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Let a planar polygon P without selfintersections be given through the plottools:-polygon command.
How to find its triangulation as a set of triangles (The indication of common sides is desired too.) in an optimal way with Maple? This is used in the finite element method.

Triangulation

Let a convex polygon, for example Q:=polygon([[0,2],[1,4],[4,4],[5,1],[3,0]]), be given.
How to find the disk of the biggest radius which is contained in Q?
How to find the disk of the smallest radius which contains Q? Of course, with Maple.

Let a convex polygon, for example Q:=polygon([[0,2],[1,4],[4,4],[5,1],[3,0]]), be given.
How to find the rectangle of the biggest area which is contained in Q?
A procedure is required. This problem seems to be more complex than the previous one.

Let the polygon P:=polygon([[0,2],[1,4],[2,3.5],[4,4],[5,1],[4,0.75],[3,0]])

be given.
How to find the rectangle of the minimal area which contains P? Of course, with Maple. Is it a rectangle having a side parallel to the longest diagonal of P?
The same problem in the general case: a procedure is required.

THis is part of the code I used in the geometry package:

with(geometry):

circle(c,50811.89143+x^2+y^2-61.91881776*x-446.5619114*y = 0);

line(l,1621.451347-0.1838809e-1*x-7.2593834*y = 0):                               

draw([c,l]);
intersection(X,c,l,[F1,F2]);

Hello

 

I've to do some geometric work ; the problem is that it seems to me there will be no other solution than trying a different approach of the problem, due to huge amount of time required by computation...

 

However, I would have liked to learn how my program can be fastened. I've heard of multi threaded programming model ; could it be applied here ?

To simplify, I have a initial point (its coordinates). My procedure...

Look here concerning this theorem, which states that in any triangle, the three points of intersection of the adjacent angle trisectors form an equilateral triangle, called the Morley triangle.

This is the continuation of the question . We have a convex polygon with 9 (a natural number n>3)  vertixes  such that every its point, which is not a vertex, does not belong to three diagonals of that polygon. The question is:
how to count  the number of the sets of the polygon partition by its diagonals?
I have in mind a Maple procedure, not the formula. The answer is 154.

a convex  planar polygon with 9 vertexes such that every its point, which is not a vertex, does not belong to three diagonals of that polygon? This is of interest in connection with a certain combinatorical problem.

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