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Niven's Theorem


Niven's theorem states that if x/pi and sinx are both rational, then the sine takes values 0, +/-1/2, and +/-1.

Particular cases include

sin(pi)=0
(1)
sin(pi/2)=1
(2)
sin(pi/6)=1/2.
(3)

See also

Rational Number, Sine, Trigonometry Angles

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References

Niven, I. M. Irrational Numbers. New York: Wiley, pp. 37-41, 1956.Schaumberger, N. "A Classroom Theorem on Trigonometric Irrationalities." Two-Year College Math. J. 5, 73-76, 1974.

Referenced on Wolfram|Alpha

Niven's Theorem

Cite this as:

Weisstein, Eric W. "Niven's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/NivensTheorem.html

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