Enjoyed Bryce Summers’ math proof via Green’s Theorem. His WordPress site has a number of interesting math, computer science and algorithm related blogs.

# Introduction

In this blog post, I will prove that a very elegant theorem for the area of a simple polygon based on Green’s theorem is true. Please note that Green’s theorem is a standard theorem from multi variable calculus. This theorem is very useful for computing the area of polygons in computer programming applications and in physics simulations.

# Problem Statement

Let a fixed, yet arbitrary simple polygon **P** be defined by a list of points **L** in the euclidean plane.

Let $latex L_{k}$ denote the *k*th point in **L** and let $latex L_{n + 1} = L_{1}$

Let **Area(l)** be the area of the polygon represented by the given list of points.

For any point **p **$latex in$** L** let the Cartesian *x* and *y* coordinates of **p** be denoted by **p.x** and **p.y** respectively.

Let **Area(a, b)** $latex = frac{1}{2}(a.x + b.x)(a.y – b.y)$, where **a** and **b** are…

View original post 1,054 more words

## Leave a Reply