Definition:Spherical Triangle/Side
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Definition
The sides of a spherical triangle $T$ are the arcs of the $3$ great circles which form the boundaries of $T$ between the points at which they intersect.
In the above diagram, the sides are labelled $a$, $b$ and $c$.
Length of Side
Let $ABC$ be a spherical triangle on a sphere $S$.
Let $AB$ be a side of $ABC$.
The length of $AB$ is defined as the angle subtended at the center of $S$ by $AB$.
Sources
- 1976: W.M. Smart: Textbook on Spherical Astronomy (6th ed.) ... (previous) ... (next): Chapter $\text I$. Spherical Trigonometry: $2$. The spherical triangle.
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): spherical triangle
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): spherical triangle
- Weisstein, Eric W. "Spherical Triangle." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SphericalTriangle.html