Pi A Marvelous and Mysterious Number What is

Pi: A Marvelous and Mysterious Number

What is Pi? • Pi is simply a ratio that exists in all circles:

How to measure or calculate pi accurately? ?

Approximating Pi… • 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 pi, which is a closer approximation.

Approximating Pi… • Rhind Papyrus (ca. 1650 BC), there is evidence that the Egyptians calculated the area of a circle by a formula that gave the approximate value of 3. 1605 for pi.

Approximating Pi… • The first calculation of pi was done by Archimedes of Syracuse (287– 212 BC), one of the greatest mathematicians of the ancient world.

• 3. 140845. . . < π < 3. 142857. . .

Approximating Pi… • A similar approach was used by Zu Chongzhi (429– 501), a brilliant Chinese mathematician and astronomer. • 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 pi using Archimedes method, he would have had to start with an inscribed regular 24, 576 -gon and perform lengthy calculations involving hundreds of square roots carried out to 9 decimal places. 3. 1415926 < π < 3. 1415927

Approximating Pi… • Mathematicians began using the Greek letter π in the 1700 s. Introduced by William Jones in 1706, use of the symbol was popularized by Euler, who adopted it in 1737.

Pi Approximations in the Age of Computers • John Wrench, and L. R. Smith were the first to use an electronic computer (the ENIAC) to calculate π (it took 70 hours).

Pi Approximations in the Age of Computers • 1983. Yasumasa Kanada, Sayaka Yoshino and Yoshiaki Tamura, 16, 777, 206 decimal places • 1989 Gregory V. Chudnovsky & David V. Chudnovsky, 1, 011, 196, 691 decimal places • 2002 Yasumasa Kanada & 9 man team, 1, 241, 100, 000 decimal places

Chronology of Pi Calculations https: //en. wikipedia. org/wiki/Chronology_of_co mputation_of_%CF%80