Pi (from Greek perifereia, "circumference"): the 16th letter of the Greek alphabet and the circumference of a circle with a radius of 1. Pi is the best known ►real number — that is, the bestknown number with an infinite number of nonrepetitive digits after the decimal point. _{} Since antiquity mathematicians have cut their teeth attempting to calculate the mathematical constant π. The first attempt was made in the Bible (Kings I 7.23): "Then he made the molten sea. It was round, ten cubits from brim to brim, and five cubits high, and a line of 30 cubits measured its circumference." Thus, according to the Bible's directions for the construction of a round bathtub, the value of π is 30/10 = 3.0. For what is supposed to be the infallible word of God, this is not too impressive, especially since around the same time the Egyptians were able to calculate much more precise values. Their approximate value of π was (4/3)^{4}, which comes short of the actual value by less than 1%. ►Archimedes estimated the value of π as 3.14145 by approximation, using a polygon with 192 sides. After that, however, there were no further attempts to determine π until the end of the middle ages. In 1593 the French mathematician François Viète discovered an esthetically pleasing π calculation formula, which however proved to be difficult to apply in practice: the infinite product _{} In 1596 Ludolph van Ceulen delivered a calculated π value that was exact up to 35 digits after the decimal point. He had dedicated 30 years of his life to reaching this result. His calculation did not rely on Viète's formula but proceeded in the manner of Archimedes' method by adding the lengths of the sides of a gigantic polygon with 2^{62} sides: π_{Ludolph} = 3.1415926535897932384626433832795029 Ludolph van Ceulen was so proud of this number that he had it engraved on his tombstone. It was long assumed that this achievement was unsurpassable. However, in 1650 the British mathematician ►John Wallis came up with a new formula: _{} Wallis arrived at this product by a successive approximation to the circular integral _{}in the range from 0 to Pi. But even Wallis's formula converges rather slowly, so that many terms must be multiplied to obtain just a few πdigits after the decimal point . The same can be said for the first πapproximation as ►infinite sum published almost simultaneously in 1671 and 1674, respectively, by the Scottish mathematician James Gregory and the German philosopher/mathematician ►Gottfried Wilhelm Leibniz: _{} The first useful approximation with a quick convergence rate was discovered in 1736 by the then 19yearold Swiss mathematician Leonhard Euler: _{} In 1761 Johann Lambert proved that π has infinitely many digits after the decimal point and therefore is an ►irrational number. The transcendence of π was discovered in 1882. Since then we know that it is impossible to determine the exact value of π by means of a finite formula. Contemporary research on π seeks to identify some patterns or regularities among the digits after its decimal point. To date none have been found. The sequence of digits appears to be entirely random. This also means that any arbitrary sequence of digits must be contained somewhere in the infinite number of digits after the decimal point of π. Thus, Pi contains an encoded version of a complete library of all books that have ever been or will ever be written, including this dictionary and all books on the calculation of π. At this point the Japanese have adopted the number π. The current record for the number of digits after the decimal point has reached 5 trillion and was established 2010 by Shigeru Kondo and Alexander Yee with a selfmade super computer. If you want to participate in the Pi digits record hunt, you can begin with the following liteC (►www.3dgamestudio.de) program that calculates the first 1000 digits: int main() { video_screen = 0; wait(1); printf("\nThe first digits of Pi:\n"); long a=10000, b=0, c=14000, d, e=0, f[16000], g, i=0; for(; b<c; b++) f[b]=a/5; for(; c>0; c=14) { d=0; g=c*2; for(b=c;b>0;d*=b) { d+=f[b]*a; g; f[b]=d%g; d/=g; g; b; if (b == 0) break; } printf("%.4d",e+d/a); e=d%a; i++; if (i%19==0) { wait(0.2); printf("\n"); } } printf("\n%i digits printed",i); } The world record for memorizing digits of π after the decimal point was set by Akira Haraguchi on July 2, 2005, who memorized a total of 83431 digits. In case you aspire to top this achievement, try memorizing the following numbers — but be aware that to break Haraguchi's record, you'd need to memorize 30 times as many digits as there are here: 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679
8214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038196
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