What made you realize that math is beautiful?(math.stackexchange.com)
math.stackexchange.com
What made you realize that math is beautiful?
http://math.stackexchange.com/questions/323334/what-was-the-first-bit-of-mathematics-that-made-you-realize-that-math-is-beautif/323455#323455
"Mathematics, rightly viewed, possesses not only truth, but supreme beauty — a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as poetry."
In fact, as one can see, Russell goes out of his way to specify that he's not speaking of visual beauty, but another kind. I know of many examples of mathematical beauty -- here's one I've been investigating recently:
A planet or comet in an elliptical orbit conserves energy -- its kinetic energy (based on its velocity) and its potential energy (based on its distance from the parent body) always sum to a constant. In his Second Law, Kepler noted that an elliptical orbit sweeps out equal areas in equal times, which is true, but Kepler didn't actually know why. It turns out that his Second Law demonstrates the conservation of energy.
Two equations describe the energy in an elliptical orbit -- one describes the orbit's kinetic energy:
The other describes the orbit's potential energy:
In the kinetic equation, velocity governs the dynamic change in kinetic energy, and in the potential equation, the object's distance from the parent body (r) governs the dynamic change in potential energy. Amazingly, if you create a model of an elliptical orbit, the orbiting object speeds up and slows down in a way that forces a perfect constant sum of potential and kinetic energy -- and, as a side effect, shows perfect agreement with Kepler's Second Law.
Read more here: http://arachnoid.com/conservation_of_energy/index.html#Plane...
And make sure to scroll down to see the orbit animation.