My Favorite Equation

Recently a student sent me an article about a popular book that outlines history in terms of 17 revolutionary equations. 

Here’s what I wrote back to him:

Just for the record, here's my all-time favorite equation:

First, let me admit that the way I just wrote it involves some abuse of notation. Properly, it should be written this way:

But I think the former form is justified for the visual effect.

To the eye, it seems to equate two closed curves that have symmetry: A regular triangle, with 3-fold rotational symmetry (the minimum possible) and the circle with infinite rotational symmetry (the maximum possible).

But as a mathematical formula, it represents the “generalized Laplacian equation."

This equation is one of the broadest statements of balance in nature. Phenomena as different as three-dimensional thermodynamic equilibrium and four-dimensional relativistic motion can be described by this equation.

To me, it's a reminder that "mutually-canceling polarities" play a fundamental role both in the physical world as described abstractly by scientists and in the spiritual world as described concretely by mystics.