[BITList] Happy π (pi) day!

[John Feltham]

From a correspondent…


ooroo


 

Happy π day!

Yes, it’s π (pi) day, so once again we celebrate an amazing coincidence of calendar and math.

This is the date of the year that matches the first three digits of the decimal expansion of what should be everyone's favorite mathematical constant, π, because, of course, March 14 is 3/14, and the first three digits of π are 3.14.  This is a day that geeky mathematicians and engineers celebrate, while the rest of you just look at us funny.  Some people even celebrate the π minute (1:59 PM), the π second (1:59:26 PM), and the π moment (1:59:26.5358979… PM), which will happen during our π day social today!

I also recently discovered Europeans think they can’t celebrate π day because they write their dates in an odd fashion (14/3/2012).  However, if you happen to come across any Europeans today, tell them to use the ISO date standard (2013-3-14).  Now the whole world can celebrate π day!

By the way, if you’re coming to the π day social in the Alexandria office, due to overwhelming response, we’ve moved the social to the 4th floor conference room.  See you at 1:45!

Now, for your reading pleasure, below are some π facts for your personal edification.  (Look! no exclamation point after that sentence.)

Enjoy the rest of your week!

1) π is the number of times a circle's diameter will fit around its circumference.
2) The sequence of digits in π so far passed all known tests for randomness, though mathematicians are still looking for a proof that the digits are uncorrelated.
3) Here are the first 100 decimal places of π
            3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679
4) The fraction (22 / 7) is an often used approximation for π. It is accurate to ~0.04025%.
5) Another fraction used as an approximation to π is (355 / 113) which is accurate to ~0.00000849%
6) A yet even more accurate fraction of π is (104348 / 33215). This is accurate to ~0.00000001056%.
7) π 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, superstrings, general relativity, normal distribution, distribution of primes, geometry problems, waves, navigation....
8) There is no zero in the first 31 digits of π.
9) π is irrational. An irrational number is a number that cannot be expressed in the form (a/b) where a and b are integers.
10) π is also a transcendental number. (Transcendental means it is not a solution to any polynomial equation with rational coefficients.)
11) The Babylonians found the first known value for π in around 2000BC -They used (25/8).  This reference to π is on a Middle Kingdom papyrus scroll, written around 1650 BC by Ahmes the scribe.  This means π has been around about 400 times longer than some other weird constants people try to promote.
12) The first person to use the Greek letter π 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.
13) The old memory champion was Hideaki Tomoyori, born Sep. 30, 1932. In Yokohama, Japan, Hideaki recited π from memory to 40,000 places in 17 hrs. 21 min. including breaks totaling 4 hrs 15 min on 9-10 of March in 1987 at the Tsukuba University Club House.
14) After Tomoyori came Hiroyoki Gotu, who memorized an amazing 42,000 digits.
15) The current π memorization champ is Akira Haraguchi, who took 16 hours to recite exactly 100,000 digits of π!
16) π is the 16th letter of the Greek alphabet.
17) A quick definition of π: A transcendental number, approximately 3.14159, represented by the symbol π, which expresses the ratio of the circumference to the diameter of a circle and appears as a constant in many mathematical expressions.
18) 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. And in fact, if you take 10 million digits of π, you actually get exactly 200.
19) In 1931 a Cleveland businessman published a book announcing that π is exactly 256/81.
20) If a billion decimals of π were printed in ordinary type, they would stretch from New York City, to the middle of Kansas.
21) The square root of 9.869604401 is approximately π. The square root of an irrational number is irrational too.
22) A long time ago people thought there was an illness attached to trying to 'square a circle' called Morbus Cyclometricus.
23) After saying (correctly) that π/2 is the value of x between 1 and 2 for which cosine x vanishes Edmund Landau was dismissed from his position in 1934 for teaching in an 'un-German' style.
24) 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 π: 3, 31, 314, 31415, 314159, 3141592, etc. the first thousand numbers of the series include only 4 primes.
25) Given an accurate measurement of the width of the known universe (assume a spherical cow, I mean, universe), 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 π would be necessary.
26) 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 π on a computer.
27) A rapidly converging formula for calculation of π found by Machin in 1706 was pi/4 = 4 * arctan (1/5) - arctan (1/239).
28) In 1949 it took ENIAC (Electronic Numerical Intergrator and Computer) 70 hours to calculate 2,037 decimal places of π.
29) Another name for π in Germany is 'die Ludolphsche Zahl' after Ludolph van Ceulen, the German mathematician who devoted his life to calculating 35 decimals of π.
30) In 1882 Ferdinand Lindemann proved the transcendence of π.
31) By the year 1701 the first 100 digits of π had been calculated.
32) In 1768 Johann Lambert proved π is irrational.
33) Simon Plouffe was listed in the 1975 Guinness Book of World Records for reciting 4096 digits of π from memory.
34) 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!
35) In ancient Greece the symbol for π denoted the number 80.
36) Taking the first 6,000,000,000 decimal places of π, 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' behavior.
37) It is easy to prove that if you have a circle that fits exactly inside a square, then
π = 4 x (Area of circle) / (Area of square)
38) π 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 π when it is in binary format - like drawing weird pictures of it, or even listening to it. As π has an infinite number of places, it is quite possible that any message you liked could be heard somewhere in π. It has even been suggested it contains the VOICE OF GOD. In Carl Sagan's book 'Contact' the places of π are found to contain a message from the beings that built the universe.
39) Half the circumference of a circle with radius 1 is exactly π. The area inside that circle is also exactly π!
40) It is impossible to 'square the circle'. i.e.: You can't draw a square with the same area as a circle using a standard Euclidean straight-edge and compass construction in a finite number of steps. The Greeks were obsessed with trying to do this.
41) In around 200 BC Archimedes found that π 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.
42) The volume of a sphere is 4/3 πr3 and its surface area is 4 πr2.
43) 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)
44) π 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 π'... 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.
45) Kochansky found that π is NEARLY a root of the equation 9x4 - 240x2 + 1492
46) Ludolph Van Ceulen (1540 - 1610) spent most of his life working out π to 35 decimal places. π is sometimes known as Ludolph's Constant
47) 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%
48) At position 763 there are six nines in a row. This is known as the Feynman Point
49) π in base π is 10
50) All permutations of 3 arbitrary digits have been found in π
51) 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.
52) 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"
53) The sequence 314159 re-appears in the decimal expansion of π at place 176451. This sequence appears 7 times in the first 10 million places (not including right at the start)
54) If you approximate the circle as a square then the value you get for π 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?
55) 2 π in radians form is 360 degrees. Therefore π radians is 180 degrees and 1/2 π radians is 90 degrees.
56) All the digits of π can never be fully known.
57) And finally. here's a π limerick:
Three point one four one five nine two
It’s been around forever – it’s not new
It appears everywhere; in here and in there
It’s irrational I know but it’s true!

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