The document discusses the history and properties of the mathematical constant pi (π). It covers: - Pi is the ratio of a circle's circumference to its diameter. - Pi is an irrational number that repeats endlessly. Early cultures estimated pi to around 3 or 3.14. Archimedes first approximated it as between 223/71 and 22/7. - Pi is useful for calculating the circumference and area of circles. Many fields of science rely on pi in their equations.

1. All About Pi Created by Jan Abernethy March 2006

2. What is Pi? Pi is defined as the ratio of the circumference to the diameter of a circle Pi is usually denoted with this greek symbol: π π = circumference diameter

3. What is the “Value” of Pi? Pi is an irrational number – its decimals repeat forever Mathematicians estimate digits of pi to use it in real world settings. Click here to find digits of pi. Pi is usually rounded off to about 3.1415 3.141592551104866223558431126381048812355898112276391048823661691 12648104891237105711355110577023712221136511058672371277113652105 86823713861136671058762371496113682105891237171611369410589123723 75113696105806987498576984769847609873409867439857694387569803475 28937465283974658927364587923645897236458723645987236859742365298 76458726345897623897465283746587293465897236458726458972436952384 92322547392938475623987562897465298376598726549872365987236598726 87968197871987261987618719876187632198716239874168971236489761238 97641238976143298761911010101032178648764387263874687638763286234 23189432943213458745984753489760975645784326574365743256743657432 65743256743265743276543265743265743268743268743268743268732468742 38763468727364872364872634872634876238476287346872164872648726348 71623487216348762138746218764318726348712634876123876482173647126 34872163487621387462873647213648271364872136487126348726487126387 62487263847623876418276348716234871623874682734687126348721634872 61873461287364871263487126348761238746128736418732648712648754354 39875438935409453809543805349854309854309801010101029389813287243 87634287643287648723648762384762387462873648726348726348726348726

4. History of Pi The hunt for pi began in Egypt and in Babylon about two thousand years before Christ. The Egyptians obtained the value (4/3) 4 and the Babylonians the value 3 1/8 for pi. About the same time, the Indians used the square root of 10 for pi. These approximations to pi had an error only as from the second decimal place.

5. Who Discovered Pi? Archimedes was the first to theoretically approximate pi He calculated that pi was “trapped” between 223 / 71 and 22 / 7 , or roughly 3.1428 Today we use better approximations, most of which are derived by computers Hi, I’m Archimedes… Pi = Between 223/71 and 22/7

6. The Death of Archimedes Archimedes was born in 287 BC in a Greek state called Syracuse, Sicily. The city of Syracuse was taken over by the Romans and Archimedes was killed. It is said that he was busy drawing circles in the dust and writing mathematical equations at the time of his death THAT’S HOW IMPORTANT PI WAS TO ARCHIMEDES!!!!!

7. Currently the value of pi is known to 6.4 billion places ! 3.14128… 22/7 250 BC Archimedes Equivalence Discovery When? Who? 3.1415926535… Pi Today Computers 3.16227766... square root of 10 2000 BC Indians 3.125 3 1/8 2000 BC Babylonians 3.160493827... (4/3) 4 2000 BC Egyptians THE DISCOVERY OF PI

8. The Usefulness of Pi Pi is extremely useful in calculating the area and circumference of a sphere: A = πr 2 and C = 2πr. Many disciplines of science use π in their equations to describe the world In fact DNA, rainbows, the human eye, music, color, and ripples all have some natural roots in pi.

9. Let's review some DEFINITIONS

10. Diameter and Radius The distance across a circle through its center is called its diameter, D . The radius, R of a circle is the distance from the center of a circle to a point on the edge of the circle. So a circle's diameter is twice as long as its radius: D = 2 × R . diameter, D radius, R

11. radius

12. diameter

13. C i r c u m f e r e n c e The distance around a circle is its circumference

14. π = Pi = circumference divided by diameter Every time you use these formulas, you will come up with 3.14159265… π = circumference diameter circumference 2 x radius

15. The space inside a circle is called the Area area, A

16. I drew polygons of more than 90 sides! Take it from me… the area of a circle is π r 2

17. APPROXIMATELY The symbol means When speaking of pi we always use Example: π 3.14 ~ = ~ = ~ =

18. LET’S REVIEW THE FORMULAS! π = circumference diameter

19. SOME NAMES FOR PI 3.14 22 7 ___ pi π Hope you enjoyed learning about Pi!!! ~ = ~ =