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Heavenly MathematicsThe Forgotten Art of Spherical Trigonometry$
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Glen Van Brummelen

Print publication date: 2017

Print ISBN-13: 9780691175997

Published to Princeton Scholarship Online: May 2018

DOI: 10.23943/princeton/9780691175997.001.0001

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Areas, Angles, and Polyhedra

Areas, Angles, and Polyhedra

Chapter:
(p.110) 7 Areas, Angles, and Polyhedra
Source:
Heavenly Mathematics
Author(s):

Glen Van Brummelen

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691175997.003.0007

This chapter explains how to find the area of an angle or polyhedron. It begins with a discussion of how to determine the area of a spherical triangle or polygon. The formula for the area of a spherical triangle is named after Albert Girard, a French mathematician who developed a theorem on the areas of spherical triangles, found in his Invention nouvelle. The chapter goes on to consider Euler's polyhedral formula, named after the eighteenth-century mathematician Leonhard Euler, and the geometry of a regular polyhedron. Finally, it describes an approach to finding the proportion of the volume of the unit sphere that the various regular polyhedra occupy.

Keywords:   area, angle, polyhedron, spherical triangle, polygon, Albert Girard, Leonhard Euler, regular polyhedron, sphere

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