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Topic: The original geometry problem
Replies: 5   Last Post: Dec 7, 2010 11:34 PM

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Mary Krimmel

Posts: 629
Registered: 12/3/04
Re: The original geometry problem
Posted: Dec 7, 2010 12:20 AM
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> Any problem stated as "let ABC and P inside" or "let
> a quadrilateral" may be reduced to a "let ABC a
> triangle and
> D a point inside the circumcircle of ABC", eventually
> renaming the
> points.
> Any such problem in which all angles are multiples of
> 10 deg can
> then be overlayed on a regular 18-gon and its
> diagonals and is then
> equivallent to "in a regular 18-gon these such
> diagonals intersect
> in one point".

Philippe, I haven't quoted most of your original message because it is long and not hard to find. The theorem and the attached files showed what I now realize I had been groping for, but never could have found. Thank you for this superb demonstration.

Here are two embarrassingly naive questions: (1) Is the regular 18-gon constructible? I think not; but if it is, then where can I find a demonstration (verbal instruction)?
(2)In what sense is an angle in a problem "given", when it cannot be used to construct a solution or proof? Perhaps there is no final answer to this question. I appreciate your recent remark that the answer to "What is pure geometry" is subjective.

Thanks for responses from anyone.

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