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Computers are being used more and more to solve geometric problems, like modeling physical objects such as brains and bridges.

How many different possible triangulations can be constructed for a regular hexagon?

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How many triangles will the triangulation of a simple polygon with \(51\) sides contain?

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Suppose a convex polygon has vertices \( v_{0}, \ldots, v_{n}\). In any triangulation we can assign a weight to each triangle to be the length of its perimeter. Let the cost of a triangulation be the sum of the weights of its component triangles. Write an algorithm to find a triangulation with the minimum cost.

If \(A\) the minimum cost of triangulation for a convex polygon with the the coordinates below, what is the value of \(\left\lfloor A \right\rfloor \)?

\[(-2,3), (4,0), (8,7), (5,10), (1,10)\]

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