History of PI
The Egyptians knew how to work well with reasons. Soon discovered that the ratio of the length of a circumference and its diameter is the same for any circle, and its value is a "slightly larger than 3."It is this reason that we call pi.Whereas part of a circumference length edo diameter, we have:c / d = pi= c pi. dThe calculation of the exact value of pi has occupied mathematicians for centuries.To arrive at the value of pi expressed by 3 sixth, which is about 3.16, the Egyptians 3500 years ago left a square inscribed in a circle, whose side measured nine units. Square folded sides for a polygon with eight sides, and calculated the ratio between the perimeters of the octagons inscribed and circumscribed circumference and diameter.The Egyptians achieved a better approach than the Babylonians, for whom "the length of any circumference was three times its diameter," which indicated a value of 3 for pi.By the third century BC, Archimedes - the most famous mathematician of antiquity, who lived and died in Syracuse, Greece - also sought to calculate the ratio between the length of a circle to its diameter.Starting with a regular hexagon, Archimedes calculated the perimeters of the polygons obtained successively doubling the number of sides to reach a 96-sided polygon.Calculating the perimeter of the polygon of 96 sides, managed to pi a value between 3 10/71 and 3 10/70. That is, for Archimedes pi was a number between 3.1408 and 3.1428.With a polygon of 720 sides inscribed in a circle of radius 60 units, Ptolemy, who lived in Alexandria, Egypt, around the third century AD, was able to calculate the value of pi as 377/120, which is approximately equal to 3 , 1416, an even better approximation than that of Archimedes.The fascination for the calculation of the exact value of pi has also taken account of the Chinese. In the third century AD, Liu Hui, a copier of books, he managed to get the value of 3.14159 with a polygon of 3072 sides.But at the end of the fifth century, the mathematician Tsu Ch'ung-chih went even further: as the value of pi found a number between 3.1415926 and 3.1415927.At this time, the great Indian mathematician Aryabhata made this statement recorded in a small book written in verse:"Add to 4-100, multiply-add and for 8 to 62 000. The result is a circle of diameter approximately 20 000".If you noted that the length of a circle is given by Pi = c. d, is easy to see that the solution of the equation of Aryabhata:(4 + 100). 8 62 000 = + pi. 20,000104. 8 62 000 = + pi. 20,000832 + 62 000 = pi. 20,00062 832 = pi. 20,00062,832 / 20,000 = pIindicates the value of pi as 3.1416.62 832/20 000 = 3.1416The greater the number of decimal places, the better the approximation obtained for pi.By the fifteenth century, the best value for pi was found by the Arab mathematician al-Kashi: 3.1415926534897932.But most impressive was the calculation made by the Dutch mathematician Ludolph van Ceulen (1540-1610) in the late sixteenth century.Starting with a polygon of 15 sides and doubling the number of sides 37 times, Ceulen obtained a value for pi to 20 decimal places.Soon after, using a greater number of sides, he got closer to 35 decimal places!Such must have been the thrill of Van Ceulen that in his death, his wife had engraved on the tomb with the value of pi to 35 decimal places.Imagine how he would feel if he knew that in the twentieth century calculariam computers in seconds, the value of pi to 100, 1000, 10 000, million decimal places!Pi = 3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706428810975665933446128475682337867831652712019091456485669234603486104543266482 ...Many of the mathematical symbols that we use today to the Swiss mathematician Leonhard Euller (1707-1783).It was Euller who in 1737 became known symbol for pi. It was also at this time that mathematicians were able to demonstrate that it is an irrational number.
