By Daniel J. Velleman
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Extra resources for American Mathematical Monthly, volume 117, number 4, April 2010
S. L. Loney, Plane Trigonometry, Cambridge University Press, Cambridge, 1893. J. L¨utzen, Joseph Liouville 1809–1882: Master of Pure and Applied Mathematics, Springer-Verlag, New York, 1990. T. Muir, The Theory of Determinants in the Historical Order of Development, vol. 3, Macmillan, London, 1920; reprinted by Dover, New York, 1960. G. Polya, Mathematics and Plausible Reasoning, vol. 1, Induction and Analogy in Mathematics, Princeton University Press, Princeton, NJ, 1954. R. Remmert, Theory of Complex Functions (trans.
C. A. , by J. Edwards, Bull. Y. Math. Soc. 1 (1892) 217–223; also in A Century of Mathematics in America, Part III, P. , American Mathematical Society, Providence, RI, 1989. 1090/ S0002-9904-1892-00079-1 R. F. Scott, Note on a theorem of Professor Cayley’s, Messenger of Math. 8 (1879) 155–157. A. Weil, Elliptic Functions According to Eisenstein and Kronecker, Ergebnisse der Mathematik und ihrer Grenzgebiete, vol. 88, Springer-Verlag, Berlin, 1976; reprinted by Springer in the Classics in Mathematics series, 1999.
Cosn−2 a1 cosn−2 a2 .. cosn−2 an I have come to the end of my story, and I have to admit that its premise—Theorem 1 is important—remains undemonstrated. I hope there is an interesting application that I have yet to discover. ACKNOWLEDGMENTS. This paper has gone a long way beyond my original conception, thanks in large part to stimulating comments and helpful suggestions of two referees. REFERENCES 1. F. J. van den Berg, Ontwikkeling van eenige algebra¨ısche en van daarmede gelijkvormige goniometrische identiteiten, Verslagen en mededeelingen der Koninklijke Akademie van Wetenschappen, Afdeeling Natuurkunde, 2nd series 14 (1879) 340–359.
American Mathematical Monthly, volume 117, number 4, April 2010 by Daniel J. Velleman