Ramanujan's constant

Ramanujan's constant

Ramanujan's constant is the transcendental number [MathWorld|title=Transcendental Number|urlname=TranscendentalNumber gives e^{pisqrt{d, d in Z^*] e^{pi sqrt{163.

Its value is extraordinarily close to an integer:

:262,537,412,640,768,743.999 999 999 999 25ldots [MathWorld|title=Ramanujan's Constant|urlname=RamanujanConstant; can also be verified on an arbitrary-precision calculator.] approx 640,320^3+744.

Alternatively,

:262,537,412,640,768,743.999 999 999 999 25ldots [http://groups.google.com.ph/group/sci.math.research/browse_thread/thread/3d24137c9a860893?hl=en#] approx 12^3(231^2-1)^3+744

where similar simple expressions can be given for the other Heegner numbers.

History

It was discovered in 1859 by the mathematician Charles Hermite. [cite book
last = Barrow
first = John D
title = The Constants of Nature
publisher = Jonathan Cape
date = 2002
location = London
id = ISBN 0-224-06135-6 ] In a 1975 April Fool article in "Scientific American" magazine, [cite journal
last = Gardner
first = Martin
title = Mathematical Games
journal = Scientific American
volume = 232
issue = 4
pages = 127
date = April 1975
publisher = Scientific American, Inc ] "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.

References

External links

*
* [http://www.geocities.com/titus_piezas/Ramanujan_a.htm Ramanujan's Constant And Its Cousins]


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