No matter how the globe is triangulated, Euler’s formula holds. Euler’s Gem provides a bridge between geometry and topology. In geometry, lengths and angles are fixed.

When invited to elucidate its meaning, the visitor just chuckled. In fact, this equation, familiar to mathematicians and greatly admired for its elegance, is known as Euler’s Identity.

We provide a proof of Euler’s sine product formula using simple techniques of calculus and illustrate how our method can be used to prove similar product formulas for cosine as well as hyperbolic sine ...

A stretch too far, perhaps, but Nahin’s tale of the formula ei π + 1 = 0, which links five of the most important numbers in mathematics, is remarkable.