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  1. Tafel Der Natürlichen Logarithmen Der Zahlen: In Der Form Und Ausdehnung Wie D.D. Gewöhnlichen Oder Brig'schen Logarithmen Berechnet (German Edition) by Zacharias Dase, 2010-04-08

21. 07.11.02 Behind The Ministry: Part 2 - National Community Church
In 1844, Johann Martin zacharias dase calculated Pi correctly to 200 places inless than 2 months. dase could count the number of sheep in a flock after a
http://www.theaterchurch.com/partner/Article_Display_Page/0,,PTID325928|CHID7194
National Community Church
  • Who we are Where we are Get connected ... Home
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    Overview Evotional Pastor's Blog Sermons Online ... Resources
    07.11.02 Behind the Ministry: Part 2
    "The Theory of Multiple-Giftedness"
    Pastor Mark Batterson
    Behind the Minsitry: Part 2
    In 1983, a Harvard professor named Howard Gardner wrote a groundbreaking book titled Frames of Mind. The book popularized the theory of multiple intelligences (MI). Gardner argued that intelligence couldn't be measured by an ACT, GRE, or IQ test. He argued for the existence of multiple intelligences. In other words, different people are smart in different ways! Frames of Mind identified seven types of intelligence. Here's a paraphrased list: word smart, picture smart, music smart, body smart, number smart, people smart, and self smart.
    When Amadeus Wolfgang Mozart was a boy, he visited the Sistine Chapel in Rome. He was enchanted by a piece of music by Gregorio Allegri and wanted a copy of the music, but the Sistine chapel had decreed that that particular piece of music, the Miserere, could only be performed inside the Sistine chapel and could not be copied under any circumstances. Mozart attended one more performance then used his "phonographic" memory to write out the entire musical score. I have no idea if Mozart was body smart, number smart, or people smart, but I think it's safe to say that Amadeus Wolfgang Mozart was music smart.
    In 1844, Johann Martin Zacharias Dase calculated Pi correctly to 200 places in less than 2 months. Dase could count the number of sheep in a flock after a single glance. He could multiply two eight-digit numbers in 54 seconds, two forty-digit numbers in 40 minutes, and two 100-digit numbers in 8 hours. He was a human calculator. Dase could perform calculations for weeks on end. He would stop calculating at bedtime, store everything to memory, and pick up right where he left off after breakfast. I have no idea if Dase was music smart, word smart, or self smart, but I think it's safe to say that Johann Martin Zacharias Dase was number smart.

22. RF Cafe - Pi
p was calculated to 200 places in 1844 by Johann Martin zacharias dase (18241861).and since , then , which is the first infinite series ever found for p,
http://www.rfcafe.com/references/mathematical/pi.htm
Your Onramp to the Information Superhighway
About RF Cafe

Visitors Since May 2000 Your browser does not support inline frames or is currently configured not to display inline frames. Forums Search RF Cafe Home Site Map ... Advertise on RF Cafe Pi ( There are so many pages on the Internet with information on that I will not even attempt to outdo them. However, if you happened upon this website and are looking for series expansions for calculating , then you have come to the right place. Here are a few of the most popular. The earliest renditions of resulted from estimating the relationship of measurements of the circumference of a circle to its diameter. Here are a few early values, which were all ratios of whole numbers because at the time it was inconceivable that something "irrational" could exist:
  • 3 = value implied in the Bible in I Kings 7:23 = upper bound by Archimedes = lower bound by Adriaan = Otho’s value = Ptolemy’s value (he used 3.14167 in his calculations). A few others:
Here’s an interesting property I just noticed myself about Ptolemy's value (even though it is of no consequence): the numerator is the impedance of free space, and the denominator times

