At the same time, computing it was a challenge for some of the best mathematicians who ever lived. The number pi is simple to define and captures a fundamental geometric fact. However, in the 1760s, the French-Swiss mathematician Johann Heinrich Lambert proved that the decimal expansion of pi does not follow any simple rule for its digits pi is irrational, meaning that its decimal expansion does not repeat or terminate. A simple rule to describe all digits in one go, or to pinpoint pi, as the ancient Greeks had hoped to do. With modern computers, as of August 2021, the record stands at 62.8 trillion digits.Īs the knowledge of the digits of pi expanded, people tried to detect a pattern. Progress accelerated with better analytical tools. A millennium would pass before further significant advances led the 14th century Indian mathematician Madhava of Sangamagrama to reach 11 decimal places. Improvements to seven decimal places were achieved by Chinese mathematicians in the 5th century AD, based on a new technique discovered in the 3rd century by mathematician and writer Liu Hui. Being just a simple ratio, how hard could it be?Īrchimedes placed pi between 223/71 and 22/7, so between 3.140 and 3.142, while Ptolemy found the first approximation correct to three decimal places: 3.141. The ancient Greeks only studied flat geometry and so for them the constant pi was truly a universal wonder whose precise value they sought to pinpoint. For circles drawn on curved surfaces, such as the spherical surface of Earth, the division is not constant at all, and pi ceases to exist.įlat geometry, also known as Euclidean geometry, is the universe of mathematical objects where pi exists. While pi exists through the constancy of the result of dividing circumference by diameter for all circles, it’s important to note that this constancy is not quite as universal as the ancient Greeks thought. But the fascination with the number pi goes back millennia. The Greek letter pi (π) was introduced in 1706 to denote that constant ratio between the circumference of a circle to its diameter. You just stumbled upon a universal law of circular objects.
If you decide to experiment with other circular shapes, you will find that no matter how large or small the objects are, as long as they are round, the ratios will all be very close to 3.14. You will discover that the ratios of the circumference to the diameter in both cases are remarkably close to each other. Next time you eat soup, repeat the process with the bowl. Finally, divide the circumference by the diameter, and record the result. Then, lay your spoon on top of the cup, making sure it lies across the centre of the cup, and measure the length from side to side – the diameter. Wrap a piece of string around the circumference of the cup, and measure the length of the string.