What is Ramanujan's Constant?

e^(π√163): terrifyingly close to a whole number

Table of Heegner numbers and how close e to the pi root is t

Related topics

Pi (π) → Gelfond's Constant → Euler's Number e → Euler's Identity → Taylor Series →

Key facts about Ramanujan

Srinivasa Ramanujan (1887-1920) was a self-taught Indian mathematician who produced extraordinary results. His 1914 series 1/pi = (2*sqrt(2)/9801) * sum of (4n)!(1103+26390n)/((n!)^4 * 396^(4n)) adds about 8 decimal digits per term and remains the basis of modern pi computation. His partition function formula was the first exact result for p(n). Ramanujan's constant e^(pi*sqrt(163)) ≈ 262537412640768743.99999999999925 is nearly an integer due to properties of the j-function.

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Why is Ramanujan's constant so close to an integer?

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