People have calculated billions of digits of pi because of the human desire to do something thats ne

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• People have calculated billions of digits of pi
  because of the human desire to do something
  thats never been done before. When George
  Mallory was asked why he wanted to climb Mt.
  Everest, he replied, Because its there. Well,
  pi is certainly here. Like the outer planets,
  its built into the fabric of our physical
  universe and it will always be explored. -
  The Story of Pi, Cal.Tech.

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What is pi?

• The ratio of the circumference to the diameter of
  ANY circle is constant. It is between 3 and
  . It is close to but NOT EQUAL to 3.14 or
  .

Its digits will NEVER terminate or repeat
(proved in 1766)
...but will ALWAYS continue to fascinate
mankind.
See Peel Circle for pi PPT.gsp
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Irrational Transcendental

• IRRATIONAL
• Cannot be expressed as the quotient of 2
  integers
• This also means it cannot be written as a
  decimal for it will never terminate or repeat.
  (speculated early proved 1767)

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Our Pi String 1998-2002

• Each student adds beads to it on -Day.

3.1415926535 8979323846 2643383279 5028841971
6939937510
5820974944 5923078164 0628620899 8628034825
3421170679 (100) 8214808651 3282306647
0938446095 5058223172 5359408128 4811174502
8410270193 8521105559 6446229489 5493038196
(200) 4428810975 6659334461 2847564823
3786783165 2712019091 4564856692 3460348610
4543266482 1339360726 0249141273 (300)
7245870066 0631558817 4881520920 9628292540
9171536436 7892590360 0113305305 4882046652
1384146951 9415116094 (400) 3305727036
5759591953 0921861173 8193261179 3105118548
0744623799 6274956735 1885752724 8912279381
8301194912 (500) 9833673362 4406566430
8602139494 6395224737 1907021798 6094370277
0539217176 2931767523 8467481846 7669405132
(600) 0005681271 4526356082 7785771342
7577896091 7363717872 1468440901 2249534301
4654958537 1050792279 6892589235 (700)
4201995611 2129021960 8640344181 5981362977
4771309960 5187072113 4999999837 2978049951
0597317328 1609631859 (800) 5024459455
3469083026 4252230825 3344685035 2619311881
7101000313 7838752886 5875332083 8142061717
7669147303 (900) 5982534904 2875546873
1159562863 8823537875 9375195778 1857780532
1712268066 1300192787 6611195909 2164201989...
(1000)
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Where Can we find pi?

• IN EVERYTHING CIRCULAR (of course)

(See torus.gsp)
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WHERE ELSE?

• Area under bell (Gaussian) curve
  Carl Gauss, prince of mathematics
• Electricity - formulas for alternating currents
  and radiation from radio TV antennas

1777-1855
German
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Connections to integers
(Leibniz)
(John Wallis 1655)
(Leonard Euler)
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Earliest Known Record of Picirca 1650 BC
No number has captured the attention and
imaginations of people throughout the ages as
much as the ratio of a circles circumference to
its diameter.

• On the Rhind Papyrus,
• Egyptian scribe, Ahmes,
• wrote this ratio as
• 4 times the square of eight-ninths

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More Attempts to rationalize (all prior to Arabic
numerals and decimals)
Babylonians, same time as Egyptian Rhind Papyrus,
1650 BC
Ptolemy (Alexandria, Egypt) 150 AD Also used by
Columbus on his voyage to the New World
Archimedes (Syracuse, 287-212 BC) Found pi to be
between these two fractions. This average error
is only 0.0002!
Tsu Chung Chi China, 450 AD
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Archimedes, 250 BC
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Interesting digits

• Starting at digit 772 - 9999998 occurs
• Starting at digit 509,400 - 112552 occurs
• Starting at digit 1,286,368 - 980-7280 occurs
• In 1st million, no 123456 but 012345 twice
• 357 358 359 360 361 362 363
• 9 0 3 6 0
  0 1

largest 7-digit sum in the first million digits!
A special date - can you guess it?
A special telephone number - do you know it?
123456789 first appears at 523,551,502nd digit
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Cant get enough pi digits
Circa 1600 - decimal fractions logarithms
invented

• 1596 Ludolph van Ceulen (Dutch) calculates 35
  digits
• 1706 John Machin calculates 100 digits
• 1874 William Shanks calculates 707 digits
• 1947 Ferguson (using desk calculator) finds 808
  digits
• 1949 ENIAC computer (DoD U. of Pen.) finds
  2037 digits
• 1973 CDC 7600 (Paris) finds 1,000,000 digits
  (23 hrs)
• 1989 1,000,000,000 digits (USSR Chudnovsky
  brothers, NY)
• 1999 Hitachi SR8000 (Tokyo) 206,158,430,000
  digits (37 hrs)

All by hand - months
But Ferguson finds error in 527th onward
used Gauss-Legendre algorithm
Why still do this? to find out more about pi
to test computer
architecture efficiency ... to test software
for accuracy and speed
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-TV

• STAR TREK (1 min.)
• STARGATE (4 min.)

