Thursday, November 19, 2009

Visual maths

Many old jokes are based on the stereotype of mathematicians as impractical freaks (as opposed to, say, chemists). Here’s one from my university days (as told by the lecturer in physical chemistry):
How to calculate the area of this figure? (Draws a squiggly figure on a blackboard.) A mathematician spends three days establishing the nature of the function and two days taking the integral. By the end of the week, the problem is solved. A chemist draws the figure on graph paper, cuts it out and weighs it on an analytical balance. The problem is solved in 10 minutes.
Note that the chemist, apart from being ‘simply’ practical, also provides more direct answer to the question.

I prefer graphics to formulae. If I can’t draw a graph, I won’t grasp a concept. Luckily, there are some great resources on the web. For instance, MatematicasVisuales contains a nice collection of Java applets which elegantly visualise a number of mathematical concepts. Examples range from geometry to probability.

This applet illustrates some aspects of the braid theory. Click on ‘draw’, enter a braid word, e.g. BcbACb, and see your braid! The applet also can ‘reduce’, or simplify, the braid diagram, as well as to solve the braid isotopy problem (‘compare’).


1 comment:

Tamara Kulikova said...

Right now you can probably find an applet where you can draw a squiggly figure, provide a scale and get the area back. Which is the approach you took to solve a particular problem that prompted this post.

I am more like that lecturer, I guess - get the scissors and colored paper and check out that braid on your tabletop :)