When was the mathematical symbol π (pi) discovered? And what are its peculiarities?

Most of us probably know “pi” as a word often used in geometry. However, what some people don’t realize is that it is actually the sixteenth letter of the ancient Greek alphabet, and it is pronounced as “pie.” For those who don’t know, the ancient Greek alphabet consists of 24 letters, with the first letter being alpha and the last one being omega. Because of this arrangement, ancient Greeks will say “from alpha to omega” instead of “from A to Z.”

Pi in Geometry

When “pi” is used in geometry, it is not anymore considered a letter of the alphabet, but as a symbol denoting the exact ratio of the circumference of a circle to its diameter, which is approximately 3.14159256. In order to arrive at that specific value for the circumference of a circle, one has to multiply its designated diameter with “pi”. It can look complex at first, but it is relatively simple if you used it in a formula or equation. The symbol π also helps in providing answers to complex problems without having in-depth knowledge of mathematics or geometry.

To better understand the symbol, we are going to provide an example. If the diameter of the Earth at the equator is exactly 12,756.274 kilometers, how many days would a vehicle traveling at the speed of 40 kilometers per hour take to circumnavigate the planet along the equator? Take note that no information about the circumference is given in the problem. The answer for its circumference is 40,075 kilometers, which is achieved by multiplying the diameter (12,756.274 kilometers) with pi or π (3.14159256), and then if you divide the circumference by 40, you will find out that the time taken in days as 41 days 17 hours and 57 minutes, but this exact answer is achieved by converting every 24 hours to one day. Finding the circumference from every problem is easy because of the pi, as you just need to use it whenever you are calculating the diameter of the Earth at the equator with the time required for circumnavigating it.

History of Pi

The value of pi (3.1416…) was first discovered and calculated by the prolific Greek mathematician Ptolemy. As the decimal system was not invented during Ptolemy’s time, the value that was calculated by him for the symbol was not entirely accurate. It was only after the decimal system was prominently utilized in the 17th century that mathematicians found out that there were supposed to be infinite fractional digits after the whole number 3 at the beginning of the value.

A mathematician in England named William Shanks spent almost 15 years of his life trying to solve the mystery of the symbol’s infinite value. In 1874, he was able to calculate the 707th place or number after the decimal. Unfortunately, after calculating the 707th number, the accuracy of his total value was questioned by many, including those who became mathematicians after his time.

Shanks’ calculations were checked using the world’s first computer in 1945, and a great error to his calculations was detected. It was discovered that Shanks made an error in calculating the 527th place after the decimal point and the number 3, and that mistake led to all the values or numbers after the 537th, specifically 180 places, to be inaccurate. It was a shame that Shanks had devoted almost all his time as a mathematician over incorrect calculations, but what’s worse is that he didn’t found out about his error when he was still alive. The terrible news would have devastated Shanks, but it was still fortunate that his dedication to solving the mysteries of the symbol is praised by almost all mathematicians until today.

As the value of “pi” is considered an irrational number, after being calculated to have an infinite number of figures after the decimal point, an exact value of the symbol that any person declares to the world cannot be accurate. In modern times, most mathematicians have given up calculating the value of “pi,” as computers are now more capable of performing this task than humans. The longest calculation for the value of “pi” was deduced by the supercomputer Cray-2 in 1986. The computer calculated the value for up to 2,630,600,000 numbers or places after the decimal point.