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
integrity: 14

Related Entries

Explore Next Part