History of Pi
History of Pi There are many people who have discovered and proved what pi is. As time goes on people discover more and more of the seemingly random numbers. Four of the people who proved pi are the Liu Hui, Archimedes of Syracuse, James Gregory, and the Bible. The first proof I will be talking about is Liu Hui’s. Liu Hui was a Chinese mathematician whose method for proving pi was to find the area of a polygon inscribed in a circle. When the number of sides on the inscribed polygon increased, its area became closer to the circumference of a circle and pi. For finding the side length of an inscribed polygon Liu Hui used a simple formula. (13Ma3) To find the side length of an inscribed polygon of 2n sides, if the side length of a polygon with n sides is known he used the following formula:
In this formula k stands for a temporary variable, and Sn stands for the side length of an inscribed polygon with n sides. (13Ma3) We will start with a hexagon inside of a circle. The radius of the circle is one, the area is pi. The side length of the hexagon is 1. To calculate the next k value, all we need to do is do an addition and a square root like in the following:
The area of a regular polygon is A=1/2nsa. The n stands for number of sides, s stands for side length, and a stands for apothem. As the number of sides increases, the apothem becomes closer and closer to the radius so we let a=1. We now have the formula for the area of a polygon with n sides. This formula is Pn=1/2nSn. In this formula Pn represents the area of a polygon with n sides. If you go through the formula you will get pi and eight of its decimal places when there are 98,304 sides, which will give you 3.14159265. (13Ma3) The next proof I will be talking about is Archimedes’. The method Archimedes used for finding pi was to take the perimeters of polygons inscribed and circumscribed about a given circle. However instead of trying to measure the polygons one by one, he used a theorem
In this formula k stands for a temporary variable, and Sn stands for the side length of an inscribed polygon with n sides. (13Ma3) We will start with a hexagon inside of a circle. The radius of the circle is one, the area is pi. The side length of the hexagon is 1. To calculate the next k value, all we need to do is do an addition and a square root like in the following:
The area of a regular polygon is A=1/2nsa. The n stands for number of sides, s stands for side length, and a stands for apothem. As the number of sides increases, the apothem becomes closer and closer to the radius so we let a=1. We now have the formula for the area of a polygon with n sides. This formula is Pn=1/2nSn. In this formula Pn represents the area of a polygon with n sides. If you go through the formula you will get pi and eight of its decimal places when there are 98,304 sides, which will give you 3.14159265. (13Ma3) The next proof I will be talking about is Archimedes’. The method Archimedes used for finding pi was to take the perimeters of polygons inscribed and circumscribed about a given circle. However instead of trying to measure the polygons one by one, he used a theorem
Cited: (n.d.). Retrieved March 13, 2013, from http://creation.com/does-the-bible-say-pi-equals-3 (n.d.). Retrieved March 13, 2013, from http://www.trans4mind.com/personal_development/mathematics/various/piGregory.htm (n.d.). Retrieved March 13, 2013, from http://itech.fgcu.edu/faculty/clindsey/mhf4404/archimedes/archimedes.html (n.d.). Retrieved March 13, 2013, from http://luckytoilet.wordpress.com/2010/03/14/liu-huis-algorithm-for-calculating-pi/ Grigg, R. (n.d.). Retrieved March 13, 2013, from http://creation.com/does-the-bible-say-pi-equals-3