From the original series, 1967 - episode 36
Wolf in the Fold. The main computer of the
Starship Enterprise is possessed by an evil alien
entity. Kirk, Spock and the gang have a plan to
send the entity into deep space but must first
find a way to keep the computer busy so it
doesnt detect their plan.
Courtesy of Randy Coombs (3/00) The main
characters are trying to uncover a secret hidden
by a mysterious puzzle. The legend is that the
ancient Norse god, Thor, created the puzzle so
that when mankind developed enough to solve the
puzzle, we would be ready for the secret behind
it!
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More misc. pi facts
German 1879-1955

• Albert Einstein
• born 3 / 14 / 1879 (Pi-Day)
• Symbol introduced by Leonard Euler, 1737
• Waclaw Sierpinski born March 14, 1882 in Warsaw
  Poland famous for his fractal creation.

Although used first by William Jones in 1706
(short for periphery), he did not have the
weight to make it popular. Once the renowned
Euler (Oiler) picked it up (previously using
p or c) it became the standard.
Swiss 1707-1783
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More misc. pi facts

• To find the circumference of a circle the size of
  the known universe, accurate to within the radius
  of one proton, how many decimal places of pi
  would be needed? only 39!
• Consider the following series of integers, each
  using one more digit of pi 3, 31, 314, 3141,
  31415, 314159, 3141592, etc. Out of the first
  1000 numbers in this series, only 4 are prime!
• The world record for pi-recitation (from memory)
  is held by Hiroyuki Gotu, age 21. (Seattle
  Times 2-26-1995)
• 9 hours ... 42,000 digits!

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Pi In print

• Bible - I Kings vii.23 (Solomons Temple)
• Jules Verne - 20,000 Leagues Under the Sea
• A 1970 advertisement -

And he made a molten sea, 10 cubits from brim to
brim, round in compass ... and a line of 30
cubits did compass it round about. (cubit
dist. from elbow to tip of fingers) Large brass
casting in Solomons Temple
The Nautilus was stationary, floating near a
mountain which formed a sort of quay(lake)
imprisoned by a circle of walls, measuring 2
miles in diameter and 6 in circumference
CADAEIB
F
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Pi Song

• To the tune of
• O Christmas Tree

Oh, number PiOh, number PiYour digits are
unending,Oh, number PiOh, number PiNo pattern
are you sending.You're three point one four one
five nine,And even more if we had time,Oh,
number PiOh, number PiFor circle lengths
unbending.
http//www.winternet.com/mchristi/piday.html
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pi scent
Cologne by Givenchy
This was their 1999 advertisement at
http//www.givenchy.com/givenchy/givenchy.html

• The Inspiration
• The answer lay in the quest itself. From the
  exploration of new territories to the conquest of
  space, men have always endeavored to push back
  the frontiers of the known world and reveal the
  mysteries of the unknown. Mans essential
  character lies in his strength and determination
  in pushing back his limits.
• The Name
• Resonant with history and mystery, is a
  link between past, present and future. Pi is the
  universal number, the transcendental number, the
  ruling number. Since Archimedes discovery of
  , more than 2000 years ago, has been the
  object of a ceaseless quest. This letter of the
  Greek alphabet is used in mathematics to express
  the constant ratio of the circumference of a
  circle to its diameter. Today man is still
  seeking to establish s unlimited decimals.
• The Bottle
• Designed by Serge Mansau for Givenchy, the
  bottle is a study in purity. Its two sculpted
  backs, with their irregular density, modulate the
  amber tones of the fragrance. The bottles
  broad, full base gives it a masculine foundation
  and allure. To complete this construction, an
  innovative closing system crowns the bottle. The
  curved shape of the cap, in bronze-colored metal,
  symbolically evokes the name.

