Lesson Objectives 1 You will gain a deeper

Lesson Objectives 1. You will gain a deeper understanding of the fundamental concept of pi. 2. You will discover that there is a special relationship between circumference and the diameter of a circle. 3. You will discover the approximate value of pi. 4. You will understand how the number 3. 14 for pi was determined. 5. You will write a paragraph explaining what pi is.

EASY AS A Pi Developed by Ivan Seneviratne

The History of Pi The importance of pi has been recognized for at least 4, 000 years. We know that the Egyptians and the Babylonians knew about the existence of the constant ratio pi, although they didn't know its value nearly as well as we do today. They had figured out that it was a little bigger than 3.

Discovering Pi 1. Draw two circles of different sizes. 2. Measure the circumference and the diameter of the two circles with a piece of string and ruler. 3. Write down the respective values in a table that has the 3 columns, distance around , distance across middle and mystery ratio. 4. Demonstrate that by dividing the circumference of an circle by its diameter you end up with pi. 5. Write your conclusions.

Archimedes' Approximation of Pi The first mathematician to calculate pi with reasonable accuracy was Archimedes. He wrote a book called “The Measurement of a Circle” around 250 B. C. stating that Pi is a number between 3 10/71 and 3 1/7. The method involves approximating pi by the perimeters of polygons of 12, 24, 48, and finally 96 sides inscribed and circumscribed about a given circle. Archimedes (287 -212 BC)

The Pi Symbol The modern symbol for pi was first used in “Our Modern Sense” in 1706 by William Jones, a Welsh mathematics teacher. Pi, the 16 th letter in the Greek alphabet, was chosen as the letter to represent the number 3. 141592. . . because the letter pi in Greek, pronounced like our letter 'p', stands for 'perimeter'. William Jones (1675– 1749)

Pi Piece of Pi In 1768, Johann Lambert proved that Pi is an Irrational number. It means that the digits never end or repeat in any known way. Today, The most decimal places to which pi has been calculated is 1, 241, 100, 000 (1. 2411 trillion digits) decimal places by Yasumasa Kanada and Yoshiaki Tamura of The university of Tokyo, Japan on 20 th October 2005 using a HITACHI SR 8000/MPP Super Computer. Johann Lambert (1728 -1777)

The Pi Pi is a name given to the ratio of the circumference of a circle to its diameter. For the sake of usefulness people often need to approximate pi. The fraction 22 / 7 is a well used number for Pi. When a circle's diameter is 1, its circumference is π. π = 3. 14…

The Many Uses of Pi ü Calculate circumference ü calculate the area of a circle ü The volume of a cylinder ü Describe the DNA double helix ü Calculate field strength ü Calculation of time period in Simple Harmonic Motion ü Determining the distribution of primes ü Analyzing the ripples on water ü In Cryptography

Acknowledgments q Images www. acceleratingfuture. com www. maths. manchester. ac. uk www. mathematik. de www. daviddarling. info/encyclopedia This presentation is developed by Ivan Seneviratne © 2007 purely for personal use. ivanthexplorer@yahoo. co. uk