Niven's theorem
id:
niven-s-theorem-289-11927826
title:
Niven's theorem
text:
In mathematics, Niven's theorem, named after Ivan Niven, states that the only rational values of θ in the interval 0° ≤ θ ≤ 90° for which the sine of θ degrees is also a rational number are: In radians, one would require that 0 ≤ x ≤ π/2, that x/π be rational, and that sin x be rational. The conclusion is then that the only such values are sin 0 = 0, sin π/6 = 1/2, and sin π/2 = 1. The theorem appears as Corollary 3.12 in Niven's book on irrational numbers. The theorem extends to the other trigo
brand slug:
wiki
category slug:
encyclopedia
description:
The only rational angles in first quadrant whose sine is rational are 0, 30 and 90 degrees
original url:
https://en.wikipedia.org/wiki/Niven%27s_theorem
date created:
date modified:
2023-10-03T18:19:46Z
main entity:
{"identifier":"Q4116459","url":"https://www.wikidata.org/entity/Q4116459"}
image:
fields total:
13
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14