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The lemniscate constants

Todd, John (1975) The lemniscate constants. Communications of the ACM, 18 (1). pp. 14-19. ISSN 0001-0782. http://resolver.caltech.edu/CaltechAUTHORS:20161222-113835018

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Abstract

The lemniscate constants, and indeed some of the methods used for actually computing them, have played an enormous part in the development of mathematics. An account is given here of some of the methods used—most of the derivations can be made by elementary methods. This material can be used for teaching purposes, and there is much relevant and interesting historical material. The acceleration methods developed for the purpose of evaluating these constants are useful in other problems.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1145/360569.360580DOIArticle
http://dl.acm.org/citation.cfm?doid=360569.360580PublisherArticle
Additional Information:© 1975 ACM. This is an abbreviated version of an Invited Householder Lecture, given at the ACM Southeast Regional Meeting, Nashville, Tenneessee, April 19, 1974. Another version of this paper was presented to the Bolyai János Matematikai Társulat in Keszthely, Hungary, in September 1973. Full details will be published in a monograph with the same title. The preparation of this paper has been supported in part by the National Science Foundation.
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Funding AgencyGrant Number
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Subject Keywords:lemniscate, acceleration, elliptic functions, Euler transformation
Classification Code:CR Categories: 1.2, 5.0
Record Number:CaltechAUTHORS:20161222-113835018
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20161222-113835018
Official Citation:John Todd. 1975. The lemniscate constants. Commun. ACM 18, 1 (January 1975), 14-19. DOI=http://dx.doi.org/10.1145/360569.360580
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:73155
Collection:CaltechAUTHORS
Deposited By: Kristin Buxton
Deposited On:23 Dec 2016 00:12
Last Modified:23 Dec 2016 00:12

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