By James E. White
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This Interactive Web Book explores the geometry behind Heron's formula for the area of a triangle in terms of its sides. The formula may be understood by asking which quadrilateral with assigned side lengths has the largest area. This book has several experiments embedded in its pages, one of which allows the reader to vary the shape of the quadrilaterals to discover the surprising answer, and thereby, to discover Heron's formula.
Nearly all of the topics discussed will be accessible to a student who is comfortable with Algebra and Geometry. The crucial step of the argument, however, uses elementary Calculus and may, as a surprising application of the ideas of Limit and Derivative, be taken as a motivation for studying those concepts.
You may download, extract, and print the Word 2000 version of this book here.
Table of Contents
Maximizing Areas and a Formula of Heron
|A Quick Look at Quadrilaterals|
|Build a Quadrilateral|
|Maximizing the Area of a Quadrilateral|
|Embed a Quadrilateral in a Circle|
|Embeddings in Circles|
Look at Quadrilaterals