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Get Full Access to Discrete Mathematics And Its Applications - 7 Edition - Chapter 5.2 - Problem 19e
Get Full Access to Discrete Mathematics And Its Applications - 7 Edition - Chapter 5.2 - Problem 19e

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# Pick's theorem says that the area of a simple polygon P in

ISBN: 9780073383095 37

## Solution for problem 19E Chapter 5.2

Discrete Mathematics and Its Applications | 7th Edition

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Problem 19E

Pick's theorem says that the area of a simple polygon P in the plane with vertices that are all lattice points (that is. points with integer coordinates) equals I(P)+B(P)/2-1. where I(P) and B(P) are the number of lattice points in the interior of P and on the boundary of P, respectively. Use strong induction on the number of vertices of P to prove Pick's theorem. [Hint: For the basis step, first prove the theorem for rectangles, then for right triangles, and finally for all triangles by noting that the area of a triangle is the area of a larger rectangle containing it with the areas of at most three triangles subtracted. For the inductive step, take advantage of Lemma 1.]

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##### ISBN: 9780073383095

This full solution covers the following key subjects: theorem, area, points, triangles, pick. This expansive textbook survival guide covers 101 chapters, and 4221 solutions. The answer to “Pick's theorem says that the area of a simple polygon P in the plane with vertices that are all lattice points (that is. points with integer coordinates) equals I(P)+B(P)/2-1. where I(P) and B(P) are the number of lattice points in the interior of P and on the boundary of P, respectively. Use strong induction on the number of vertices of P to prove Pick's theorem. [Hint: For the basis step, first prove the theorem for rectangles, then for right triangles, and finally for all triangles by noting that the area of a triangle is the area of a larger rectangle containing it with the areas of at most three triangles subtracted. For the inductive step, take advantage of Lemma 1.]” is broken down into a number of easy to follow steps, and 120 words. Since the solution to 19E from 5.2 chapter was answered, more than 308 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Discrete Mathematics and Its Applications, edition: 7. Discrete Mathematics and Its Applications was written by and is associated to the ISBN: 9780073383095. The full step-by-step solution to problem: 19E from chapter: 5.2 was answered by , our top Math solution expert on 06/21/17, 07:45AM.

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