Abstract
In this chapter we shall be interested in the concept of area in a neutral geometry. We shall start off with the definition of an area function and an investigation of the properties of a Euclidean area function. In Sections 10.2 and 10.3 we will prove the existence of area functions for Euclidean and hyperbolic geometries respectively. In the last section we will consider a beautiful theorem due to J. Bolyai which says that if two polygonal regions have the same area then one may be cut into a finite number of pieces and rearranged to form the other.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1981 Springer-Verlag Inc.
About this chapter
Cite this chapter
Millman, R.S., Parker, G.D. (1981). Area. In: Geometry. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-0130-1_10
Download citation
DOI: https://doi.org/10.1007/978-1-4684-0130-1_10
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4684-0132-5
Online ISBN: 978-1-4684-0130-1
eBook Packages: Springer Book Archive