# The Hofstadter Transcendental Triangle Variety

The Hofstadter point is a transcendental triangle center. So this gets me thinking: well, if I have three noncollinear complex numbers, that’s a triangle, right? And for three complex numbers $u,v,w$ I can treat them as elements of $\mathbb{C}$

So here’s the recipe: the Hofstadter Transcendental Triangle Variety $X$ is the set of points in $(u,v,w)\in\mathbb{C}^{3}$ such that given some point $\rho\in\mathbb{C}$, the “Hofstadter mean” of those three points is $\rho$.