Definition:Spherical Triangle

Definition

A spherical triangle is a geometric figure described on the surface of a sphere which is bounded by the arcs of three great circles which intersect in $3$ vertices:

Side

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.

Vertex

The vertices of a spherical triangle $T$ are the intersections of the arcs of the $3$ great circles which form the boundaries of $T$.

Also known as

Some sources refer to a spherical triangle as an Euler triangle, for Leonhard Paul Euler.

Also see

• Results about spherical triangles can be found here.

Sources

• 1976: W.M. Smart: Textbook on Spherical Astronomy (6th ed.) ... (previous) ... (next): Chapter $\text I$. Spherical Trigonometry: $2$. The spherical triangle.
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): 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
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): spherical triangle

• Weisstein, Eric W. "Spherical Triangle." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SphericalTriangle.html