Various historical aspects of pi (22/7) in about 5 pages
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Answer:
Pi (π) has been known for almost 4000 years—but even if we calculated the number of seconds in those 4000 years and calculated π to that number of places, we would still only be approximating its actual value. Here’s a brief history of finding π.
The ancient Babylonians calculated the area of a circle by taking 3 times the square of its radius, which gave a value of pi = 3. One Babylonian tablet (ca. 1900–1680 BC) indicates a value of 3.125 for π, which is a closer approximation.
The Rhind Papyrus (ca.1650 BC) gives us insight into the mathematics of ancient Egypt. The Egyptians calculated the area of a circle by a formula that gave the approximate value of 3.1605 for π.
The first calculation of π 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 actual 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 π but only an approximation within those limits. In this way, Archimedes showed that π is between 3 1/7 and 3 10/71.
A similar approach was used by Zu Chongzhi (429–501), a brilliant Chinese mathematician and astronomer. Zu Chongzhi would not have been familiar with Archimedes’ method—but because his book has been lost, little is known of his work. He calculated the value of the ratio of the circumference of a circle to its diameter to be 355/113. To compute this accuracy for π, he must have started with an inscribed regular 24,576-gon and performed lengthy calculations involving hundreds of square roots carried out to 9 decimal places.
Mathematicians began using the Greek letter π in the 1700s. Introduced by William Jones in 1706, use of the symbol was popularized by Leonhard Euler, who adopted it in 1737.
An eighteenth-century French mathematician named Georges Buffon devised a way to calculate π based on probability. You can try it yourself at the Exploratorium's Pi Toss exhibit.
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Answer:
Pi - the ratio between the circumference and diameter of a circle - is perhaps one of the most famous numbers in all of mathematics.
Step-by-step explanation:
- The concept of pi is ancient - it's been known to humanity for at least four thousand years. The symbol π was devised by British mathematician William Jones in 1706 to represent the ratio and was later popularised by Swiss mathematician Leonhard Euler.
- In 2000 BCE, Babylonian mathematicians performed the first known calculation of the area of a circle using the circumference of an inscribed hexagon, and derived an approximate value of pi 3.125.
- Around 250BCE Archimedes made a major breakthrough in calculating a more accurate value of pi by using the Pythagorean theorem. He approximated the area of a circle by comparing the areas of a polygon inscribed inside the circle and one that surrounded it.
- By doing so, he proved that there was a constant between the area of a circle and the square of its radius.
- In centuries that followed, mathematicians around the world were able to extend the number of known decimal places of pi by performing extensive calculations. By 1600, pi had been calculated up to 35 digits using the method of inscribed polygons .
- One of the earliest formulae for calculating pi was proposed by English mathematician John Wallis in 1656.
- Eventually , though, in the early twentieth century ,Indian mathematician Srinivasa Ramanujan developed an incredibly efficient formula for calculating pi based on its reciprocal fraction, which was later incorporated into computer algorithms.
- In modern times , the number pi has become ubiquitous in popular culture ,in ways that reach far beyond its roots in ancient geometry. There is even a holiday dedicated to pi, appropriately knowns as Pi Day, which is observed annually on March 14 - 3/14.
- Each year on March 14,math lovers gather for pie eating ,pi recitation contests, and discussions on the significance of pi.
- The constant ,which developed from a simple fascination with circles and numbers, has altered the course of science and mathematics, charmed the most brilliant minds of human history, and captivated millions around the world.
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