Ramanujan's constant
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For more details on this topic, see Heegner number.
Ramanujan's constant is the transcendental number[1] 
.
Its value is extraordinarily close to an integer:
Alternatively,
where similar simple expressions can be given for the other Heegner numbers.
[edit] History
This number was discovered in 1859 by the mathematician Charles Hermite.[4] In a 1975 April Fool article in Scientific American magazine,[5] "Mathematical Games" columnist Martin Gardner made the (hoax) claim that the number was in fact an integer, and that the Indian mathematical genius Srinivasa Ramanujan had predicted it — hence its name.
Note that Ramanujan did make use of such numbers in his work, for instance a fast converging series expansion he gave for π is related to 
, but of course he made no such prediction.
[edit] References
- ^ Weistein, Eric W., "Transcendental Number" from MathWorld. gives
, based on Nesterenko, Yu. V. "On Algebraic Independence of the Components of Solutions of a System of Linear Differential Equations." Izv. Akad. Nauk SSSR, Ser. Mat. 38, 495-512, 1974. English translation in Math. USSR 8, 501-518, 1974. - ^ Weistein, Eric W., "Ramanujan's Constant" from MathWorld.; can also be verified on an arbitrary-precision calculator.
- ^ http://groups.google.com.ph/group/sci.math.research/browse_thread/thread/3d24137c9a860893?hl=en#
- ^ Barrow, John D (2002). The Constants of Nature. London: Jonathan Cape. ISBN 0-224-06135-6.
- ^ Gardner, Martin (April 1975). "Mathematical Games". Scientific American (Scientific American, Inc) 232 (4): 127.
