The Life of Pi

1
The Life of Pi
By David Anderson, Kurtis Baum, Harry Chin, and
Zach Pepple
2
What is pi?

• No, pi is not a delicious treat or an infamous
  American movie, but a competition between
  mathematicians throughout history.
• Pi is, however, the ratio of the circumference of
  a circle to its diameter. Two major hurdles to
  overcome throughout history were pis
  irrationality and the lack of fundamental
  mathematical properties. Deciding if the number
  was constant was a problem perplexing scientists
  until 1789 and the development of trigonometry
  (and calculus) were paramount in the pursuit of
  the perfect, dare we say scrumptious, figure of
  pi.
• Irrational? Huh? Be rational!
• Pi is irrationalmeaning that it is an unending
  decimal, so it is never accurate when you hit
  that p button on your calculator.

3
Pre-heating the oven for Pi

• At first, the Bible attempted to decipher the
  numerical value of pi. There is a verse, Kings
  17 23, which states
• And he made a molten sea, ten cubits from the one
  brim to the other it was round all about, and
  his height was five cubits and a line of thirty
  cubits did compass it about.
• Thus the estimate of pi circumference 30
  3

diameter
10
Could you believe the Bible was wrong!?
4
The True Prevailing Views

• During the same time as the Biblical passage was
  written, the Egyptians (3.125) and Mesopotamians
  (3.162) had their own, more accurate values for
  pi.

5
The spark to later theory

• Archimedes began the never-ending race to pi.
  While he made no claim to the actual value of pi
  (the necessary trigonometry and decimal notation
  had not yet been invented) he used very difficult
  geometry that many others following him based
  their findings upon. It was impressive that he
  came to a number 3.1418 (error of .0002), but his
  math was flawedand so were many of his
  successors . The last to use his method found pi
  to 36 places (Van Ceulen).

Archimedes de Syracuse 287-212 B.C.
6
Trigonometry comes into play

• In 1701, John Machin used an improvement (by
  implementing trig) to find the value of pi to 100
  places. Many followed his calculations and
  continued them to find an even more exact figure
  of pi.

John Machin 1680-1751
7
Trivial pisuit?

• In 1768 Johann Lambert proved that pi cannot be
  rational through trigonometry (tanx or ex cant
  be rational).
• That set off an urge in William Shanks to find as
  many places as possiblehe found 707 of them.

22/7
8
Not So Fast!

• Augustus De Morgan discovered that Shanks 707
  places had a mysterious shortage of 7s. And in
  1945, it was proven by D.F Ferguson that Shanks
  made an error in his calculations after his 527th
  place. Ferguson then went on to be the last
  person to evaluate pi before the dawn of
  calculators (620 places). Subsequently, he was
  the first to use the desk calculator to find
  pi710 places.

707! Ha! Try 620 the hard way!
707
9
Calculator Wizards of the WorldUNITE!!!

• 3.141592653589793238462643383279502884197169399375
  10582097494459230781640628620899862803482534211706
  79821480865132823066470938446095505822317253594081
  28481117450284102701938521105559644622948954930381
  96442881097566593344612847564823378678316527120190
  91456485669234603486104543266482133936072602491412
  73724587006606315588174881520920962829254091715364
  36789259036001133053054882046652138414695194151160
  94330572703657595919530921861173819326117931051185
  48074462379962749567351885752724891227938183011949
  12983367336244065664308602139494639522473719070217
  98609437027705392171762931767523846748184676694051
  32000568127145263560827785771342757789609173637178
  72146844090122495343014654958537105079227968925892
  35420199561121290219608640344181598136297747713099
  60518707211349999998372978049951059731732816096318
  59502445945534690830264252230825334468503526193118
  81710100031378387528865875332083814206171776691473
  03598253490428755468731159562863882353787593751957
  78185778053217122680661300192787661119590921642019
  89380952572010654858632788659361533818279682303019
  52035301852968995773622599413891249721775283479131
  51557485724245415069595082953311686172785588907509
  83817546374649393192550604009277016711390098488240
  12858361603563707660104710181942955596198946767837
  44944825537977472684710404753464620804668425906949
  12933136770289891521047521620569660240580381501935
  11253382430035587640247496473263914199272604269922
  79678235478163600934172164121992458631503028618297
  45557067498385054945885869269956909272107975093029
  55321165344987202755960236480665499119881834797753
  56636980742654252786255181841757467289097777279380
  00816470600161452491921732172147723501414419735685
  48161361157352552133475741849468438523323907394143
  33454776241686251898356948556209921922218427255025
  42568876717904946016534668049886272327917860857843
  83827967976681454100953883786360950680064225125205
  11739298489608412848862694560424196528502221066118
  63067442786220391949450471237137869609563643719172
  87467764657573962413890865832645995813390478027590
  10

• The Age of Calculators and Computers continue to
  find a more exact value of pias we speak! The
  last recorded, most accurate figure of pi is by
  Takahashi Kanada on his Hitachi SR8000 a
  whopping 206158430000 places!
• FYI- Your TI-83 p button only rounds to the 9th
  decimal place!

Pi to 2000 decimal places
10
Thanks for your Time!...

• but this pis never going to be done!

Pi just keeps going and going