The God Equation: Euler’s Formula

The jour­ney begins with one of the most cel­e­brat­ed equa­tions in math­e­mat­ics:

where:

• $e$ (Euler’s number, pro­nounced “OY-ler’s number”) is the base of nat­ur­al log­a­rithms, ap­prox­i­mate­ly 2.71828.
• $i$ (the imag­i­nary unit, pro­nounced “eye”) is de­fined by $i^2 = -1$.
• $\cos(x)$ and $\sin(x)$ are the cosine and sine trigono­met­ric func­tions.

This el­e­gant for­mu­la is more than a bridge be­tween ex­po­nen­tials and trigonom­e­try—it is, in Hock­ney’s frame­work, the fun­da­men­tal pat­tern from which ex­is­tence emerges.