"Lifting Map"

[modularformsboy]

I feel like a college freshman again.

There's a one-to-one correspondence between the set of circles in the plane and intersections of planes with the parabaloid z = x^2 + y^2. So you can turn the InCircle question into a half space test by passing your test point through the "Lifting Map" (x, y) -> (x, y, x^2+y^2)

Comments

[lindseykuper]

Ah! That's a special case of the kernel trick!