Here is a fantastic website sight called Dimensions that is beyond impressive when it comes to illustrating the beauty of Mathematics. Watching these videos is like listening to music. You don't have to entirely understand it all to appreciate it.
Next time your middle or high school student is questioning the value of spending another moment of his life devoted to his math homework - just let him watch some of these videos. Or - if you are homeschooling - this is "all you'll ever need" - at least in terms of inspiration - to teach math, math history or anything else to do with math.
Math ultimately is a search for truth and understanding , rather than a form of calculation and measurement. It is the koans in math that really make it interesting. Nothing like math to take us to the limits of logic and therefore beyond the mind itself - much like beauty.
I can even imagine toddlers being fascinated by these videos - like listening to Mozart. One does not need to be able to compose such music in order to enjoy it.
http://www.dimensions-math.org/Dim_regarder_E_E.htm
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