Non-differentiable continuous functions exist

Translation: continuous curves do exist which have no tangent. I do believe men have been shot and killed for making less controversial statements.

This statement, if understood, should shock you out of your socks. It basically means that there are continuous curves that have no tangent! Can you imagine what such a curve looks like? Hint: are you good at fractions?

http://www.math.washington.edu/~conroy/general/weierstrass/weier.htm

http://en.wikipedia.org/wiki/Weierstrass_function

http://www.math.cmu.edu/%7Ebobpego/21132/nowhdiff.pdf