Abstract
The geometric interpretation of complex numbers as points of the plane appeared for the first time in the 18th century. After that there arose the natural idea of generalizing complex numbers in such a way that they could be interpreted as points of three-dimensional space. One of the earliest attempts of this kind was due to Caspar Wessel. It appeared in his previously mentioned Attempt to represent direction [624]. Having thought of the operation of multiplication of complex numbers in geometric terms, Wessel associated to a point in space with rectangular coordinates x, y, z the expression x + yε + zη, where ε and η are two different imaginary units, and interpreted by means of these numbers rotations about the Oy- and Oz-axes. Wessel used his “algebra” to solve problems involving spherical polygons.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1988 Springer Science+Business Media New York
About this chapter
Cite this chapter
Rosenfeld, B.A. (1988). Application of Algebras. In: A History of Non-Euclidean Geometry. Studies in the History of Mathematics and Physical Sciences, vol 12. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8680-1_10
Download citation
DOI: https://doi.org/10.1007/978-1-4419-8680-1_10
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6449-1
Online ISBN: 978-1-4419-8680-1
eBook Packages: Springer Book Archive