The preoccupations of mathematicians can seem curious and strange to normal people. They sometimes expend great energy proving results that appear glaringly obvious. One such result is called the ...

We show that every rectifiable simple closed curve in the plane can be continuously deformed into a convex curve in a motion which preserves arc length and does not decrease the Euclidean distance ...

First stated by Camille Jordan in 1887, the Jordan Curve Theorem says that any simple closed curve in a plane divides the plane into two disjoint regions (inside and outside of the curve). First ...