Continuous Nowhere Differentiable Functions

Abstract

In this presentation we study functions that are continuous everywhere on their domain but differentiable nowhere.  One such function is the function whose graph is called the Kiesswetter curve.  First we construct the curve and the piece-wise function that represents that curve.  We prove several key properties of the function that gives us insight to why this function is continuous on the unit interval.  We then prove the continuity and nondifferentiability of the function.