29) A long time ago people thought there was an illness attached to trying to 'square a cirle' called Morbus Cyclometricus.
30) Pi in fraction form is - 837393900/266550757.
31) After saying (correctly) that pi/2 is the value of x between 1 and 2 for which cos 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 was pi/4 = 4 * arctan (1/5) - arctan (1/239).
37) In 1949 it took ENIAC (Electronic Numerical Intergrator 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.
41) In 1706 William Jones first gave the Greek letter "π" 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/(sqrt 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
* = 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 / Euclidean straight-edge and compass construction in a finite number of steps. The Greeks were obsessed with trying to do this.
51) Pi is a 'transcendental' number. This means that it is not the solution to any finite polynomial (eg: 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*r3 and its surface area is 4/*r2.
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 10/* (97 + 9/22)1/4 9/5 + (9/5)1/2 (19 (7)1/2) / 16 1.1 x 1.2 x 1.4 x 1.7 (296/167) 2
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
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 place176451. 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 14 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
Its been around forever - its not new
It appears everywhere In here and in there
Its irrational I know but its true !