Linkdump from today's mathematical explorations
Beautifully graphs with clear explanations and interpretations are one of my favorite things. This blog post by the 538 blog is a prime example of just that.
http://fivethirtyeight.com/features/four-strikes-and-youre-out/
While discussing counterexamples with a student today I mentioned the Weierstrass function. Here is an great blog post which gives some backstory to the development of and reaction to the function that is everywhere continuous and nowhere differentiable. A thumb on the nose to Newton.
http://nautil.us/issue/11/light/maths-beautiful-monsters
http://www.math.washington.edu/~conroy/general/weierstrass/weier.htm
The Weierstrass function is just one of many "Pathological Functions": http://en.wikipedia.org/wiki/Pathological_%28mathematics%29
There are many here http://math.stackexchange.com/questions/740/useful-examples-of-pathological-functions and here http://mathoverflow.net/questions/22189/what-is-your-favorite-strange-function. There is also an excellent book titled Counterexamples in Analysis which covers even more of these pathological functions in great detail. http://www.amazon.com/Counterexamples-Analysis-Dover-Books-Mathematics/dp/0486428753
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