Recurrent proofs of the irrationality of certain trigonometric values

Details Recurrent proofs of the irrationality of certain trigonometric values Recurrent proofs of the irrationality of certain trigonometric values

2009-11-10

arxiv.org/abs/0911.1933v1

Amer. Math. Monthly, 117:4 (2010) 360-362.

Mathematics

Number Theory

Scientific paper

10.4169/000298910X480838

We use recurrences of integrals to give new and elementary proofs of the
irrationality of pi, tan(r) for all nonzero rational r, and cos(r) for all
nonzero rational r^2. Immediate consequences to other values of the elementary
transcendental functions are also discussed.

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