Patrick Schmidt ? The Koch Curve and its Properties, Advisor Dr. Otero
Reading Helge Von Koch?s paper, On a Continuous Curve without Tangents Constructible from Elementary Geometry, made me aware of some glaring abnormalities about the Koch curve. The area underneath the curve has a finite value; however the length of the perimeter is infinite. Also, the curve is continuous everywhere, but has no points which are differentiable. My research has gone in depth to discover how these properties are possible.