only a few times in a lifetime. The first match is at 19 for... NA Nadia Rahim 22 Sep Science 7 min How many ancestors did you have a thousand years ago? Doubling every generation gives you about a trillion ancestors a thousand years back, more people than have ev... NA Nadia Rahim 21 Sep Chinese Culture 8 min A Ziwei chart is four numbers and some arithmetic The static chart is a function of the year stem, the lunar month, the lunar day and the birth hour. Locating t... EV Eva Chin 21 Sep Chinese Culture 7 min Most of a Chinese almanac entry is arithmetic, and the rest disagrees The day's stem and branch, officer, mansion and clash all follow from the date by formula. The suitable and av... EV Eva Chin 21 Sep Science 10 min A4 is the answer to an equation, and US Letter is not the answer to anything Two constraints — a ratio of √2 and an area of one square metre — have exactly one solution, and that solution... NA Nadia Rahim 20 Sep Science 6 min The Fluid Blowup Proofs Are Machine-Checkable. The Competing Claim Was a Press Call. Buckmaster and Alpöge published three preprints with Lean formalisations anyone can run. The results are for f... NA Nadia Rahim 9 Sep Personality 5 min Why two websites give you different life path numbers Numerology has two standard ways of doing the arithmetic, and for about one birthday in eight they disagree. T... AM Amelia Wong 31 Aug Chinese Culture 5 min The pattern behind the order of the 64 hexagrams The I Ching's numbered sequence has a strict rule running through it that almost no introduction mentions — an... EV Eva Chin 31 Aug