Heron's Formula
By James E. White
Press F11 for Full Screen
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.
