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Inequalities for the perimeter of an ellipse

Published online by Cambridge University Press:  23 January 2015

G. J. O. Jameson
G. J. O. Jameson*
Affiliation:
Dept. of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF, e-mail: g.jameson@lancaster.ac.uk
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Extract

The perimeter of the ellipse x2/a2 + y2/b2 = 1 is 4J (a, b), where J (a, b) is the ‘elliptic integral’

This integral is interesting in its own right, quite apart from its application to the ellipse. It is often considered together with the companion integral

Of course, we may as well assume that a and b are non-negative.

Type
Articles
Information
The Mathematical Gazette , Volume 98 , Issue 542 , July 2014 , pp. 227 - 234
Copyright
Copyright © Mathematical Association 2014 

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References

1. Lord, Nick, Recent calculations of π; the Gauss-Salamin algorithm, Math. Gaz. 76 (July 1992) pp. 231–242.Google Scholar
2. Lord, Nick and Seiffert, H.-J., Solution to Problem 76D, Math. Gaz. 77 (March 1993) p. 126.Google Scholar
3. Jameson, G. J. O., An approximation to the arithmetic-geometric mean, Math. Gaz. 98 (March 2014) pp. 85–95.Google Scholar