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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.

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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.

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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.
Funding AgencyGrant Number
Subject Keywords:lemniscate, acceleration, elliptic functions, Euler transformation
Issue or Number:1
Classification Code:CR Categories: 1.2, 5.0
Record Number:CaltechAUTHORS:20161222-113835018
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Official Citation:John Todd. 1975. The lemniscate constants. Commun. ACM 18, 1 (January 1975), 14-19. DOI=
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:73155
Deposited By: Kristin Buxton
Deposited On:23 Dec 2016 00:12
Last Modified:03 Oct 2019 16:25

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