1. The problem statement, all variables and given/known data Consider a function f that can be put in the form f(p) = g(|p|) where g : [0,+∞) -> ℝ is C1 with g(0) < 0 and g'(t) > 0 for all t ≥ 0 Assume that |∇f(p)| = 1 for all p ≠ 0 and prove that the set f(p) = 0 is a circle. 2. Relevant equations Given above 3. The attempt at a solution I know i can use |∇f(p)| = 1 because some circle parametrization will be (cos(p), sin(p)) but I can't figure out really where to start.