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# Pi101

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its a great number pi

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• In 1888, a Indiana country doctor named Edwin Goodwin claimed he had been “supernaturally taught” the exact measure of the circle and even had a bill proposed in the Indiana legislature that would copyright his mathematical findings. The bill never became law thanks to a mathematical professor in the legislature who pointed out that the method resulted in an incorrect value of pi.
• ### Pi101

1. 1. Copyright Audrey Weeks 2003 “People have calculated billions of digits of pi because of the human desire to do something that‟s never been done before . When George Mallory was asked why he wanted to climb Mt. Everest, he replied, „Because it‟s there‟. Well, pi is certainly here. Like the other planets, it‟s built into the fabric of our physical universe and it will always beFormalOur Story of explored.” Decimal Fractions Invented Geometry Logarithms InventedPi Begins Begins Calculus Discovered1650BC 600BC 300BC 1100 1600 2001 Thales Euclid Algebra Invented Computers & Pythagoras Arabic Numerals (1,2,3...) Invented Calculators (Worlds 1st Novel Written) Invented (general public not even aware of the date) 3.1415926535897932384626433832795028841971693993751058209749445923078 ...
2. 2. What is pi? Copyright Audrey Weeks 2003   diameter circumference The ratio of the circumference to the diameter of ANY circle is constant. It is between 3 and 3 1 .It is close to but 7 NOT EQUAL to 3.14 or 22 . 7Its digits will NEVER ...but will ALWAYS terminate or continue to fascinate repeat… mankind. 3.1415926535897932384626433832795028841971693993751058209749445923078 ...
3. 3. Copyright Audrey Weeks 2003 Irrational & Transcendental• IRRATIONAL   22   3.14 7 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.• TRANSCENDENTAL Unlike 3 which solves x 2  3 No sequence of algebraic operations using integers(powers,roots,sums,etc.)can be equal to its value. 3.1415926535897932384626433832795028841971693993751058209749445923078 ...
4. 4. Where Can we find pi? Copyright Audrey Weeks 2003 IN EVERYTHING CIRCULAR (of course) h r 1 SA  2  dh   r 2C  d h 1 V  3  r 2hA   r2 r SA   dh  2 r 2 V   r 2h SA  4 r 2 SA  4 r 2 a V  4  r3 V  2 2 r 2a 3 3.1415926535897932384626433832795028841971693993751058209749445923078 ...
5. 5. Copyright Audrey Weeks 2003occurs in hundreds of equations in many sciences including thosedescribing the DNA double helix, a rainbow, ripplesspreading from where a raindrop fell into water,superstrings, general relativity, normal distribution,distribution of primes, geometry problems, waves,navigation....Electricity - formulas for alternating currents andradiation from radio & TV antennasClock designers use pi when designing pendulums for clock.Medicine benefits from pi when studying the structurethe eye.Aircraft designers use it to calculate areas of the skin ofthe aircrafts. 3.1415926535897932384626433832795028841971693993751058209749445923078 ...
6. 6. Copyright Audrey Weeks 2003  (Leibniz)    41  1 3  1 5  1 7  1 9  1  11 13 1  1 15  ...    2  6  1  1  1  1  1  1  1  1 ...   1 4 9 16 25 36 49 64    2 2 4  2         4 6 6 8 8 10 10   ... (John Wallis 1655) 1  3 3 5 5 7 7 9 9 11   3  2    (Leonard Euler) 2 5 6 7 11 13 17 19  6 10 14 18 18    23 22  29  30  ...  3.1415926535897932384626433832795028841971693993751058209749445923078 ...
7. 7. Copyright Audrey Weeks 2003 25  3.125 The Babylonians found the first known value for 8 Pi in around 2000BC -They used (25/8). 377  3.1416 Ptolemy (Alexandria, Egypt) 150 AD 120 Also used by Columbus on his voyage to the New World 223  3.1408450704... Archimedes (Syracuse, 287-212 BC) 71 22 Found pi to be between these two fractions.  3.142857 7 This average error is only 0.0002! 355  3.141592920354 ... Tsu Ch’ung Chi 113 China, 450 AD 21434  3.14159265258... Srinivasa Ramanujan (India, 1887-1920) 22 4  97  2 1 1 If 16,539 replaced by ,  97  21 1  2143 22 2 1 2 1 1 4 3 1 1 (This is an irrational approximation.) 16539... 3.1415926535897932384626433832795028841971693993751058209749445923078 ...
8. 8. Copyright Audrey Weeks 2003 Earliest Known Record of Pi - 1650 BCNo number has captured the attention andimaginationsof people throughout the ages as much as theratio of a circle’s circumference to its diameter. The earliest known reference to Pi is on a Middle Kingdom papyrus scroll, written around 1650 BC by Ahmes the scribe. He wrote this ratio as “4 times the square of eight-ninths”   8 2   4    256  approx. 3.1604938...  9 81   less than 1% error !    3.1415926535897932384626433832795028841971693993751058209749445923078 ...
