Newton s Approximation of Pi. By: Sarah Riffe and Jen Watt
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1 Newton s Approimation of Pi By: Sarah Riffe and Jen Watt
2 Outline Who was Isaac Newton? What was his life like? What is the history of Pi? What was Newton s approimation of Pi?
3 History of Isaac Newton 7 th Century Shift of progress in math relative freedom of thought in Northern Europe
4 The Life of Newton Born: Christmas day 64 Died: 77 Raised by grandmother
5 66 Newton s Education Began at Trinity College of Cambridge University 660 Charles II became King of England Suspicion and hostility towards Cambridge
6 Newton, the young man single minded Would not eat or sleep over an intriguing problem Puritan Book of sins
7 664 Newton s Studies Promoted to scholar at Trinity Plague Newton s most productive years
8 Newton s Discoveries 665 Newton s generalized binomial theorem led to method of fluions 666 Inverse method of fluions Began observations of rotation of planets
9 668 Newton s Accomplishments Finished master s degree Elected fellow of Trinity College 669 Appointed Lucasian chair of mathematics
10 Newton s 704 Elected President of the Royal Society 705 Knighted by Queen Anne 77 Buried in Westminster Abbey
11 The History of Pi Archimedes classical method Using Polygons with inscribed And Circumscribed circles
12 Found Pi between 3/7 and /7 3.4
13 Important Dates of Pi 50 AD First notable value for Pi by Caludius Ptolemy of Aleandria Pi /0 3.46
14 480 AD TSU Ch ung-chih from China gave rational approimation Pi 355/ AD Hindu mathematician Aryabhata Pi 6,83/0,
15 50 AD Bhaskara Pi 3,97/50 Pi /7 Pi 754/
16 49 AD Al- Kashi Astronomer approimated Pi to 6 decimal places 579 AD Francois Viete from France Approimated Pi to 9 decimal places
17 585 AD Adriaen Anthoniszoon Rediscovered Chinese ratio 355/3 377/0> Pi > 333/ AD Adriaen Von Roomen Found Pi to the 5 th decimal place by classical method using polygons with ^30 th sides
18 60 AD Ludolph Van Ceulen of the Netherlands Pi ~ 30 decimal places Used polygons with sides 6 AD Willebrord Snell (Dutch) 6 Able to get Ceulen s 35 th decimal place by only side polygon 30
19 630 AD Grienberger Pi to 39 decimal places 67 James Gregory from Scotland obtained infinite series arctan ( )
20 699 AD Abraham Sharp Pi ~ 7 decimal places 706 AD John Machin Pi ~ 00 th decimal place
21 79 AD De Lagny of France Pi ~ decimal places 737 AD William Jones from England First to use Pi symbol for ratio of the circumference to the diameter
22 767 AD Johan Heinrich Lambert Showed Pi is irrational 794 AD Adrien-Marie Legendre Showed Pi-squared is irrational
23 84 AD William Rutherford Calculated Pi to 08 places 844 AD Zacharis Dase found Pi correct to 00 places using Gregory Series π arctan + arctan 5 + arctan 8
24 853 AD Rutherford returns Finds Pi to 400 decimal places 873 AD William Shanks from England Pi to 707 decimal places 88 AD F. Lindeman Shows Pi is transcendental
25 948 D.F. Ferguson of England Finds errors with Shanks value of Pi starting with the 58 th decimal place Gives correct value to the 70 th place J.W. Wrench Jr. Works with Ferguson to find 808 th place for Pi Used Machin s formula π 4 3arctan 4 + arctan 0 + arctan 985
26 949 AD Electronic computer The ENIAC Compute Pi to the,037 th decimal places 959 AD Fancois Genuys from Paris Compute Pi to 6,67 decimal places with IBM 704
27 96 AD Wrench and Shanks of Washington D.C. compute Pi to 00,65 th using IBM AD M. Jean Guilloud and co-workers attained approimation for Pi to 50,000 decimal places on a STRETCH computer
28 967 AD M. Jean Guilloud and coworkers found Pi to the 500,000 places on a CDC M. Jean Guilloud and coworkers found Pi to millionth place on CDC AD Kazunori Miyoshi and Kazuhika Nakayma of the University of Tsukuba Pi to million and 38 decimal places in hours on a FACOM M-00 computer
29 986 AD DH Bailey of NASA Ames Research Center ran a Cray- supercomputer for 8 hours Got Pi to 9,360,000 decimal places Yasamasa Kanada from University of Tokyo Used NEC SX- super computer to compute Pi to 34,7,700 decimal places
30 Purpose to Continue to Compute Pi See if digits of Pi start to repeat Possible normalcy of Pi Valuable in computer science for designing programs
31 Information Already known + ( y 0) or + + y 4 4
32 Solve for y ) ( ) ( / 9/ 7/ 5/ 3/ / / / / y
33 Area (ABD) by fluion / 3 / / 5 / / 7 / / / /......
34 , / 3 3 /
35 Area (ABD) by geometry BD ( ) ( ) ) ( BD BC DBC Area
36 4 3 3 ) ( 3 ) (sec π π π r semicircle Area tor Area
37 Area( ABD) Area(sector) Area( DBC) π π
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