A Warm Slice of Pi

By:

Michael Gross

Majeed Mogharreban

Anjan Tibrewala

Daniel Raino

Definition

• Pi is the constant ratio of the circumference to the diameter of a circle

History of π

• Bible – ratio = 3• In the Egyptian Rhind Papyrus, which is

dated about 1650 BC, there is good evidence for 4(8/9)2 = 3.16 as a value for π

• The first theoretical calculation seems to have been carried out by Archimedes of Syracuse (287-212 BC). He obtained the approximation 223/71 < π < 22/7.

Chronology

Rhind papyrus 2000 BC 1 3.16045 (= 4(8/9)2)Archimedes 250 BC 3 3.1418 (average of the bounds)

Vitruvius 20 BC 1 3.125 (= 25/8)Chang Hong 130 1 3.1622 (= 10 1̂/2)

Ptolemy 150 3 3.14166Wang Fan 250 1 3.155555 (=142/45)

Liu Hui 263 5 3.14159Tsu Ch'ung Chi 480 7 3.141592920 (= 355/113)

Aryabhata 499 4 3.1416 (=62832/2000)Brahmagupta 640 1 3.1622 (= 10 1̂/2)Al-Khwarizmi 800 4 3.1416

Fibonacci 1220 3 3.141818Madhava 1400 11 3.141592654Al-Kashi 1430 14 3.141592654

CommentsMathematician Date Places

Otho 1573 6 3.1415929Viète 1593 9 3.141592654

Romanus 1593 15 3.141592654Van Ceulen 1596 20 3.141592654Van Ceulen 1596 35 3.141592654

Newton 1665 16 3.141592654Sharp 1699 71

Seki Kowa 1700 10Kamata 1730 25Machin 1706 100

De Lagny 1719 127 Only 112 correctTakebe 1723 41

Matsunaga 1739 50von Vega 1794 140 Only 136 correctRutherford 1824 208 Only 152 correct

Strassnitzky, Dase 1844 200

Clausen 1847 248Lehmann 1853 261Rutherford 1853 440Shanks 1874 707 Only 527 correct

Ferguson 1946 620

Mathematician Date Places Comments

Pi Record

• Yasumaga Kaneda got 536,870,000 digits in August 1989. It took 67 hours and 13 minutes on a Japanese supercomputer.

Applications

• Area of circles

• Volume of spheres

• Cylinders

• Cones

• Round stuff

• Slicing pie

• Ice cream!

Calculation Collaboration

Formulasxtan(180/x) = π

x[rcos(180/x)rsin(180/x)] = π r^2

lim

limX->

X->

Bibliography

• “History of Pi.” http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Pi_through_the_ages.html

• “Chronology of Pi.” http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Pi_chronology.html

• Pappas, Theoni. More Joy of Mathematics. © 1991 Wide World Publishing. San Carlos, CA.

• J.J.’s Picture Archive. ©2002 Carbondale, IL.

The End