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The Last Word


Bazza

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Oh, certainly: everyone learned their math out of Euclid. If you go reading a lot of the treatises from that era ... Kepler and Newton I know from reading them ... all of the arguments and developments are of a geometric nature based out of Euclid. Kepler's 2nd Law (equal areas swept out in equal intervals of time) was framed that way. It is identical to the law of conservation of angular momentum in what it says about how planets move around their orbits. The latter is formed in terms of infinitesimals (at all times the rate of change of L, where L-vector = r-vector cross-product v-vector, = 0) in the calculus-based way mechanics is taught now. The geometric methods are sort of cumbersome, and hard to generalize to other situations (systems of more than two objects in mutual orbits, for instance).

 

They struggled, though, with infinite sums of infinitesimal elements, as the infamous Zeno's Paradox shows.

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Well, if you let the arguments in the classical statement of the paradox confuse you, you have utterly no hope of passing a calculus class. And there do seem to be people who let those arguments confuse them, and predictable carnage happens when they try taking calculus.

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