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Pi mnemonics
A mnemonic is a verse to assist memory
Count the letters in each word!
May I have a large container of coffee? (8)
How I want a drink, alcoholic of course, after
the heavy lectures involving quantum mechanics.
All of thy geometry, Herr Planck, is fairly hard
(24)
Que jaime à faire apprendre un nombre utile aux
sages! Immortel Archimède, artisite ingénieur,
(31) Qui de ton jugement peut priser la
valeur? Pour moi, ton problème eut de pareils
avantages.
Sir, I send a rhyme excelling In sacred truth and
rigid spelling. Numerical sprites elucidate For
me the lexicon's dull weight. (21)
Dir, o Held, o alter Philosoph, du
Riesengenie! Wie viele Tausendre bewundern
Geister Himmlisch wie du und göttlich! Noch
reiner in Aeonen Wird das uns strahlen Wie im
lichten Morgenrot! (30)
Sol y Luna y Mundo proclaman al Eterno Autor del
Cosmo. (11)
Wie? O! Dies
(24) Mach ernstlich so vielen viele
Müh! Lernt immerhin, Jünglinge, leichte
Verselein, Wie so zum Beispiel dies dürfte zu
merken sein!
Yes. I know a great geometric pi number which
Mrs Weeks geometry classroom studies carefully
out at the Campbell Hall School. (21)
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CAN YOU FIND 402 digits of PI ?
Circle Digits By Michael Keith

• For a time I stood pondering on
• circle sizes. The large computer mainframe
  quietly processed
• all of its assembly code. Inside my entire hope
  lay for figuring out an elusive expansion
• value pi. Decimals expected soon. I nervously
  entered a format procedure. The mainframe
  processed
• the request. Error. I, again entering it,
  carefully retyped. This iteration gave zero
  error printouts in all - success.
• Intently I waited. Soon, roused by thoughts
  within me, appeared narrative mnemonics relating
  digit to verbiage! The idea
• appeared to exist but only in abbreviated fashion
  - little phrases typically. Pressing on I then
  resolved, deciding firmly about a
• sum of decimals to use - likely around four
  hundred, presuming the computer code soon halted!
  Pondering these ideas, words
• appealed to me. But a problem of zeros did exist.
  Pondering more, solution subsequently appeared.
  Zero suggests a punctuation
• element. Very novel! My thoughts were culminated.
  No, periods, I concluded. All residual marks of
  punctuation - zeros. First digit
• expansion answer then came before me. On
  examining some problems unhappily arose. That
  imbecillic bug! The printout I possessed
• showed four nine as foremost decimals. Manifestly
  troubling. Totally every number looked wrong.
  Repairing the bug took much effort.
• A pi mnemonic with letters truly seemed good.
  Counting of all the letters probably should
  suffice. Reaching for a record would be
• be helpful. Consequently, I continued, expecting
  a good final answer from computer. First number
  slowly displayed on the flat
• screen - 3. Good. Trailing digits apparently
  were right also. Now my memory scheme must
  probably be implementable. The
• technique was chosen, elegant in scheme by self
  reference a tale mnemonically helpful was
  assured. An able title suddenly
• existed - Circle Digits. Taking pen I began.
  Words emanated uneasily. I desired more
  synonyms. Speedily I found
• my (alongside me) Thesaurus. Rogets is probably
  an essential in doing this, instantly I decided.
  I wrote and
• erased more. The Rogets clearly assisted
  immensely. My story proceeded (how lovely!)
  faultlessly.

360 words - ignore periods other punctuation 0
words gt 9 letters 2 digits word for no. digit
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Interesting web sites
Joy of Pi www.joyofpi.com Friends of Pi
Club http//www.astro.univie.ac.at/wasi/PI/pi_cl
ub.html Search Digits in Pi http//www.angio.net/
pi/piquery The Pi Trivia Game http//eveander.com/
trivia/ The Pi Project ? http//rene.ma.utexas.e
du/users/tyilk/PiProj/Index.htm Brief History of
Pi ? http//rene.ma.utexas.edu/users/tyilk/PiProj
/PiHistory.htm Recite Digits in
Languages http//www.cecm.sfu.ca/pi/yapPing.html L
isten to Pi on Polyphon http//home.t-online.de/ho
me/HAEL.YGGS/polyphon.htm Pi Day
Songs http//www.winternet.com/mchristi/piday.ht
ml At the Exploratorium http//www.exploratorium.e
du/learning_studio/pi