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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.
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
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)
Cannot be expressed as a root of an algebraic equation with finite terms, rational coefficients - transcends algebra (first speculated by Euler 1748, proved by Lindemann 1882)
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 10507922796892589235 (700)4201995611 21290219608640344181 5981362977 47713099605187072113 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)
Each student adds beads to it on -Day.
IN EVERYTHING CIRCULAR (of course)
P (2 integers have no common factors) =
P (lattice pt. is visible from origin) =
P (needle lands on line) =
(John Wallis 1655)
can be used to find decimal digits of pi
Leibniz - 1st infinite series for pi
Newton - converges quicker
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
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
Srinivasa Ramanujan (India, 1887-1920)
(This is an irrational approximation.)
1767 - Johann Lambert proved irrational
1794 - Adrien-Marie Legendre proved irrational
1840 - Joseph Liouville proved transcendental nos. exist(used limits of continued fractions)
1873 - Charles Hermite provede transcendental
1882 - Ferdinand Lindemann proved transcendental
largest 7-digit sum in the first million digits!
9 0 3 6 0 0 1
A special date - can you guess it?
A special telephone number - do you know it?
123456789 first appears at 523,551,502nd digit
Circa 1600 - decimal fractions & logarithms invented
All by hand - months
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)
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
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.
STAR TREK (1 min.)
STARGATE (4 min.)
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!
born 3 / 14 / 1879 (Pi-Day)
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.
9 hours ... 42,000 digits!
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
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.
To the tune of
O Christmas Tree
Cologne by Givenchy
This was their 1999 advertisement at http://www.givenchy.com/givenchy/givenchy.html
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.
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.
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.
A mnemonic is a verse to assist memory
Count the letters in each word!
May I have a large container of coffee? (8)
Que jaime faire apprendre un nombre utile aux sages!
Immortel Archimde, artisite ingnieur, (31)
Qui de ton jugement peut priser la valeur?
Pour moi, ton problme 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 gttlich!
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 Mh!
Lernt immerhin, Jnglinge, leichte Verselein,
Wie so zum Beispiel dies drfte zu merken sein!
Yes. I know a great geometric pi number which Newhouses geometry classroom studies carefully out at the Port Charlotte High School. (21)
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.
The end, above all, would soon joyfully overtake. So, this memory helper story I
incontestably complete. Soon I will locate publisher. There a narrative will
I trust immediately appear, producing fame.
360 words - ignore periods other punctuation = 0 words > 9 letters = 2 digits word for no. = digit
Fools Rush In
A bill for an act introducing a new mathematical truth and offered as a contribution to education to be used only by the State of Indiana, free of cost by paying any royalties whatever on the same, provided it is accepted and adopted.
...It has been found that the circular area is to the quadrant of the circumference,as the area of an equilateral rectangle is to the square on one side. The diameter employed as the linear unit according to the present rule in computing the circles area is entirely wrong (This makes no sense if meant to be eq. tri, then here!)
Furthermore, it has revealed the ratio of the chord and arc of 90o as 7:8, and the ratio of the diagonal and one side of a square as 10:7, and the ratio of the diameter and circumference is 5/4:4(so now )
In further proof of the value of the authors proposed contribution to education and State of Indiana (claims the Dr. solved other classic unsolvable problems). [sq. circle] (These ancient problems have been proven to be unsolvable.) [trisect angle]
Author of Bill - Edwin J. Goodman, M.D. of Indiana - Introduced Jan. 18, 1897
Feb. 5 - House votes 67 to 0 in favor; bill forwarded to the Senate
Feb. 10 - Pf. Waldo (Purdue, checking school grant) overhears; coaches Senate
Feb. 12 - Senate votes to postpone further consideration of this bill
Joy of Piwww.joyofpi.com
Friends of Pi Clubhttp://www.astro.univie.ac.at/~wasi/PI/pi_club.html
Search Digits in Pihttp://www.angio.net/pi/piquery
The Pi Trivia Gamehttp://eveander.com/trivia/
The Pi Project ?http://rene.ma.utexas.edu/users/tyilk/PiProj/Index.htm
Brief History of Pi ?http://rene.ma.utexas.edu/users/tyilk/PiProj/PiHistory.htm
Recite Digits in Languageshttp://www.cecm.sfu.ca/pi/yapPing.html
Listen to Pi on Polyphonhttp://home.t-online.de/home/HAEL.YGGS/polyphon.htm
Pi Day Songshttp://www.winternet.com/~mchristi/piday.html
At the Exploratoriumhttp://www.exploratorium.edu/learning_studio/pi