Maths

13 breaks

Patterns, chance and the numbers hiding in everyday things.

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Why a treatment can win in every group and still lose overall: Simpson's paradox Treatment B beats Treatment A overall, yet A wins for small stones and for large stones. That is Simpson's paradox, and it is real data from a kidney-stone… Maths4 min read Why no walk can cross all seven bridges of Königsberg once: Euler's odd-places rule Seven bridges, two islands, two river banks: in 1700s Königsberg nobody could find a walk crossing each bridge exactly once. Euler didn't search harder, he… Maths4 min read Why sunflower seeds never leave gaps: the golden angle and the Fibonacci spirals Sunflower seeds are not placed in spirals on purpose. Each new seed turns a fixed angle from the last, and only one angle, about 137.5 degrees, leaves no bare… Maths4 min read Why random dice rolls draw a perfect fractal: the chaos game and the Sierpiński triangle Pick three dots, then keep jumping halfway towards a randomly chosen one. It sounds like it should leave a grey smudge, but after a few thousand jumps a… Maths3 min read Why a dropped stick can find π: Buffon's needle Drop a stick on a floor of planks and count how often it lands across a seam. The count secretly contains π: for a needle as long as the plank width, the… Maths4 min read Why 23 people are enough for a shared birthday: counting pairs, not people Put 23 people in a room and the chance that two share a birthday is already 51%. It feels far too low a number, because we picture one person matching our… Maths3 min read Why random bounces pile up into a bell curve: the Galton board Every ball in a Galton board makes the same blind choice at each peg: left or right, a coin flip. Yet drop enough of them and the pile always grows into the… Maths4 min read Why switching doors wins twice as often: the Monty Hall problem Three doors, one car. You pick one, the host opens a goat door, and offers a swap. Most people say it's 50/50. It isn't: switching wins twice as often as… Maths4 min read Why 1 leads far more often than 9: Benford's law of first digits Look only at the first digit of any long list of real-world numbers, such as river areas, populations or the figures in a company's accounts. You'd expect each… Maths3 min read How dropping needles on a floor reveals the number π: Buffon's needle Toss a match onto a plank floor and ask: does it touch a crack? Do it thousands of times and the fraction that do will quietly spell out π, though no circle is… Maths3 min read Why 23 people are enough for two to share a birthday Put 23 people in a room and there's a better-than-even chance that two of them share a birthday. That sounds wrong, because 23 is tiny next to 365. The catch… Maths4 min read Why turning a wobbly table can stop it rocking: the quarter-turn proof Your café table rocks. Before you wedge a folded napkin under a leg, try turning the whole table on the spot. On most floors, somewhere within a quarter-turn… Maths5 min read