23. References For Dase
References for zacharias dase. Version for printing Books WW Rouse Ball, CalculatingProdiges, in Mathematical Recreations and Essays (1892).
http://www-groups.dcs.st-andrews.ac.uk/history/References/Dase.html
References for Zacharias Dase
Version for printing Books:
  • W W Rouse Ball, Calculating Prodiges, in Mathematical Recreations and Essays Main index Birthplace Maps Biographies Index
    History Topics
    ... Anniversaries for the year
    JOC/EFR December 1996 School of Mathematics and Statistics
    University of St Andrews, Scotland
    The URL of this page is:
    http://www-history.mcs.st-andrews.ac.uk/References/Dase.html
  • 24. Biography-center - Letter D
    dase, zacharias wwwhistory.mcs.st-and.ac.uk/~history/Mathematicians/D ase.html;Dassanowsky, Elfi von www.german-way.com/cinema/dass.html
    http://www.biography-center.com/d.html
    Visit a
    random biography ! Any language Arabic Bulgarian Catalan Chinese (Simplified) Chinese (Traditional) Croatian Czech Danish Dutch English Estonian Finnish French German Greek Hebrew Hungarian Icelandic Indonesian Italian Japanese Korean Latvian Lithuanian Norwegian Polish Portuguese Romanian Russian Serbian Slovak Slovenian Spanish Swedish Turkish
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    25. Precomputer History Of Pi
    In 1844, Johann dase (aka, zacharias Dahse), a calculating prodigy (or idiotsavant ) hired by the Hamburg Academy of Sciences on Gauss s recommendation,
    http://personal.bgsu.edu/~carother/pi/Pi2.html
    The Precomputer History of
    That the ratio of circumference to diameter is the same (and roughly equal to 3) for all circles has been accepted as "fact" for centuries; at least 4000 years, as far as I can determine. (But knowing why this is true, as well as knowing the exact value of this ratio, is another story.) The "easy" history of concerns the ongoing story of our attempts to improve upon our estimates of . This page offers a brief survey of a few of the more famous early approximations to The value of given in the Rhynd Papyrus (c. 2000 BC) is Various Babylonian and Egyptian writings suggest that each of the values were used (in different circumstances, of course). The Bible (c. 950 BC, 1 Kings 7:23) and the Talmud both (implicitly) give the value simply as 3. Archimedes of Syracuse (240 BC), using a 96-sided polygon and his method of exhaustion, showed that and so his error was no more than The important feature of Archimedes' accomplishment is not that he was able to give such an accurate estimate, but rather that his methods could be used to obtain any number of digits of . In fact

    26. Mathematics Fun, Fiction, Function, Fantasy
    Carl Friedrich Gauss, André Marie Ampere, George Parker Bidder (Senior andJunior), Johann Martin, zacharias dase, Jacques Inaudi, Shakuntale Devi.
    http://www.lifesmith.com/mathfun.html
    Mathematics Fun
    Fact Fiction
    Function Fantasy Home Art Math Business Here is a collection of mathematical activities and curiosities...enjoy them! Guess Your Birthday! Divisibilty Rules! Send More Money! Good Mathematical Card Trick ...
    Take me there!
    Guess Your Birthday! Here's a fun trick to show a friend, a group, or an entire class of people. I have used this fun, mathematical trick on thousands of people since 1963 when I learned it. Tell the person (or class) to think of their birthday...and that you are going to guess it. Step 1) Have them take the month number from their birthday: January = 1, Feb = 2 etc.
    Step 2) Multiply that by 5
    Step 3) Then add 6
    Step 4) Then multiply that total by four
    Step 5) Then add 9
    Step 6) Then multiply this total by 5 once again
    Step 7) Finally, have them add to that total the day they were born on. If they were born on the 18th, they add 18, etc. Have them give you the total. In your head, subtract 165, and you will have the month and day they were born on! How It Works: Let M be the month number and D will be the day number. After the seven steps the expression for their calculation is:

