The clay tablet Plimpton 322, inscribed in Mesopotamia around 1800 BCE, lists columns of numbers tied to the sides of right triangles, such as the trio 119, 120 and 169. More than a millennium before Pythagoras, scribes had mastered this relationship. What was the tablet for? School exercises or a calculation table: historians are still debating.
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.