All you need to know about Pi!

70 Fun and Interesting facts about Pi

1) Pi is the number of times a circle's diameter will fit around its circumference

2) Most people would say that a circle has no corners, but it is more accurate to say that it has an infinite number of corners

3) The sequence of digits in Pi so far passed all known tests for randomness.

4) Here are the first 100 decimal places of Pi: 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679

5) The fraction (22 / 7) is a well used number for Pi. It is accurate to 0.04025%

6) Another fraction used as an approximation to Pi is (355 / 113) which is accurate to 0.00000849%

7) A more accurate fraction of Pi is (104348 / 33215). This is accurate to 0.00000001056%

8) Pi occurs in hundreds of equations in many sciences including those describing the DNA double helix, a rainbow, ripples spreading from where a raindrop fell into water, super strings, general relativity, normal distribution, distribution of primes, geometry problems, waves, navigation....

9) There is no zero in the first 31 digits of Pi

10) Pi is irrational. An irrational number is a number that cannot be expressed in the form (a / b) where a and b are integers


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11) It is not known if Pi is normal. No one has proved that Pi isn't normal, so people generally assume that it is

12) Pi is a transcendental number. (Transcendental means= Not capable of being determined by any combination of a finite number of equations with rational integral coefficients)

13) In 1991, the Chudnovsky brothers in New York, using their computer, m zero, calculated pi to two billion, two hundred sixty million, three hundred twenty one thousand, three hundred sixty three digits (2, 260, 321, 363)

14) The Babylonians found the first known value for Pi in around 2000BC -They used (25/8)

15) The Bible uses a value of Pi of 3. Here is a verse from I Kings 7,23: And he made a molten sea, ten cubits from 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

16) The first person to use the Greek letter Pi was Welshman William Jones in 1706. He used it as an abbreviation for the periphery of a circle with unit diameter. Euler adopted the symbol and it quickly became a standard notation

17) The old memory champion was Hideaki Tomoyori. In Yokohama, Japan, Hideaki recited pi from memory to 40,000 places in 17 hrs 21 min, including breaks, on 9th-10th of March in 1987

18) The Pi memory champion is Hiroyoki Gotu, who memorised an amassing 42,000 digits

19) The area of a circle is Pi x Radius squared, and the circumference is Pi x Diameter

20) Pi is the 16th letter of the Greek alphabet


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21) Definition of Pi - A transcendental number, approximately 3.14159, represented by the symbol 3, that expresses the ratio of the circumference to the diameter of a circle and appears as a constant in many mathematical expressions

22) Satan doesn't appear in Pi too quick, the first time 666 appears is at position 2440

23) Pi can be expressed as a quotient in many combinations. Check this out for size!

    Numerator (764 digits):                                 
    24601380675524336658795853487354792913292306568969976877608701100262917729585706849233715783903919
    37171513218882242019518769612066499493009354168622266340276676415272215474998961283764063375923338
    63689554298607720004035657994488555593232140745010681297502224546256051028371011790250996204144964
    81130346904857052062782826052958131860952042802044100028854746645521520483944215121734765448869545
    26901033613274572132739090675526553922123924526003264599964661896573227971062222029920656769855375
    38511948110405622204474470532643566011505737479452380041899434971566926691041109161732519983641534
    22577324308312788651701237200095139973856152299587895589111481221906281366923502797749683094698958
    550724794878831826807297839819134297181448807108467216789321646063528500671573

    Denominator (763 digits): 
    78308626827902588671978037725722610710537259596576392890030512437770404378896603666975454220443788
    08603867750077503157389538176385370643248809541395623763673093868627020326833797949443497330060009
    33599983971392530578731202721246434740449237170357566548445684160719738962315588261884450755072543
    45574205683088510307116356904613173146733551541429347920248771854058062857644730443541865367808048
    61722273426879642923003728080328379000326405932814556846570539573602395903377609928606276781689190
    21820523440624917382116622380154418576373148253000628335769108852578906735260881120272053797903651
    09911284076465310134405840374799690505537745059405868868812704127670105401694918997241112683848484
    01494498919297253141199221432074342304207693419463047831590185791306679700028

    Total digits in numerator and denominator combined are 1527.

24) If you take 10 million random digits, statistically on average you would expect 200 cases where you get 5 digits in a row the same. If you take 10 million digits of Pi, you get exactly 200

25) In 1931 a Cleveland businessman published a book announcing that Pi is exactly 256/81

26) If a billion decimals of pi were printed in ordinary type, they would stretch from New York City, to the middle of Kansas

27) The square root of 9.869604401 is approximately Pi. The square root of an irrational number is irrational too

28) For a circle to equal Pi the diameter must be 1

29) A long time ago people thought there was an illness attached to trying to 'square a circle' called Morbus Cyclometricus

30) Pi in fraction form is (837393900/266550757)


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31) After saying (correctly) that Pi/2 is the value of x between 1 and 2 for which Cosine of x vanishes, Edmund Landau was dismissed from his position in 1934 for teaching in an 'un-German' style

32) In the following series of natural numbers, constructed by taking successively larger strings of digits from the beginning of the decimal expansion of the number pi: 3, 31, 314, 31415, 314159, 3141592, etc., the first thousand numbers of the series include only 4 primes

33) If one were to find the circumference of a circle the size of the known universe, requiring that the circumference be accurate to within the radius of one proton, only 39 decimal places of Pi would be necessary

34) The earliest known reference to Pi is on a Middle Kingdom papyrus scroll, written around 1650 BC by Ahmes the scribe

