Eventually, in the twentieth century, Indian mathematician Srinivasa Ramanujan created an efficient formula for calculating pi based on its reciprocal fraction. In 1706, William Jones introduced the greek letter of pi that we all know is “π” and it was later popularized by Leonhard Euler at the start of 1737.Progress has slowed for the next few hundred years as more calculations were made, but there was little conceptual development. He established a formula involving the multiplication of an infinite series of fractions based off “½π.” By the end of the eighteenth century over 100 decimals of pi had been found. The earliest formula for calculating pi was proposed by an English mathematician named John Wallis in 1656. During the seventeenth century new techniques were discovered in the field of mathematics which allowed for improved calculations of pi using infinite series. However, there was little theoretical progress beyond Archimedes. By 1600, pi had been calculated to 35 digits using the method of inscribed polygons. Based on his results it is thought that he would have used similar methods to those of Archimedes. A notable mathematician that contributed to this idea was a Chinese astronomer named Zu Chongzi, who came up with the value of 355/13. Some centuries have passed since the breakthrough of Archemides, and mathematicians all over the world were able to extend the number of decimal places by using complex calculations. He was able to get an upper bound of 22/7 and a lower bound of 223/71 for the value of pi. He proved that there was a ratio that was constant between the area of a circle and the square of its radius. He estimated the area of a circle by comparing the areas of different polygons within the circle and the ones around it. He was able to find a more accurate value of pi using the pythagorean theorem. Around 250 BCE, Archimedes, who was a Greek mathematician, made an impressive discovery and breakthrough. Both estimates were close to the actual value of pi, however it was still far off from the true number. The earliest approximations of pi are 3.125 in Babylon (1900-1600 B.C.) and 3.1605 in Ancient Egypt (1650 B.C.). Between 3,000 and 4,000 years ago, people used trial and error estimations of pi, without considering potential mistakes. You may be wondering how the 100 trillion digit number came into existence, we have to look so far into the past. We are going to go through the origins of pi or 3.14 and see what we uncover and what we can learn from “π.” Pies for Pi Day (Creative Commons) Photograph of Domenica-Fetti Archimedes (1620) (Photographer Credit, Unknown (Wikimedia Commons) What many people do not know is the true history behind the number that sent many mathematicians into a frenzy. Most people only know the number as 3.14, but pi is an irrational number that neither ends, nor contains a repeating pattern. Pi represents the ratio between the circumference of a circle and the diameter of the circle or “”. Pi (which is commonly referred to as “π”) is one of the most well-known mathematical constants on the planet.
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