The history of pi

The school level project. Hope this helps!!

1. The History of PI Mathematics Project

2. Team Members…

3. What is pi?? A number can be placed into several categories based on its properties. Is it prime or composite? Is it imaginary or real? Is it transcendental or algebraic? These questions help define a number's behaviour in different situations. In order to understand where π fits in to the world of mathematics, one must understand several of its properties: π is irrational and π is transcendental. Another important concept to understand is that of how π is calculated and how the methods have changed over time. π is:- "1: the 16th letter of the Greek alphabet... 2 a: the symbol pi denoting the ratio of the circumference of a circle to its diameter b: the ratio itself: a transcendental number having a value to eight decimal places of 3.14159265"

4. As said in the beginning, “There is more to Pi than meets the eye The computation of Pi to 10,000 places may be of no direct scientific usefulness. However, its usefulness in training personnel to use computers and to test such machines appears to be extremely important. Thus the mysterious and wonderful Pi is reduced to a gargle that helps computing machines clear their throats .

5. Pi history The early Babylonians and Hebrews used “3”as a value for Pi. Later, Ahmed, an Egyptian found the area of a circle . Down through the ages, countless people have puzzled over this same question, “What is Pi? The Greeks found Pi to be related to cones, ellipses, cylinders and other geometric figures.

6. Some people became famous by discovering ways to calculate Pi LEIBNITZ (1671) Pi= 4(1/1-1/3+1/5-1/7+1/9-1/11+1/13+...) WALLIS Pi= 2(2/1*2/3*4/3*4/5*6/5*6/7*...) MACHIN (1706) Pi=16(1/5- 1/(3+5^3) +1/(5+5^5) -1/(7+5^7)+...) x - 4(1/239 -1/(3*239^3) + 1/(5*239^5)-...) SHARP (1717) Pi= 2*Sq.Rt(3)(1-1/3*3 + 1/5*3^2 - 1/7*3^5...) EULER (1736) Pi= Sq.Rt(6(1+1/1^2+1/2^2+ 1/3^2...)) BOUNCKER Pi= 4 --- 1+1 --- 2+9 --- 2+25 +...

7. Approximations of Pi Philosopher Date Approximation Ptolemy around 150 A.D. 3.1416 Zu Chongzhi 430-501 AD. 355/113 al-Khwarizmi around 800 A.D. 3.1416 al-Kashi around 1430 A.D. 3.14159265358979 Viète 1540–1603 3.141592654 Roomen 1561–1615 3.14159265358979323 Van Ceulen around 1600 A.D. 3.14159265358979323846264338327950288

8. Pi in everyday life We use it for Drawing, machining, plans, planes, buildings, bridges, geometry problems, radio, TV, radar, telephones, estimation, testing, simulation, global paths, global positioning, space science, orbit calculation, Space ships, satellites, Speedometers at vehicles… etc. Pi is used by every career whether you are a electrical engineer, statistician, biochemist, or physicist. Pi is indeed a necessity for life .

9. Pi facts ”Pi Day” is celebrated on March 14. The official celebration begins at 1:59 p.m. to make an appropriate 3.14159 when combined with the date. Albert Einstein was born on Pi Day (14/3/1879) in Ulm Wurttemberg, Germany. Pi goes on for ever Decimals have no pattern and don’t repeat .

10. This animation demonstrates the idea of Pi

11. Digit dancing The development of high speed electronic computing equipment provided a means for rapid computation. Inquiries regarding the number of Pi’s digits -- not what the numbers were individually, but how they behave statistically -- provided the motive for additional research.

12. Where can you find mathematical PI? The early Babylonians and Hebrews used three as a value for Pi. Later, Ahmes, an Egyptian found the area of a circle . Down through the ages, countless people have puzzled over this same question, “What is Pi?" From 287 - 212B.C. there lived Archimedes, who inscribed in a circle and circumscribed about a circle, regular polygons. The Greeks found Pi to be related to cones, ellipses, cylinders and other geometric figures.

13. It’s curious how certain topics in mathematics show up over and over. In the late 1940's two new mathematical streams (electronic computing and statistics) put Pi on the table again. Anyone for Pi?

14. Pi Day is an unofficial holiday commemorating the mathematical constant π (pi). Pi Day is observed on March 14 (or 3/14 in month/day date format), since 3, 1 and 4 are the three most significant digits of π in the decimal form. In 2009, the United States House of Representatives supported the designation of Pi Day . Pi Approximation Day is observed on July 22 (or 22/7 in day/month date format), since the fraction 22 ⁄ 7 is a common approximation of π . Pi DAY

15. Date abstractions from π Pi Day is observed on March 14 because of the date's representation as 3/14 in month/day date format. This representation adheres to the commonly used approximation of 3.14 for π. The fractional approximation of π, 22 ⁄ 7 , resembles the date July 22 in the day/month format, where it is written 22/7. Pi Approximation Day is therefore observed on July 22 . Pi Pie at Delft University

16. 22/7 exceeds π Proofs of the famous mathematical result that the rational number 22/7 is greater than π (pi) date back to antiquity. 22/7 is a widely used Diophantine approximation   of π(the approximation of real numbers by rational numbers). It is a convergent in the simple continued fraction expansion of π. It is greater than π, as can be readily seen in the decimal expansions of these values: The approximation has been known since antiquity. Archimedes wrote the first known proof that 22/7 is an overestimate in the 3rd century BCE, although he may not have been the first to use that approximation. His proof proceeds by showing that 22/7 is greater than the ratio of the perimeter of a circumscribed regular polygon with 96 sides to the diameter of the circle. Another rational approximation of π that is far more accurate is 355/113.

17. When mathematicians are faced with quantities which are hard to compute, they try, at least, to pin them between two other quantities which they can compute. The Greeks were not able to find any fraction for Pi. Today we know that Pi is NOT a rational number and cannot be expressed as a fraction. Pi is everywhere

18. The History of Pi

19. The search for PI

20. The End!