9. 9. Archimedes, 250 Copyright Audrey Weeks 2003 3 10BC 3 7 71  1 12.1 cm2  Area Circle = Circumference of Circle Area Square = cm2 3.9  Diameter r Area Circle Area Square but also ... r 6 5 4 3 2 1 He began with a regular hexagon 0 and kept doubling sides to a 96-gon! 3 4 5 6 Inner polygon perimeter / 2r Later , the Chinese continued this doubling to ov er 3000 sides to ge t 3.14159. Outer polygon perimeter / 2rArchimedes derived the value of pi based on the area of a regular polygon inscribed withinthe circle and the area of a regular polygon within which the circle was circumscribed. ... 3.1415926535897932384626433832795028841971693993751058209749445923078
10. 10. I have proof! Copyright Audrey Weeks 20031767 - Johann Lambert proved  irrational First, he proved - If x is rational, (x  0), then tan x cannot be rational. 1728-1777 i.e., If tan x is rational, then x must be irrational or 0. Swiss    Since tan 4 = 1, 4 must be irrational. Q.E.D.1794 - Adrien-Marie Legendre proved  2 irrational French1840 - Joseph Liouville proved transcendental nos. exist (used limits of continued fractions) French1873 - Charles Hermite proved e transcendental  transcendental French1882 - Ferdinand Lindemann proved German 3.1415926535897932384626433832795028841971693993751058209749445923078 ...
11. 11. Copyright Audrey Weeks 2003Starting at digit #772 - 9999998 occurs largest 7-digit sum in the first million digits!In 1st million, no “123456” but 012345 twice 123456789 first appears at 523,551,502nd digitThe fraction (22 / 7) is a well used number for Pi.It is accurate to 0.04025%.Another fraction used as an approximation to Piis (355 / 113) which is accurate to 0.00000849%A more accurate fraction of Pi is(104348 / 33215).This is accurate to 0.00000001056%.There is no zero in the first 31 digits of Pi. 3.1415926535897932384626433832795028841971693993751058209749445923078 ...
12. 12. Copyright Audrey Weeks 20031596 … Ludolph van Ceulen (Dutch) calculates 35 digits (which were named the Ludolphine Number) All by hand - months1706 … John Machin calculates 100 digits But Ferguson finds1874 … William Shanks calculates 707 digits error in 527th onward1947 … Ferguson (using desk calculator) finds 808 digits1949 … ENIAC computer (DoD & U. of Pen.) finds 2037 digits1973 … CDC 7600 (Paris) finds 1,000,000 digits (23 hrs)1989 … 1,000,000,000 digits (USSR Chudnovsky brothers, NY)2002… Hitachi SR8000(supercomputer)1.24 trillion digits (400hr. It took a Hitachi SR 8000 supercomputer over 400 hours to compute pi to 1.24 trillion digits Why still do this? …to find out more about pi …to test computer architecture & efficiency ... to test software for accuracy and speed 3.1415926535897932384626433832795028841971693993751058209749445923078 ...
13. 13. Copyright Audrey Weeks 2003 STAR TREK 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 doesn’t detect their plan. Spock foils the evil computer by commanding it to “compute to last digit the value of pi .” 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! Comedian John Evans once quipped: “What do youget if you divide the circumference of a jack-o-lantern by its diameter? Pumpkin π . 3.1415926535897932384626433832795028841971693993751058209749445923078 ...
14. 14. Copyright Audrey Weeks 2003 More misc. pi factsAlbert Einstein German 1879-1955 born 3 / 14 / 1879 (Pi-Day)Symbol introduced by Leonard Euler, 1737The first person to use the Greek letter Pi wasWelshman William Jones in 1706. He used it as an Swissabbreviation for the periphery of a circle with unit 1707-1783diameter. Euler adopted the symbol and it quicklybecame a standard notation.Pi is it was taken from the Greek letter"Piwas". It is also the 16th Greek alphabet. Both π and the letter p are the sixteenth letter in the Greek and English alphabets, respectively 3.1415926535897932384626433832795028841971693993751058209749445923078 ...
15. 15. Copyright Audrey Weeks 2003Consider the following series of integers, each using onemore digit of pi: 3, 31, 314, 3141, 31415, 314159, 3141592,etc. Out of the first 1000 numbers in this series, only 4 areprime!The world record for pi-recitation (from memory) is held byHiroyuki Gotu, age 21. 9 hours ... 42,000 digits!Before the π symbol was used, mathematicians described piin round-about ways such as “quantitas, in quam cummultipliectur diameter, proveniet circumferential,” whichmeans “the quantity which, when the diameter is multipliedby it, yields the circumference. 3.1415926535897932384626433832795028841971693993751058209749445923078 ...
16. 16. Copyright Audrey Weeks 2003Since there are 360 degrees in a circle and pi is intimately connectedwith the circle, some mathematicians were delighted to discover thatthe number 360 is at the 359th digit position ofpi .At position 763 there are six nines in a row. This is known as thePi is also referred to as theLeonardo da Vinci (1452-1519) and artistAlbrecht Durer both briefly worked on“squaring the circle,” or approximating pi . 3.1415926535897932384626433832795028841971693993751058209749445923078 ...
