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# Re: Geometry, algebra, and computers

It seems that prior to the time of Newton all proofs were geometric.
Newton lived at a time of transition from geometric to algebraic >proofs
and apparantly delayed publication of his papers while he found
the 'correct' geometric proof for propositions already proven
algebraically. Modern communication may be opening up to us new forms
of proof. We may live at a similar time of transition. If we do,
then we will be employing double proofs in the same way that Newton
did. An example is the observation of beats between two waves. These
are easily seen in a computer simulation but we still feel it
necessary to derive the algebraic expression and explain it to the
students.

My question is: Do you employ any 'double' explanations in your >physics
teaching? One of which is algebraic while the other uses
modern communications such as videos and computer simulations.

Michael,
You missed part of Newtons motovation for using geometry. He felt
that classical geometry was a proven system that had stood the test of time
and he wanted to append his theory on to that structure and not the new
fangled Cartesian Geometry with whose followers he had many dissagreements.
It was removing the fluxian theory (his calculus) that caused the delay. His
fluxian theory looks far more like geometry then the Leibnizian calculus we
use today.
....
Gary Karshner

I think that if you get and read the first part (up until Newton goes to
the Mint) of Westfall's book on Newton, Never at rest, (still I think the
most authoritative) you would not come away with either of these
descriptions.

From almost the first time I taught I can remember using multiple
demonstrations. Geometric and then algebraic for example.

Dewey

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Dewey I. Dykstra, Jr. Phone: (208)385-3105
Professor of Physics Dept: (208)385-3775
Department of Physics/SN318 Fax: (208)385-4330
Boise State University dykstrad@varney.idbsu.edu
1910 University Drive Boise Highlanders
Boise, ID 83725-1570 novice piper
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