    27. 7 - Das Nil Admirari Der Philosophie Wird Einmal Gründlich
    Translate this page Herr zacharias dase hat die Gefälligkeit gehabt, in meiner Wohnung neue Beweiseseiner ausscrordeutlichen Gaben abzulegen. Wenn schon seine Leistungen im
    http://users.lk.net/~stepanov/mnemo/album.html
    D as " Nil admirari " der Philosophie wird einmal gründlich widerlegt durch die Leistungen des Herrn Dase im Gebiete des Zeichen- und Zahlengedächtnisses, von denen der Unterzeichnete mehrmals Zeuge zu sein das Vergnügen hatte. Hier verhalten sich Mathematiker zu einer Thatsache des Geistes, die man nicht begreifen, nur erfahren kann, wie Kinder, welche mühsam buchstabiren gegen den Sprachkünstler Mezzofanti. Lässt er uns auch einen Blick in seine Methode thun, so können wir doch der erstaunlichen Schnelligkeit nicht folgen, mit welcher er 10 steilige Zahlen zu einem Produkte verwebt, oder ein Produkt wieder entwirrt in der Division benannter und unbenanuter, ganzer und gebrochener Zahlen, und dem Ausziehen von Quadrat- und Kubikwurzeln. Wie wir andere z. B. das Wort "Anschaulichkeit" mit einem Blicke lesen und alle Buchstaben und deren Aufeinanderfolge vor- und rückwärts kennen, so braucht Herr Dase eine 12 stellige Zahl nur anzublicken, um sie sogleich auf der schwarzen Tafel seines Gedächtnisses angeschrieben zu sehen, und vor- und rückwärts die Ziffern hersagen zu können. Ja dieses Gedächtniss behält 65 stellige Zahlen, wenn sie durch Rechenoperationen vor ihm entstanden sind, und giebt sie, wenn man darnach verlangt, zu jeder Zeit wieder, wenn auch das Mannigfaltigste dazwischen seine Thätigkeit in Ansprach genommen hatte. Unmittelbare Anschauung und wunderbare Fertigkeit in vermittelter Thätigkeit durch eigenthümliche Methoden sind hier vereinigt. Und diese Thätigkeit geschieht ohne Anstrengung, ist unverkennbar ein mit Lust verbundenes Spiel des Geistes, der in einem frischen, gesunden und kräftigen Körper wohnt, der damit ein anspruchloses Benehmen verbindet, was ihm sogleich die Herzen aller Anwesenden gewinnt, die auch darin ihre Erwartung übertroffen finden, dass sie sich aufs Interessanteste unterhalten und die kürzeste Stunde gehabt haben.

    28. The Magic Of NUMBERS. Robert Tocquet. 1960
    zacharias dase, born in Germany in 1824, distinguished himself from the majorityof lightning calculators by the fact that he placed his ability at the
    http://users.lk.net/~stepanov/mnemo/magice.html
    Mnemonic Articles The Magic of NUMBERS
    Robert Tocquet. 1960 (First publicated in France in 1957 by Pierre Amiot as "2 + 2 = 4") While the facts given in this book are sound, the author's intention is to amuse rather than instruct. For this reason "textbook" terminology has been avoided wherever possible. Chapret 1 Yesterday and Today L IGHTNING CALCULATORS, especially when illiterate, have drawn the attention of the public in all Ages by their extraordinary abilities. They can solve in their heads, sometimes instantaneously and without apparent effort, problems often so complicated that most of us, even mathematicians accustomed to juggle with figures, could solve them only with pencil and paper and over a much longer time, without being sure even then of succeeding. Some of them, too, when they have been set a problem, can talk freely with bystanders, discussing subjects completely foreign to the question they are dealing with, and then suddenly give the required solution, as if a cerebral mechanism had been working within them without their knowledge.
    As a general rule, and this is a fact which should be emphasised immediately, the lightning calculators, apart from the faculty they have of handling figures with exceptional virtuosity, are of below average intelligence; sometimes they are even mentally retarded. Thus, Colburn was always at the bottom of his class, Buxton could not even write his name and Inaudi did not learn to read or write until he was over twenty years of age. There are certain exceptions, however, to this rule, for some have been known who have educated themselves normally and there have even been geniuses who were phenomenal calculators: Ampere, Arago, Georges Bidder, Whately and Gauss being examples.

    29. Memory And Mental Calculation World Records
    Johann Martin zacharias dase (Germany, 18241861) multiplied two 20 digit numbersin 6 minutes, two 48 digit numbers in 40 minutes and two 100 digit numbers
    http://www.recordholders.org/en/list/memory.html
    Memory and Mental Calculation World Records
    Comments? Corrections? New Records? Please contact us at info@recordholders.org

    30. Weltrekorde Für Gedächtnis Und Kopfrechnen
    Translate this page Von dem bekannten Kopfrechner Johann Martin zacharias dase (Deutschland, 1824-1861)wurden im Jahre 1861 folgende Leistungen überliefert Multiplikation
    http://www.recordholders.org/de/list/memory.html
    Sie haben Kommentare, Korrekturen oder neue Rekorde? Bitte schreiben an: info@recordholders.org
    Merken von Spielkarten Spielen von Spielen mit verbundenen Augen ... die meisten Daten aus den Jahren 1600-2100 in einer Minute Links: MemoryXL
    deutsche und Weltrekorde
    Brainboard Links zu interessanten englischsprachigen Seiten finden Sie auf der englischer Version dieser Seite. Wilfried Posin: Alles im Kopf
    DETAILS / BESTELLEN

