Pi, as we all learned in school (and are reminded every March 14, on Pi Day), is defined as the ratio of a circle’s circumference to its diameter. Denoted by the Greek letter π, this curious little number is approximately 3.14, although computers have calculated it out past 22 trillion digits and counting: 3.141592653589793238462643383279502…, a sequence never repeating, never betraying any pattern, going on forever, infinity on a platter.
Take a moment to savor the result visually:
3 + 10/71 < π < 3 + 10/70.
The unknown value of pi is being trapped in a numerical vise, squeezed between two numbers that look almost identical, except the first has a denominator of 71 and the last has a denominator of 70. By considering polygons with even more sides, later mathematicians tightened the vise even further. Around 1,600 years ago, the Chinese geometer Zu Chongzhi pondered polygons having an incredible 24,576 sides to squeeze pi out to eight digits:
3.1415926 < π < 3.1415927.
Adapted from Steven Strogatz, “Infinite Powers: How Calculus Reveals the Secrets of the Universe,” published by Houghton Mifflin Harcourt