Start with a triangle, add a small triangle to the middle of each side, then repeat on every new segment, forever. You get the Koch snowflake, described in 1904 by Swede Helge von Koch. At each step, the outline grows by a third, so its perimeter becomes infinite. Yet its area stays finite: it never spills outside a circle drawn around it.
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.