Abstract: A sphere is the set of all points at a fixed distance from a given point. The given point is called the centre, and the fixed distance the radius, of the sphere. The points are those of any set on which distance is defined, that is, of a metric space. In this chapter we take this to be Euclidean 3-space with the Pythagorean metric. Sensibly letting the centre be the origin of coordinate and the radius be the unit of length, we get the unit sphere $${{\mathbb{S}}^{2}} = \{ (x,y,z) \in {{\mathbb{R}}^{3}}|{{x}^{2}} + {{y}^{2}} + {{z}^{2}} = 1\} .$$
Publication Year: 2001
Publication Date: 2001-01-01
Language: en
Type: book-chapter
Indexed In: ['crossref']
Access and Citation
AI Researcher Chatbot
Get quick answers to your questions about the article from our AI researcher chatbot