Mathematical Magic, Magical Mathematics

"Mathematics is like a beautiful garden. It is full of beautiful flowers, which, if we take care of them, we can witness wonderful magic."
(Rózsa Péter)

Ever since Euler, we have admired the relationship named after him:

e^iπ=-1

It seems almost mysterious how we can get an integer from the operation between two transcendental numbers: e and π, and the imaginary number i. It has long been known – to anyone fascinated by mathematics – that the above formula is the exponential form of -1 in the complex numbers. Paul J. Nahin has devoted a whole book¹ to this fabulous formula of Euler.

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¹ Dr. Euler’s Fabulous Formula – Cures Mathematical Ills, Paul J. Nahin, Princeton University Press, 2006.

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