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More generally, an account that starts at $1, and yields (1+R) dollars at simple interest, will yield eR dollars with continuous compounding.
Suppose that a gambler plays a slot machine that pays out with a probability of one in n and plays it n times. Then, for large n (such as a million) the probability that the gambler will win nothing at all is (approximately) 1 ⁄ e.
An immortal, eternal virgin, yes, one who is frozen in time. Must Time destroy her beauty, or can there be temporal mathematical beauty, too?
I find the theorem on unique factorisation of integers into primes beautiful.
any one else struck by the beauty of math?
Maths is a very broad field, with a lot of variety, I think most people would consider something mathematical to be beautiful, if they looked at enough. But I think that's true for pretty much any field that's broad and varied. For example, disease is quite repugnant but, if the edition of Encyclopedia Britannica that my mother owns is reliable, any animal with advanced rabies, even a sheep, will attack a dog, and rabies reaches full strength when harboured by dogs. I think this has a kind of beauty, of course it's a different beauty from the beauty of Archimedes' informal method of proof, but that, again, is quite different from the beauty of Vietnamese cuisine, etc.
There's also the question of mathematical pathologies and false proofs, can these be beautiful? or just amusing?
In the case of maths, is it really a question of beauty, or is it appreciation? It might be interesting to consider ugly proofs, does anyone have any examples?
I went from studying the visual side of math into the study of Shogi, of all things.
I play at BrainKing, if you'd like a game, feel free to send me an invitation.
You didn't say what you played. FICS is chess.
The Shogi variants have eaten up my free time.
At the moment I only play shogi, three checks chess and tablut.I've secured permission for BrainKing to host Kyoto shogi and renge shogi, but no action on that yet.
I just looked up tablut. Seems like a nice game. I didn't know of 3 checks chess. Looked it up. Sounds good. I would give 3 checks chess a try, for sure.
I can hard-ly play GO...or Chess.
[CENTER]Used to play Chequers with great-grand-father Greenland we called him. He lived there (retired peoples Home). I remember he smoked cigars and my Mother cleaning afterwards.
Is tablut abbess ?
Checkers is a great little game in itself. The kings can move backward, and that is their only power. And yet in a forward world it's quite a power. Also the simple symbolism of stacked pieces. Pretty great. And let's not forget the triple or quadruple jump. In Chess, you can only capture one piece at a time.
On this page there's a short discussion of ugly and elegant proofs, according to Einstein's taste
I went from studying the visual side of math into the study of Shogi, of all things. This is Japanese chess, and in some ways it's superior to "Chess." At the moment, I like this phrase: ratio is visual. Not that ratio is only visual...
At the moment, I see strategic board games as dynamic mathematical sculptures. Does anyone around here enjoy chess, shogi, stratego ? Has anyone here ever created such a game, or modified one? It's always been an interest of mine. Lately, I've cooked up a variant of Shogi that further emphasizes its mono-directionality.
Anyone else see the art/beauty in this sort of thing?
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