Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 5 - Number Theory and the Real Number System - 5.4 The Irrational Numbers - Exercise Set 5.4 - Page 299: 110

Answer

The first one to calculate the value of pi was Archimedes. Archimedes calculated value of pi is between 31/7 and 310/71. After that Chinese mathematician Zu Chongzhi calculated value of pi as 355/113. Then mathematician denoted pi with a Greek letter\[\pi \].

Work Step by Step

History:The first one to calculate the value of pi was Archimedes. Archimedes calculated value of pi is between 31/7 and 310/71. After that Chinese mathematician, Zu Chongzhi calculated value of pi as 355/113. Then, mathematician denoted pi with a Greek letter\[\pi \]. Applications: It is used in geometry and trigonometry, Monte Carlo method, complex and analysis, number theory and Riemann zeta function, probability and statistics and many more. Value of pi is used in calculation of circumference of circle,area of circle, volume of sphere, surface area of a sphere. For example: Consider a circle of radius 7. To find the area of the circle use the formula \[\pi {{r}^{2}}\]such as: Put value of radius in the above formula: \[\begin{align} & \pi {{r}^{2}}=\frac{22}{}\times 7\times \\ & =22\times 7 \\ & =154 \end{align}\] Curiosities: Pi is the most recognized mathematical constant in the world. The circumference and area of the circle can never be truly measured, because the value of pi can never be truly known. Pi is an irrational number, meaning its digits go on forever. Computing pi is a stress test for a computer. For example: Al-Khwarizmi around A.D. 800 calculated value of pi as 3.1416 and then Chinese mathematician Liu Hui calculated value of pi as 3.14159.
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