Abstract
The word trigonometry comes from the Greek for “triangle measurement.” More specifically, it means the study of relationships between the size of sides and the size of angles in triangles. Euclid says very little about this. He has theorems about equal angles and the sum of angles, and one angle being twice another or simply larger than another, but he never actually measures angles. He does not represent angles by numbers, nor does he represent them by lengths or areas. This suggests that angle measure may be a deep concept, perhaps beyond the scope of traditional geometry. The Greeks had some inkling of this when they tried unsuccessfully to construct the area bounded by the unit circle, the problem they called squaring the circle. In modern terms, squaring the circle amounts to constructing the number π, which is both the area of the unit circle and half its circumference. It is also the natural measure of the straight angle, formed by two right angles, so constructing π is in fact a fundamental question about the measurement of angles.
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
© 1998 Springer Science+Business Media New York
About this chapter
Cite this chapter
Stillwell, J. (1998). Trigonometry. In: Numbers and Geometry. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0687-3_5
Download citation
DOI: https://doi.org/10.1007/978-1-4612-0687-3_5
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6867-3
Online ISBN: 978-1-4612-0687-3
eBook Packages: Springer Book Archive