Kirby Urner wrote:
To break no rules - PyGeo is written in Python. In my case, necessarily.
Art
Good theorem. In a newbie geometry class, I wish they'd run through a lot
more like Pascal's (mention his age when he hit on it), using something a
lot like PyGeo (or just use PyGeo why not?).
Why not PyGeo?
Because you can only create with it by writing in Python, and Python has significant white space ;)
And no buttons.
A big thing for me, before getting into proofs, is to just make clear what a
theorem *asserts* (pretty clear in this case, not always so obvious).
I think too often we're in too big a rush to deal with the proof (which is
likely pre-supplied, if the theorem is old and/or interesting). But with
newbies, let's just linger on the wealth of assertions in our treasure chest
(like this one from Pascal).
Inductive math is legit. So says G. Polya in
"Induction and Analogy in Mathematics -- a guide to the art of plausible reasonning"
http://www.sci.uidaho.edu/polya/biography.htm
From the preface:
"A mathematical proof is demonstrative reasoning, but the inductive evidence of the physicist, the
circumstantial evidence of the lawyer, the documentatry evidence of the historian, and the statistical
evidence of the economist belong to plausible reasoning."
"Everyone knows that mathematics offers an excellant opportunity to learn deomonstrative reasoning,
but I contend also that there is no subject in the usual curricula of the schools that affords a
comparable opportunity to learn plausible reasoning"
I agree with Polya, and think it particularly relevant to computers and math as I think that
computers - again thinking of graphics mostly - is more, to me, a weapon for inductive, than deductive,
mathmatics
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