Download e-book for kindle: A Century of Mathematics in America (History of Mathematics, by Peter Duren Richard A. Askey

By Peter Duren Richard A. Askey

ISBN-10: 0821801244

ISBN-13: 9780821801246

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Extra resources for A Century of Mathematics in America (History of Mathematics, Vol 1)

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Copernicus notes himself that some ancient Greeks had posited motion for the Earth, although he knows of this only through vague references in Plutarch. He affirms the right of an astronomer to use such an earthly motion, so long as it is in a circle and uniform about the central point, to save the observable phenomena. His main influence is Ptolemy’s Almagest, and a very large portion of Copernicus’ work can be considered an attempt to transcribe the results of the Ptolemaic system into a system that is heliocentric, in which the Earth has both rotary motion about its axis and orbital motion about the Sun (or, rather, about a point near the Sun), and which is devoid of equants and has all of the planets also moving uniformly in circles of which the primary circle is a heliocentric orbit.

A horseman can toss a ball up in the air and repeatedly catch it. It isn’t left behind as he rides. The dropped and tossed objects share in the motion of ship and rider, and so are not left behind, any more than are clouds, birds and tossed objects by the Earth. Galileo’s most dramatic presentation of “relativity” is in his discussion of what would happen if one performed any dynamical experiment whatever when confined in the hold of a smoothly moving ship. Nothing one did could tell one that the ship was engaged in any one uniform motion or another, rather than being at rest at the dock.

Nothing one did could tell one that the ship was engaged in any one uniform motion or another, rather than being at rest at the dock. In the claims about the straight-line uniform motion of projectiles and in his discussions of the absence of dynamical effects of uniform straightline motion of the laboratory, Galileo is onto core fundamentals of classical dynamics, and of other theories (special relativity, for example) as well. But it is historically important to notice that he also has the idea of natural circular earthly motions and a kind of “circular inertia” as well.

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A Century of Mathematics in America (History of Mathematics, Vol 1) by Peter Duren Richard A. Askey


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