spherical triangle

We consider the spherical triangle, where is the north Pole.

His name was given to a theorem of spherical triangles.

It can be obtained from consideration of a spherical triangle dual to the given one.

He also wrote mathematical pamphlets, including one on the solution of spherical triangles.

Also, any two similar spherical triangles are congruent.

"The spherical triangle is handled as systematically here as in any modern textbook."

A spherical triangle is a geodesic triangle on the sphere.

He also discovered the law of sines for spherical triangles:

General form spherical triangle is fully determined by three of its six characteristics (3 sides and 3 angles).

For example, the sum of the interior angles of a spherical triangle exceeds 180 degrees.

Girard also showed how the area of a spherical triangle depends on its interior angles.

If the angles of the spherical triangle are chosen appropriately, the triangles will tile the sphere, one or more times.

The work is basically about flat triangles as distinguishable from spherical triangles.

I tried to do a spherical triangle backwards in my head to figure where to look for Sirius and got dizzy and gave up.

This involves resolving a spherical triangle.

The product of two versors can be compared to a spherical triangle where two sides add to the third.

The prayer hall ends with a room to the east roofed with a dome supported on spherical triangles.

The chancel windows are spherical triangles.

Unlike most other TV towers, the ground plan is a spherical triangle and not a cylindric cross section.

Note that the sides of a spherical triangle are usually measured rather by angular units than by linear, according to corresponding central angles.

Such a spherical triangle is fully defined by its two elements, and the other three can be calculated using Napier's Pentagon or the following relations.

From this and the area formula for a sphere it follows that the sum of the angles of a spherical triangle is .

The text included several solutions to the spherical triangle problem that were new, as well as extensive formulae and tables for navigation.

Spherical triangles satisfy the half-side formula :

He exhaustively cataloged the central and surface angles of these spherical triangles and their related chord factors.