Geometry pp 253-285

# Spherical Geometry

• Roger Fenn
Part of the Springer Undergraduate Mathematics Series book series (SUMS)

## Abstract

In this chapter we will mostly consider the two-dimensional sphere. For definiteness we will take the unit sphere of unit radius in three-dimensional space with centre the origin, O. This is the set of points S 2 in ℝ3 satisfying
$${x^2} + {y^2} + {z^2} = 1.$$
For clarity of exposition we consider the xy-plane, called the equatorial plane, as horizontal and the z-axis as vertical. The equatorial plane meets the sphere in a circle called the equator. Any plane passing through the origin cuts the sphere in a circle called a great circle. So the centre of a great circle and the centre of the sphere coincide. The equator is an example of a great circle. The line through the centre of the sphere perpendicular to the plane of a great circle meets the sphere in two points called the poles of the great circle. The poles of the equator are the north pole N = (0, 0,1) and the south pole S = (0, 0, —1).

## Keywords

Great Circle Spherical Geometry North Pole Angular Separation Spherical Triangle
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Springer-Verlag London 2001

## Authors and Affiliations

• Roger Fenn
• 1
1. 1.School of MathematicsUniversity of SussexFalmerUK

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