# Inequalities for the perimeter of an ellipse

@article{Jameson2014InequalitiesFT,
title={Inequalities for the perimeter of an ellipse},
author={G. J. O. Jameson},
journal={The Mathematical Gazette},
year={2014},
volume={98},
pages={227 - 234}
}
• G. Jameson
• Published 1 July 2014
• Mathematics
• The Mathematical Gazette
The perimeter of the ellipse x 2/a 2 + y 2/b 2 = 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.
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## References

SHOWING 1-5 OF 5 REFERENCES
An approximation to the arithmetic-geometric mean
• G. Jameson
• Mathematics
The Mathematical Gazette
• 2014
Given positive numbers a > b, consider the ‘agm iteration’ given by a 0 = a, b 0 = b and At each stage, the two new numbers are the arithmetic and geometric means of the previous two. It is easily
Solution to Problem 76D, Math. Gaz
• 1993
Recent calculations of n; the Gauss-Salamin algorithm, Math
• 1992
Solution to Problem 76D
• Math. Gaz