# Pi - A Math Paper

Pi - A Math Paper

Pi has been known for almost 4000 years. A Babylonian calculated the area of a circle by taking 3 times the square of its radius, which gave a value of pi = 3. There is proof that the Egyptians calculated the area of a circle by a formula that gave the approximate value of 3.1605 for pi. These two different cultures got these numbers by a series of measurements. The first calculation of pi was done by Archimedes of Syracuse (287–212 BC), one of the greatest mathematicians of the ancient world.

Archimedes approximated the area of a circle by using the Pythagorean Theorem to find the areas of two regular polygons: the polygon inscribed within the circle and the polygon within which the circle was circumscribed. Since the entire area of the circle lies between the areas of the inscribed and circumscribed polygons, the areas of the polygons gave upper and lower bounds for the area of the circle. Archimedes knew that he had not found the value of pi but only an approximation within those limits. In this way, Archimedes showed that pi is between 3 1/7 and 3 10/71.A similar approach was used by Zu Chongzhi (429–501), a brilliant Chinese mathematician. Zu Chongzhis work was misplaced many years ago so people only know very little about him. He calculated the value of the ratio of the circumference of a circle to its diameter to be 355/113.Mathematicians began using the Greek letter π in the 1700s. Introduced by William Jones in 1706, use of the symbol was popularized by Euler, who adopted it in 1737.

No matter how many different people and cultures went into finding the great number we now know as pi, they all consisted of the number 3.1….etc...