Selfsimilarity of "Riemann's nondifferentiable function"

Abstract

This is an expository article about the series f(x) = 1 X n=1 1 n 2 sin(n 2 x); which according to Weierstrass was presented by Riemann as an example of a continuous function without a derivative. An explanation is given of innitely many selfsimilarities of the graph, from which the known results about the dierentiability properties of f(x) are obtained as a consequence.