    Ulrich Vogt: Esels Welt, Mnemotechnik zwischen Simonides und Harry Lorayne
    DETAILS / BESTELLEN
    Ziffern Rekordhalter Jahr Pi-Links: www.pi-world-ranking-list.com
    www.acc.umu.se/~olletg/pi

    Olles' Pi Page
    Hier findet man u.a. den 100er- und den 1000er-Klub, in dem nur Mitglied werden kann, wer die entsprechende Zahl von Stellen von Pi auswendig kennt.
    Pi Memorama Memorize the number pi to 1000 places
    4,200,000,000 decimal digits of Pi
    Pi Links
    umfangreiche Linkseite the Uselessness of Pi David Blatner: Pi - Magie einer Zahl DETAILS / BESTELLEN Jean-Paul Delahaye: Pi - Die Story DETAILS / BESTELLEN Karl Helmut Schmidt: Pi - Geschichte und Algorithmen einer Zah l DETAILS / BESTELLEN Jorg Arndt, Christoph Haenel:

    31. Mental Calculator -- Facts, Info, And Encyclopedia Article
    zacharias dase (Click link for more info and facts about Shakuntala Devi) ShakuntalaDevi Pericles Diamandi Urania Diamandi
    http://www.absoluteastronomy.com/encyclopedia/m/me/mental_calculator.htm
    Mental calculator
    Mental calculators are people with a prodigious ability in some area of (Click link for more info and facts about mental calculation) mental calculation , such as (Click link for more info and facts about multiplying) multiplying large numbers together or ((mathematics) the resolution of an integer or polynomial into factors such that when multiplied together they give the integer or polynomial) factoring large numbers. Some mental calculators are (Click link for more info and facts about autistic) autistic , with a narrow area of great skill and poor mental development in other directions (see (Someone who has been admitted to membership in a scholarly field) savant ), but many have simply developed skills in this regard. A good many are also experienced (A person skilled in mathematics) mathematician s, (A specialist in linguistics) linguist s, writers, and so on.
    Mental calculators were in great demand in research centers such as (Click link for more info and facts about CERN) CERN before the advent of modern electronic calculators and computers. See, for instance, the modern book The Great Mental Calculators , whose introduction was written by Eberstark (see below).

    32. Free Essays - Chronology Of P
    zacharias dase in 1844 found p correct to 200 places. dase was perhaps one ofthe most extraordinary mental calculators who ever lived.
    http://www.freeessays.tv/b2142.htm
    Essays Search
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    Chronology Of P
    This is the complete (546 words) free paper for the essay titled Chronology Of P Chronology of p Search for Free Essays and Term Papers Search for: List of Essays and Term Papers

    33. Mental Calculator: Information From Answers.com
    Alexander Aitken (AC Aitken); Arthur T. Benjamin; zacharias dase Shakuntala Devi;Pericles Diamandi; Urania Diamandi; Hans Eberstark Leonhard Euler
    http://www.answers.com/topic/mental-calculator
    showHide_TellMeAbout2('false'); Business Entertainment Games Health ... More... On this page: Wikipedia Mentioned In Or search: - The Web - Images - News - Blogs - Shopping mental calculator Wikipedia @import url(http://content.answers.com/main/content/wp/css/common.css); @import url(http://content.answers.com/main/content/wp/css/gnwp.css); mental calculator Mental calculators are people with a prodigious ability in some area of mental calculation , such as multiplying large numbers together or factoring large numbers. Some mental calculators are autistic , with a narrow area of great skill and poor mental development in other directions (see savant ), but many have simply developed skills in this regard. A good many are also experienced mathematicians linguists , writers, and so on. Mental calculators were in great demand in research centers such as CERN before the advent of modern electronic calculators and computers. See, for instance, the modern book The Great Mental Calculators , whose introduction was written by Eberstark (see below). Michael O'Boyle, an American

