The God Equation via Euler’s Identity

A par­tic­u­lar­ly strik­ing case of Euler’s for­mu­la ap­pears when $x = \pi$:

or, re­arranged:

where:

• $\pi$ (the Greek letter “pi,” pro­nounced “pie”) is the math­e­mat­i­cal con­stant, ap­prox­i­mate­ly 3.14159, rep­re­sent­ing the ratio of a circle’s cir­cum­fer­ence to its di­am­e­ter.

This iden­ti­ty unites the five most im­por­tant num­bers in math­e­mat­ics: $e$, $i$, $\pi$, $1$, and $0$. As Hock­ney em­pha­sizes, this iden­ti­ty is a pow­er­ful and el­e­gant math­e­mat­i­cal state­ment, cel­e­brat­ed for its beauty and its abil­i­ty to cap­ture the unity of math­e­mat­ics in a single ex­pres­sion. It shows how the God Equa­tion, even in its sim­plest form, con­tains the seeds of all re­al­i­ty.