Lemniscate Constant
Let
be the Arc Length of a Lemniscate with
. Then the lemniscate constant is the quantity 
(Abramowitzand Stegun 1972), or 
(Todd 1975, Le Lionnais 1983). Todd (1975) cites T. Schneider (1937) as proving
to be a Transcendental Number.See also Lemniscate
References
Abramowitz, M. and Stegun, C. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, 1972. Borwein, J. M. and Borwein, P. B. Pi & the AGM: A Study in Analytic Number Theory and Computational Complexity. New York: Wiley, 1987. Finch, S. ``Favorite Mathematical Constants.'' http://www.mathsoft.com/asolve/constant/gauss/gauss.html Le Lionnais, F. Les nombres remarquables. Paris: Hermann, p. 37, 1983. Todd, J. ``The Lemniscate Constant.'' Comm. ACM 18, 14-19 and 462, 1975.
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