    34. The Mountains Of Pi
    The most powerful of these was Johann Martin zacharias dase, a prodigy from Hamburg.dase could multiply large numbers in his head, and he made a living
    http://www.barryland.com/pi.html
    The Mountains of Pi
    by
    R I C H A R D P R E S T O N G regory Volfovich Chudnovsky recently built a supercomputer in his apartment from mail-order parts. Gregory Chudnovsky is a number theorist. His apartment is situated near the top floor of a run-down building on the West Side of Manhattan, in a neighborhood near Columbia University. Not long ago, a human corpse was found dumped at the end of the block. The world's most powerful supercomputers include the Cray Y-MP C90, the Thinking Machines CM-5, the Hitachi S-820/80, the nCube, the Fujitsu parallel machine, the Kendall Square Research parallel machine, the NEC SX-3, the Touchstone Delta, and Gregory Chudnovsky's apartment. The apartment seems to be a kind of container for the supercomputer at least as much as it is a container for people. Gregory Chudnovsky's partner in the design and construction of the supercomputer was his older brother, David Volfovich Chudnovsky, who is also a mathematician, and who lives five blocks away from Gregory. The Chudnovsky brothers call their machine m zero. It occupies the former living room of Gregory's-apartment, and its tentacles reach into other rooms. The brothers claim that m zero is a "true, general-purpose supercomputer," and that it is as fast and powerful as a somewhat older Cray Y-MP, but it is not as fast as the latest of the Y-MP machines, the C90, an advanced supercomputer made by Cray Research. A Cray Y-MP C90 costs more than thirty million dollars. It is a black monolith, seven feet tall and eight feet across, in the shape of a squat cylinder, and is cooled by liquid freon. So far, the brothers have spent around seventy thousand dollars on parts for their supercomputer, and much of the money has come out of their wives' pockets.

    35. Ancient Pi: Knowers Of The Universe
    Nonetheless, in 1844, Johann Martin zacharias dase calculated to 200 decimalplaces, with the first zero appearing at the 32nd decimal place meaning,
    http://www.earthmatrix.com/ancient/pi.htm
    The Sound of Meaning: Comparative Linguistics of Ancient Egyptian, Maya and Nahuatl
    The Goldbach
    Conjecture
    and the Universe
    of Primes
    Particle Mass
    Difference
    Extract No.26
    Ancient Pi (
    Knowers of the Universe
    By
    Charles William Johnson
    ) to hundreds or even thousands of decimal places.
    If we realize that the measurement of the ratio between the diameter and the circumference of a circle is entirely theoretical and speculative, then we may also realize that the result shall always represent an approximation. In fact, the very fact that pi is always expressed in terms of an unending fraction (with mathematicians searching it to the n th number of decimal places), should cause us to accept the idea that pi can only be an approximation. (As Lambert illustrated in 1767, " is not a rational number, i.e., it cannot be expressed as a ratio of two integers"; Beckmann, p.100.)
    Throughout history, the expression of pi has taken on many variations.

    36. FELKEL, ANTON (1740 – ----)
    Another possible owner is zacharias dase (1824181), who was a lightningcalculator with little mathematical ability, who constructed many mathematical
    http://www.scs.uiuc.edu/~mainzv/exhibitmath/exhibit/felkel.htm
    Number Theory for the Millenium
    University of Illinois at Urbana-Champaign
    Rare Book Room Exhibit
    Felkel , Anton (1740 – ). Tassel aller Einfachen Factoren der durch 2, 3, 5 nicht theilbaren Zahlen von 1 bis 10 000 000 . Vienna: 1776. Glaisher wrote of Felkel's work: "The table is so curious and rare, and, besides, the facts connected with its calculation and publication are so remarkable that I here give an account in some detail." According to Glaisher, Anton Felkel (b. 1740) was a schoolmaster in Vienna, who did not begin to study mathematics until his mid 30s, and was then involved in the construction of mathematical tables for the rest of his life. Felkel corresponded with the mathematician Lambert, who had promised immortality to anyone "unwearied and resolute" enough to write a factor table to 1,000,000. There is a complicated history of correspondence, announcements of future tables, and competing table-writers. At one point, Lambert wrote that Felkel always seemed to be printing circulars instead of the table itself. The last reported sighting of Felkel is in Lisbon in 1798. Felkel gave in 1776 a table of all the prime factors (designated by letters or pairs of letters) of numbers, not divisible by 2,3 or 5, up to 408,000, requesting for entry two auxiliary tables. In manuscript, the table extended to 2 million; but as there were no purchasers of the part printed, the entire edition, except for a few copies, was used for cartridges in the Turkish war. The imperial treasury at Vienna, at the cost of which the table was printed, retained the further manuscript. (Dickson, p. 349).

