Page 7 introduces the Jordan curve theorem. The Jordan curve theorem is first deduced by this method. Let "C" be a Jordan curve in the plane R. One may ask whether other shapes can be inscribed into an arbitrary Jordan curve. The same argument works for a piecewise differentiable Jordan curve. In particular a quasicircle is a Jordan curve. A Kleinian group that preserves a Jordan curve is called a quasi-Fuchsian group. This observation may be mathematically proved using the Jordan curve theorem. The Jordan curve theorem implies that there is exactly one such coloring. It is also known that any Jordan curve admits an inscribed rectangle. A simple closed curve is also called a Jordan curve. Given the Jordan curve theorem, the Jordan-Schoenflies theorem can be proved as follows. The Jordan curve is given by a continuous function on the unit circle. The image of the real axis is a Jordan curve dividing C into two components.