In the 5th century, the Chinese astronomer Zu Chongzhi pinned pi between 3.1415926 and 3.1415927, seven correct decimals. He also proposed an easy-to-remember fraction, 355 divided by 113, accurate to six decimals. No more precise estimate would be established for nearly 900 years, until the work of the Persian al-Kashi in the 15th century.
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.