# Niven’s Theorem

Open access

## Summary

This article formalizes the proof of Niven’s theorem [12] which states that if x/π and sin(x) are both rational, then the sine takes values 0, ±1/2, and ±1. The main part of the formalization follows the informal proof presented at Pr∞fWiki (https://proofwiki.org/wiki/Niven’s_Theorem#Source_of_Name). For this proof, we have also formalized the rational and integral root theorems setting constraints on solutions of polynomial equations with integer coefficients [8, 9].

## References

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• [12] Ivan Niven. Irrational numbers. The Carus Mathematical Monographs, No. 11. The Mathematical Association of America. Distributed by John Wiley and Sons, Inc., New York, N.Y., 1956.

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# Formalized Mathematics

## (a computer assisted approach)

### Journal Information

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Target Group

researchers in the fields of formal methods and computer-checked mathematics

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