Question
In: Advanced Math
A polygon is called convex if every line segment from one vertex to another lies entirely...
A polygon is called convex if every line segment from one vertex to another lies entirely within the polygon. To triangulate a polygon, we take some of these line segments, which don’t cross one another, and use them to divide the polygon into triangles. Prove, by strong induction for all naturals n with n ≥ 3, that every convex polygon with n sides has a triangulation, and that every triangulation contains exactly n − 2 triangles. (Hint: When you divide an n-gon with a single line segment, you create an i-gon and a j-gon for some naturals i and j. What does your strong inductive hypothesis tell you about triangulations of these polygons?)
Solutions
Expert Solution
Summary: Thus, by the
principle of Strong Induction, we have proven the statement to be
asked to prove in question. The hint given the question was very
useful in the solution.
Colby Messinger answered 7 months agoRelated Solutions
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prove the lemma
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