Jump to ContentJump to Main Navigation
Heavenly MathematicsThe Forgotten Art of Spherical Trigonometry$
Users without a subscription are not able to see the full content.

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

Show Summary Details
Page of

PRINTED FROM PRINCETON SCHOLARSHIP ONLINE (www.princeton.universitypressscholarship.com). (c) Copyright Princeton University Press, 2022. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in PRSO for personal use.date: 04 July 2022

Areas, Angles, and Polyhedra

Areas, Angles, and Polyhedra

(p.110) 7 Areas, Angles, and Polyhedra
Heavenly Mathematics

Glen Van Brummelen

Princeton University Press

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

Princeton Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us.