False Proofs: Geometry

We have been looking at some classic “false proofs” or “fallacies”, where a seemingly valid proof shows something clearly false to be true. The goal is to learn from these, how to distinguish a valid proof from an error. In a post from last year, What Role Should a Figure Play in a Proof?, I …

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Area of a Plot of Land

The last four posts dealt with formulas for finding areas using lengths of sides, starting with the triangle, where that is all you need, and then quadrilaterals, where something more must be added; and then using coordinates of vertices. Now we can use those tools to solve some of the more common real-life problems we …

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Polygon Coordinates and Areas

We’ve been collecting techniques for finding areas of polygons, mostly using their side lengths. We started with triangles (Heron’s formula), then quadrilaterals (Bretschneider’s formula and Brahmagupta’s formula), and the fact that the largest possible area is attained when the vertices lie on a circle. We’ll look at one more way to find area, using coordinates …

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