Ramanujan's constant

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For more details on this topic, see Heegner number.

Ramanujan's constant is the transcendental number[citation needed] e^{\pi \sqrt{163}}.

Its value is extraordinarily close to an integer:

262,537,412,640,768,743.999\ 999\ 999\ 999\ 25\ldots [1] \approx 640,320^3+744

Alternatively,

262,537,412,640,768,743.999\ 999\ 999\ 999\ 25\ldots [2] \approx 12^3(231^2-1)^3+744

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

[edit] History

It was discovered in 1859 by the mathematician Charles Hermite.[3] In a 1975 April Fool article in Scientific American magazine,[4] 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.

[edit] References

  1. ^ Eric W. Weisstein, Ramanujan's Constant at MathWorld.; can also be verified on an arbitrary-precision calculator.
  2. ^ http://groups.google.com.ph/group/sci.math.research/browse_thread/thread/3d24137c9a860893?hl=en#
  3. ^ Barrow, John D (2002). The Constants of Nature. London: Jonathan Cape. ISBN 0-224-06135-6. 
  4. ^ Gardner, Martin (April 1975). "Mathematical Games". Scientific American 232 (4): 127. Scientific American, Inc. 

[edit] External links