Say I have a sphere of radius $6$ centered at $(3, 4, 5)$.
What's the nearest point on the surface of the sphere to point $(1, 2, 3)$, which is within the sphere?
I feel that this is a minimization problem involving calculus since we can minimize the distance. Is there a way to do this problem without calculus? I want to program it, and using calculus to solve a minimization problem may not be efficient.