Around 1400, in Kerala, southern India, the mathematician Madhava of Sangamagrama discovered how to express pi as an infinite sum of ever-smaller fractions. He used it to get a value correct to more than ten decimal places. In Europe, equivalent results were published only in the 17th century by Gregory and Leibniz. His successors in the “Kerala school” extended this work for two centuries.
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.