> Any problem stated as "let ABC and P inside" or "let > ABCD > 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.