What I Spi

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What I Spi

  1. 1. All About Pi Created by Jan Abernethy March 2006
  2. 2. What is Pi? <ul><li>Pi is defined as the ratio of the circumference to the diameter of a circle </li></ul><ul><li>Pi is usually denoted with this greek symbol: </li></ul><ul><li>π </li></ul>π = circumference diameter
  3. 3. What is the “Value” of Pi? <ul><li>Pi is an irrational number – its decimals repeat forever </li></ul><ul><li>Mathematicians estimate digits of pi to use it in real world settings. Click here to find digits of pi. </li></ul><ul><li>Pi is usually rounded off to about 3.1415 </li></ul>3.141592551104866223558431126381048812355898112276391048823661691 12648104891237105711355110577023712221136511058672371277113652105 86823713861136671058762371496113682105891237171611369410589123723 75113696105806987498576984769847609873409867439857694387569803475 28937465283974658927364587923645897236458723645987236859742365298 76458726345897623897465283746587293465897236458726458972436952384 92322547392938475623987562897465298376598726549872365987236598726 87968197871987261987618719876187632198716239874168971236489761238 97641238976143298761911010101032178648764387263874687638763286234 23189432943213458745984753489760975645784326574365743256743657432 65743256743265743276543265743265743268743268743268743268732468742 38763468727364872364872634872634876238476287346872164872648726348 71623487216348762138746218764318726348712634876123876482173647126 34872163487621387462873647213648271364872136487126348726487126387 62487263847623876418276348716234871623874682734687126348721634872 61873461287364871263487126348761238746128736418732648712648754354 39875438935409453809543805349854309854309801010101029389813287243 87634287643287648723648762384762387462873648726348726348726348726
  4. 4. History of Pi <ul><li>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. </li></ul>
  5. 5. Who Discovered Pi? <ul><li>Archimedes was the first to theoretically approximate pi </li></ul><ul><li>He calculated that pi was “trapped” between 223 / 71 and 22 / 7 , or roughly 3.1428 </li></ul><ul><li>Today we use better approximations, most of which are derived by computers </li></ul>Hi, I’m Archimedes… Pi = Between 223/71 and 22/7
  6. 6. The Death of Archimedes <ul><li>Archimedes was born in 287 BC in a Greek state called Syracuse, Sicily. </li></ul><ul><li>The city of Syracuse was taken over by the Romans and Archimedes was killed. </li></ul><ul><li>It is said that he was busy drawing circles in the dust and writing mathematical equations at the time of his death </li></ul>THAT’S HOW IMPORTANT PI WAS TO ARCHIMEDES!!!!!
  7. 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. 8. The Usefulness of Pi <ul><li>Pi is extremely useful in calculating the area and circumference of a sphere: A = πr 2 and C = 2πr. </li></ul><ul><li>Many disciplines of science use π in their equations to describe the world </li></ul><ul><li>In fact DNA, rainbows, the human eye, music, color, and ripples all have some natural roots in pi. </li></ul>
  9. 9. Let's review some DEFINITIONS
  10. 10. Diameter and Radius <ul><li>The distance across a circle through its center is called its diameter, D . </li></ul><ul><li>The radius, R of a circle is the distance from the center of a circle to a point on the edge of the circle. </li></ul><ul><li>So a circle's diameter is twice as long as its radius: D = 2 × R . </li></ul>diameter, D radius, R
  11. 11. radius
  12. 12. diameter
  13. 13. C i r c u m f e r e n c e <ul><li>The distance around a circle is its circumference </li></ul>
  14. 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. 15. <ul><li>The space inside a circle is called the Area </li></ul>area, A
  16. 16. I drew polygons of more than 90 sides! Take it from me… the area of a circle is π r 2
  17. 17. APPROXIMATELY The symbol means When speaking of pi we always use Example: π 3.14 ~ = ~ = ~ =
  18. 18. LET’S REVIEW THE FORMULAS! π = circumference diameter
  19. 19. SOME NAMES FOR PI 3.14 22 7 ___ pi π Hope you enjoyed learning about Pi!!! ~ = ~ =

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