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’).