Continuous Functions that are Differentiable Nowhere

An introduction to the Blancmange Curve, a function that is continuous everywhere but differentiable nowhere. After watching this video, the viewer should have an understanding as to how to build the Blancmange Curve from scratch by adding together an infinite number of iterations of a functions known as “Triangle Waves.” In addition to a formal proof of the continuity and non-differentiability of the Blancmange Curve, this video includes more informal ways of thinking about the function as well as a brief review of differentiation and the conditions required for differentiability. Lastly, this video should expand the viewer’s horizons by exploring a function whose properties are mathematically sound but extremely counterintuitive.
Made by: Henry Dana, Emmanuel Gomez, Daniel Rabizadeh