A fantastic site about fractals. Speaking of beauty in math.

ghareth_3 asked about math poetry.

I've never heard it called math poetry, but there are certainly beautiful equations and proofs. "Beautiful" tends to convey elegant, simple, yet non-trivial. A beautiful expression of math is one which states something that matters in a very elegant way.

Probably the expression most widely considered beautiful is the ( Read more... )

"f(x) takes on the value 1 at all the chairs" -- my professor, regarding functions defined on things other than numbers

Further to my post "Sequences and differences", I realized that finite differences are indeed very much like differentiation.

First, what is differentiation? It's the study of the slope of a continuous function (a curve on a graph). More specifically, it gives you the slope at a single point on the curve. That may not sound like it makes sense, ( Read more... )

While I was in Portland, vruba introduced me to a curiosity: Take the sequence x21, 4, 9, 16, 25, ... (i.e. 1 squared, 2 squared, 3 squared ( Read more... )