Spherical triangle

English

A spherical triangle

Noun

1. Template:Lb A triangle, described on the surface of the sphere, whose each side is an arc of some great circle.
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   • 1893, Crossley William Crosby Barlow, George Hartley Bryan, Elementary Mathematical Astronomy, W. B. Clive, page v,

     A spherical triangle, like a plane triangle, has six parts, viz., its three sides and its three angles. The sides are generally measured by the angles they subtend, so that the six parts are all expressed as angles.

     Any three parts suffice to determine a spherical triangle, but there are certain "ambiguous cases" when the problem admits of more than one solution. The formulæ required in solving spherical triangles form the subject of Spherical Trigonometry, and are in every case different from the analogous formulæ in Plane Trigonometry. There is this further difference, that a spherical triangle is completely determined if its three angles are given.

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Usage notes

• The length of a side is measured by the angle, in radians, that it subtends. In the case of the unit circle, this measure exactly equals the arc length.
• By convention, each side of a proper spherical triangle is less than $\pi$ $(180^{\circ })$.

Hypernyms

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Hyponyms

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Translations

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See also

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Further reading

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