Count a sunflower's seed spirals in each direction and you'll often find two neighbouring Fibonacci numbers, such as 34 and 55. In 2016, a citizen science study of 657 sunflowers, launched in tribute to Alan Turing, confirmed it… with a caveat: about one count in four deviated from the rule, at least partly. Nature loves Fibonacci, but doesn't treat it as an absolute law.
How many different structures can you build with six classic 2-by-4 Lego bricks of the same colour? The company used to quote just over 102 million. In 2005, Danish mathematician Søren Eilers recounted everything by computer: 915,103,765 combinations. The official estimate had been too low by a factor of about nine.
Fold an A4 sheet in half and you get an A5 with the same proportions. That only works for one ratio between length and width: about 1.414, the square root of 2. The A0 format measures exactly one square metre, and A4 is a sixteenth of it. With standard 80-gram-per-square-metre paper, an A4 sheet therefore weighs exactly 5 grams.