Thursday, April 3, 2014

Beautiful graphs and beautiful monsters

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


No comments:

Post a Comment

Thank you for sharing your thoughts.