Who Discovered Pi?
Pi is a mathematical constant. The value of pi is the ratio of a circle’s circumference to its diameter, or the ratio of a circle’s area to the square of its radius. This value is approximately equal to 3.141593 (the fraction is an irrational number).
Approximations of the constant pi have actually been around for centuries. In fact, there is evidence that the designs for the pyramids in the Old Kingdom of Egypt use approximations of the constant. However, the approximations were slightly off. The approximations were 3 plus 1/7, which is an irrational number of 3.1428.
In Gaza, the designers for the Great Pyrmid built a pyramid with a ration of approximately two pi. These same proportions were also used at the Pyramid of Meidum. Thus, historians have concluded that the Egyptians had a rough estimation of pi.
Historians further believe that the civilizations of Ancient Egypt, Babylonian, India, and Greece all understand that the ratio of the circumference to the diameter of a circle is the same for all circles, and all understood that this figure was greater than three.
There is evidence of approximations for the figure in both Egyptian writings and Babylonian writings, and the approximations are within one percent of the true value of pi.
Archimedes
The first individual to truly devote a large amount of time to determining the exact value of pi was Archimedes (who lived from 287 to 212 BC). He understood that the magnitude of pi could be bounded from below and above if one inserts circles into polygons, and then determined the outer perimeters of the polygons and the inner perimeters.
Using this method, Archimedes determined that pi was between 3 and 10/71 and 3 and 1/7. The average between these numbers is 3.13185.
Ptolemy
The next individual to study pi appears to be Ptolemy, the Roman citizen. He was a mathematician, an astronomer, a geographer, and an astrologer. In his writings, he determined that pi was 3.1416. Although historians are unsure if Ptolemy determined this figure on his own, or if he derived the figure from the writings of Apollonius of Perga.
Liu Hui
Liu Hui, a mathematician in the Wei Kingdom, agreed with this figure. Using a calculation of a 3072-gon, he determined pi was 3.1416. Then, in 480 A.D. the Chinese mathematician Zu Chongzhi proved that pi was approximately equal to 355/113. He further was able to pinpoint the value of pi between 3.1415926 and 3.1415927 using Liu Hui’s calculations and writings.
Breakthroughs in Pi
The next major breakthrough in determining the value of pi didn’t occur for another nine hundred years. The discovery of calculus and the introduction of infinite series lead to the a more precise figure for pi. Madhava of Sangamagrama, around the year 1400, discovered an infinite series that converges to pi divided by four.
This series was later rediscovered by James Gregory and Gottfried Leibniz in the seventeenth century. Although the series is correct, the calculation that series would require to determine a specific number for pi is extremely time consuming and arduous.
Almost four thousand terms would have to be added together to find the next approximate digit of pi. However, Madava was able to use the series to determine the first eleven digits of pi. In 1424, Jamshid al-Kashi determined the first sixteen digits.
Then, the German mathematician, Ludolph van Ceulen, determined the first thirty seven digits of pi. As mathematicians began to use calculus to determine more advanced infinite series, they discovered more of the digits of pi. By the nineteenth century, the first five hundred and twenty seven digits were known.
Thus, the answer to who discovered pi is not a single name. Rather, the discovery of pi was due to the arduous and time consuming work of many mathematicians and individuals over the centuries.