17. 17. Copyright Audrey Weeks 2003 Pi was first rigorously calculated by one of the greatestmathematicians of the ancient world, Hewas so engrossed in his work that he did not notice thatRoman soldiers had taken the Greek city of Syracuse.When a Roman soldier approached him, he yelled inGreek The Roman soldier simplycut off his head and went on his business. Egyptologists and followers of mysticism have been fascinated forcenturies by the fact that the Great Pyramid at Giza seems toapproximate pi. The vertical height of the pyramid has the samerelationship to the perimeter of its base as the radius of a circle hasto its circumference It is more correct to say that a circle has an infinite number ofcorners than to view a circle as being cornerless . 3.1415926535897932384626433832795028841971693993751058209749445923078 ...
18. 18. Copyright Audrey Weeks 2003The 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. Man’s 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 bottle’s broad, full base gives it a masculine foundation and allure. To complete this construction, an innovative closing system crowns 3.1415926535897932384626433832795028841971693993751058209749445923078 ... the bottle. The curved shape of the cap, in bronze-colored
19. 19. Copyright Audrey Weeks 2003Oh, number Pi Pi SongOh, number Pi There are people who tryYour digits are unending, memorize the decimal to digits of pi. The people makeOh, number Pi up songs and music based onOh, number Pi the digits of pi.No pattern are yousending.Youre three point onefour one five nine,And even more if we hadtime,Oh, number PiOh, number Pi 3.1415926535897932384626433832795028841971693993751058209749445923078 ...
20. 20. Copyright Audrey Weeks 2003 A mnemonic is a verse to assist memory No . of letters=digit 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 j’aime à faire apprendre un nombre utile aux sages!Immortel Archimède, artisite ingénieur, (31) Sir, I send a rhyme excellingQui de ton jugement peut priser la valeur? In sacred truth and rigid spelling.Pour moi, ton problème eut de pareils avantages. Numerical sprites elucidate For me the lexicons dull weight. (21) Dir, o Held, o alter Philosoph, du Riesengenie! Sol y Luna y Mundo proclaman Wie viele Tausendre bewundern Geister al Eterno Autor del Cosmo. (11) Himmlisch wie du und göttlich! Noch reiner in Aeonen Wie? O! Dies  (24) Wird das uns strahlen Mach ernstlich so vielen viele Müh’! Wie im lichten Morgenrot! (30) 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) 3.1415926535897932384626433832795028841971693993751058209749445923078 ...
21. 21. Copyright Audrey Weeks 2003 CAN YOU FIND 402 digits of PI ?“Circle Digits” 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 digitexpansion answer then came before me. On examining some problems unhappily arose. That imbecillic bug! The printout I possessedshowed 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 360 words - ignore periods I trust immediately appear, producing fame. other punctuation = 0 words > 9 letters = 2 digits THE END. word for no. = digit 3.1415926535897932384626433832795028841971693993751058209749445923078 ...
22. 22. Copyright Audrey Weeks 2003 “Fools Rush In”Author of Bill - Edwin J. Goodman, M.D. of Indiana - Introduced Jan. 18, 1897Preamble: “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 royaltiesBody: 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 circle’s area is entirely wrong…” (This makes no sense … if meant to be “eq. tri”, then   16  9 here!) 3 …“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   3.23, 2  2.041) “In further proof of the value of the author’s 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] 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 3.1415926535897932384626433832795028841971693993751058209749445923078 ...
23. 23. Copyright Audrey Weeks 2003Pi Day is a holiday held to celebratethe mathematical constant π (pi). PiDay is observed on March 14 (3/14 inAmerican date format), due to π beingequal to roughly 3.14. Sometimes it iscelebrated on March 14 at 1:59 p.m.(commonly known as Pi Minute). If π istruncated to seven decimal places,it becomes 3.1415926, makingMarch 14 at 1:59:26 p.m.At 9:26:53 on Pi Day 2015, thedate will be 3/14/15 at 9:26:53,corresponding to 3.141592653. 3.1415926535897932384626433832795028841971693993751058209749445923078 ...
24. 24. Copyright Audrey Weeks 2003 Larry Shaw, the creator ofThe first Pi Day celebration Pi Day, atwas held at the San FranciscoExploratorium in 1988, withthe Larry Shaw,staff and public marchingaround one of its circular Exploratori of the creator Pi Day, at thespaces, and then consuming um Exploratoriumfruit pies; the museum has PI day issince added pizza pies to Celebrated itsPi Day menu by pie 3.1415926535897932384626433832795028841971693993751058209749445923078 ...
25. 25. Copyright Audrey Weeks 2003Provides an Lead tointellectual developments inchallenge. computerBecause it technology.exists. Pi is the mostLead to recognizedimportant mathematicaldiscoveries in constant in themodern world. Scholars 3.1415926535897932384626433832795028841971693993751058209749445923078 ...
26. 26. Copyright Audrey Weeks 20033.1415926535897932384626433832795028841971693993751058209749445923078 ...