Pappus Chain and Circle Inversion

This is really cool. I'm sure the guy would get on my nerves after a while but I do enjoy mathematical enthusiasm.

Creation Ex Nihilo?

This is quite a good puzzle.

From Random Polygon to Ellipse

Here is a fascinating and quite unexpected result from Shape Analysis.

I came across it at Matthen's blog which is great resource for visualising simple but intriguing mathematical results.

"Draw some random points on a piece of paper and join them up to make a random polygon. Find all the midpoints and connect them up to give a new shape, and repeat. The resulting shape will get smaller and smaller, and will tend towards an ellipse".

The visualisation is here and the paper demonstrating the result is here.

Some Maths Tricks - Calculating Square Roots

I love these types of "calculating-tricks", i.e. simple procedures for calculating arithmetic operations on numbers. This one is a good one and its fun to try to see out why it works.

A full explanation can be found here.

Barry Mazur on Evidence

Brandon Watson over at Siris puts up a link to a very interesting article by Harvard mathematician, Barry Mazur, on the concept of "Evidence" in mathematics and science.