35) The old world record for computation of the most digits of pi was achieved in September/October 1995 by Yasumasa Kanada at the University of Tokyo. It took 116 hours for him to compute 6,442,450,000 decimal places of Pi on a computer

36) A rapidly converging formula for calculation of Pi found by Machin in 1706. It was Pi / 4 = 4Pi Arctan(1/5) - Arctan(1/239)

37) In 1949 it took ENIAC (Electronic Numerical Integrator and Computer) 70 hours to calculate 2,037 decimal places of Pi

38) Another name for Pi in Germany is 'die Ludolphsche Zahl' after Ludolph van Ceulen, the German mathematician who devoted his life to calculating 35 decimals of Pi

39) In 1882 Ferdinand Lindemann, proved the transcendence of Pi

40) By the year 1701 the first 100 digits of pi had been calculated


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41) In 1706 William Jones first gave the Greek letter "P" its current mathematical definition

42) In 1768 Johann Lambert proved Pi is irrational

43) Simon Plouffe was listed in the 1975 Guinness Book of World Records for reciting 4096 digits of Pi from memory

44) In 1897, the State House of Representatives of Indiana unanimously passed a bill setting Pi equal to 16/(root 3), which approximately equals 9.2376!

45) In ancient Greece the symbol for Pi denoted the number 80

46) Taking the first 6,000,000,000 decimal places of Pi, this is the distribution:

    0 occurs 599,963,005 times,
    1 occurs 600,033,260 times,
    2 occurs 599,999,169 times,
    3 occurs 600,000,243 times,
    4 occurs 599,957,439 times,
    5 occurs 600,017,176 times,
    6 occurs 600,016,588 times,
    7 occurs 600,009,044 times,
    8 occurs 599,987,038 times,
    9 occurs 600,017,038 times.

    This shows NO unusual deviation from expected 'random' behaviour

47) It is easy to prove that if you have a circle that fits exactly inside a square, then: Pi = 4 x (Area of circle) / (Area of square)

48) Pi does not have to be written in decimal (base 10) notation (3.14159265....). Here it is in binary (base 2) notation:     

    11.0010010000111111011010101000100010000101101000110000100011010011

    You can do lots more stuff with Pi when it is in binary format - like drawing weird pictures of it, or even listening to it. As Pi has 
    an infinite number of places, it is quite possible that any message you liked could be heard somewhere in Pi. It has even been 
    suggested it contains the VOICE OF GOD. In Carl Sagan's book 'Contact' the places of Pi are found to contain a message from 
    the beings that built the universe

49) Half the circumference of a circle with radius 1 is exactly Pi. The area inside that circle is also exactly Pi!

50) It is impossible to 'square the circle'. I.e. You can't draw a square with the same area as a circle using standard straight-edge and compass construction in a finite number of steps. The Greeks were obsessed with trying to do this


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51) Pi is a 'transcendental' number. This means that it is not the solution to any finite polynomial (e.g.: lots of numbers added in a series) with whole number coefficients. This is why it is impossible to square the circle

52) In around 200 BC Archimedes found that Pi was between (223/71) and (22/7). His error was no more than 0.008227 %. He did this by approximating a circle as a 96 sided polygon

53) The volume of a sphere is (4/3 Pi x R cubed) and its surface area is (4 / Pi x R squared)

54) The circle is the shape with the least perimeter length to area ratio (for a given shape area). Centuries ago mathematicians were also philosophers. They considered the circle to be the 'perfect' shape because of this. The sphere is the 3D shape with the least surface area to volume ratio (for a given volume)

55) Pi is of course the ratio of a circle's circumference to its diameter. If we bring everything up one dimension to get a '3D value for Pi'... The ratio of a sphere's surface area to the area of the circle seen if you cut the sphere in half is EXACTLY 4

56) The following are all NEARLY Pi: 101/2, Cube root of 31, 666/212

57) Kochansky found that Pi is NEARLY a root of the equation:  (9x4) - (240x2) + 1492

58) Ludolph Van Ceulen (1540 - 1610) spent most of his life working out Pi to 35 decimal places. Pi is sometimes known as Ludolph's Constant

59) If you approximate the circle with a radius of 1 as a 100 sided polygon, then its area is only accurate to 1 decimal place or 0.0658%

60) At position 763 there are six nines in a row. This is known as the Feynman Point


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61) Pi in base Pi is 10

62) All permutations of 3 arbitrary digits appear somewhere in Pi

63) Starting with the conventional 5-by-5 magic square, and then substituting the nth digit of Pi for each number n in the square, we obtain a new array of numbers. The sum of the numbers in every column is duplicated by a sum of numbers in every row

64) Write the letters of the English alphabet, in capitals, clockwise around a circle, and cross-out the letters that have right-left symmetry, A, H, I, M, etc. The letters that remain group themselves in sets of 3, 1, 4, 1, 6"

65) The sequence 314159 re-appears in the decimal expansion of Pi at place 176451. This sequence appears 7 times in the first 10 million places (not including right at the start)

66) If you approximate the circle as a square then the value you get for Pi is about 10% out. It just goes to show that you shouldn't approximate the circle as a square. Well you wouldn't make square wheels would you?

67) 2 Pi in radians form is 360 degrees. Therefore Pi radians is 180 degrees and 1/2 Pi radians is 90 degrees

68) Pi day is celebrated on March 14th at the Exploratorium in San Francisco (March 14 is 3/14) at 1:59 PST which is 3.14159

69) All the digits of Pi can never be fully known

70) Here's a Pi limerick:

    Three point one four one five nine two
    It's been around forever - its not new
    It appears everywhere,
    In here and in there
    It's irrational I know but its true!