    37. 1848 - Flugschriften Im Netz
    Translate this page Digitale Bibliothek. 1848 - Flugschriften im Netz. Person dase, Johann MartinZacharias (1824 - 1861). Signatur, SF 16 / 114 MAPP / B 10 6 (Dokument ansehen).
    http://1848.stub.uni-frankfurt.de/cgi-bin/kutili.rb?person=Dase, Johann Martin Z

    38. The Mountains Of Pi
    The most pow; erful of these was Johann Martin; zacharias dase, a prodigy fromHam-; burg. dase could multiply large num-; bers in his head,
    http://www.lacim.uqam.ca/~plouffe/Chudnovsky.html
    The mountains of Pi an article from the New Yorker, March 2, 1992. Gregory V. Chudnovsky and David V. Chudnovsky
    GREGORY VOLFOVICH CHUDNOVSKY recently built a
    supercomputer in his apart-
    ment from mail-order parts. Greg-
    ory Chudnovsky is a number theo-
    rist. His apartment is situated near
    the top floor of a run-down build-
    ing on the West Side of Manhat-
    tan, in a neighborhood near Co-
    lumbia University. Not long ago,
    a human corpse was found dumped
    at the end of the block. The world's
    most powerful supercomputers in-
    clude the Cray Y-MP C90, the
    Thinking Machines CM-5, the
    Hitachi S-820/80, the nCube, the
    Fujitsu parallel machine, the
    Kendall Square Research parallel
    machine, the NEC SX-3, the
    Touchstone Delta, and Gregory
    Chudnovskv's apartment. The
    apartment seems to be a kind of con-
    tainer for the supercomputer at least
    as much as it is a container for
    people.
    Gregory Chudnovsky's partner in
    the design and construction of the
    supercomputer was his older brother,
    David Volfovich Chudnovsky, who is
    also a mathematician, and who lives
    five blocks away from Gregory. The

    39. Inwit Publishing, Inc. And Inwit, LLC -- Writings, Links And Software Demonstrat
    In 1840 the sixteenyear-old German prodigy zacharias dase calculated p to 200places, in only two months (38). dase was perhaps the most phenomenal mental
    http://www.inwit.com/inwit/writings/historyandodditiesofpi.html
    Publications in Science and Mathematics, Computing and the Humanities
    Museum Development, Educational Curricula, and Science Fair Initiatives
    Educational Toys and Technology History and Oddities of the Number Pi by Vincent Mallette
    Journal of the Tennessee Academy of Science
    Volume 37, Number 4, October, 1962 HISTORY AND ODDITIES OF THE NUMBER Vincent Mallette [This paper was among the first in the flood of -mania research. It has been massively updated by the author since its "We have compared the probability that an unknown savant has solved the problem with the probability that there is one madman the more on the earth. The latter appears to us the greater." Genius is a superior aptitude to patience. [The hard-copy version of this paper contains 7,800 places of 390 digits printed in 4-point type on the right-hand margin of every page. From a distance the thin string of tiny numbers looks like an ornamental border, but up close every digit is readable. Altogether the 7,800 places of stretches for over 16 feet. It is sobering to realize that this precision of Daisuke Takahashi and Yasumasa Kanada of the University of Tokyo have computed to over 51 billion places of decimals By contrast, the ancient Babylonians and Hebrews flourished and died believing that

    40. Read About Pi At WorldVillage Encyclopedia. Research Pi And Learn About Pi Here!
    1844, zacharias dase and strassnitzky, 200 dps. 1847, thomas clausen, 248 dps.1853, lehmann, 261 dps. 1853, rutherford, 440 dps
    http://encyclopedia.worldvillage.com/s/b/Pi

    Culture
    Geography History Life ... WorldVillage
    Pi
    From Wikipedia, the free encyclopedia.
    The title given to this article is incorrect due to technical limitations . The correct title is For other uses of the term "Pi," see Pi (disambiguation)
    The minuscule , or lower-case, pi The mathematical constant is commonly used in mathematics and physics Greek letter is not available. In Euclidean plane geometry ratio of a circle 's circumference to its diameter , or as the area of a circle of radius unit circle analytically using trigonometric functions , for example as the smallest positive x for which sin x x for which cos x Pi is also known as Archimedes ' constant (not to be confused with Archimedes' number ) and Ludolph 's number decimal places (sequence in OEIS ) is: pi to 1,000 places 10,000 places 100,000 places , and 1,000,000 places . This page is also good for up to 200 million places: pi search page http://www.angio.net/pi/piquery Contents 1 Properties
    2.1 Geometry

    2.2 Analysis

    2.3 Complex analysis
    ...
    edit
    Properties
    irrational number : that is, it cannot be written as the ratio of two integers . This was proven in by Johann Heinrich Lambert . In fact, the number is

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