Friday, March 18, 2011

In Belated Honor of π Day

In Which a Startling Omission is Noticed, and Thence Rectified, in Manner of Honoring a Well Known Transcendent Constant, Who's Derivation By Archimedes Very Nearly Led to The Discovery of One of The Fundamental Bases of Calculus Ages Before Liebniz or Newton Had Even Been a Mere Twinkle in their Great x 10nth Grandfathers' Eyes

Ah π! While it may not have the invasive prescense of e, the bewitching mystique of ζ(3), or the underappreciated allure of γ; there is still a place in any mathematician's heart for the first transcendental1 that they meet. Presented for purposes of both Intrigue and Felicity is Ramanujan's well known Formula for π2:


The proof is left as an exercise for the reader.

1the poetically named transcendental numbers are any element of the Complex Numbers that is not the solution of any polynomial with integer coefficients

2although one is left to wonder why he even bothered writing it down, it is such an obvious equivalence