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A New Look at Surfaces of Constant Curvature

Apostol, Tom M. and Mnatsakanian, Mamikon A. (2016) A New Look at Surfaces of Constant Curvature. American Mathematical Monthly, 123 (5). pp. 439-447. ISSN 0002-9890. https://resolver.caltech.edu/CaltechAUTHORS:20160930-143148171

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Abstract

Equality of zonal areas on a sphere and pseudosphere is extended by elementary geometric methods to surfaces of revolution of constant total (Gaussian) curvature, and constant mean (Delaunay) curvature. Bicycle wheels are used to trace profiles of these surfaces. Surprisingly, cycloids appear as limiting cases of such profiles.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.4169/amer.math.monthly.123.5.439DOIArticle
http://www.jstor.org/stable/10.4169/amer.math.monthly.123.5.439PublisherArticle
Additional Information:© 2016 Mathematical Association of America.
Issue or Number:5
Classification Code:MSC: Primary 51M25
Record Number:CaltechAUTHORS:20160930-143148171
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20160930-143148171
Official Citation:Tom M. Apostol, and Mamikon A. Mnatsakanian. "A New Look at Surfaces of Constant Curvature." The American Mathematical Monthly 123.5 (2016): 439-47.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:70711
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:30 Sep 2016 21:38
Last Modified:03 Oct 2019 16:00

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