Take a look at this set of beautiful animations that illustrate / explain common mathematical concepts much better than words ever could:
I especially love the water-pouring one with the squares on the sides of the right triangle. This illustrates the Pythagorean Theorem (a² + b² = c²) in such a beautiful way. You may have seen this diagram before – the three sides of a right triangle drawn into squares. BUT the animation of pouring water from the two smaller squares into the larger square, filling it perfectly, is among the purest illustrations that math is truly an art.
What else? The one about the exterior angles of a convex polygon always adding up to 360° is so simple and so perfect. The algebraic proof of this is not too hard to understand, but it’s a lot of writing. In a few seconds, you can see a great illustration of what happens when the polygon’s sides shrink down to nothing. What is left is a bunch of angles that clearly total 360°.
I’ve chosen the two above examples to talk about mainly because they would be of the most illustrative use to my own students. Still, I love each and every one of the lovely little animations there!
Let me know what you think! Did something suddenly make sense to you?