De Cicco, John Department of Mathematics, Illinois Institute of Technology, Chicago, Illinois.
- Projective space
- Dual coordinates
- Principle of duality
- Projective group
- Cross ratio
- Euclidean and non-Euclidean geometries
- Differential of arc length
- Additional Readings
A system of geometry based upon a set of axioms different from those of the Euclidean geometry based on the three-dimensional space of experience. Non-Euclidean geometries, especially Riemannian geometry, are useful in mathematical physics. This article will describe some of the basic concepts and axioms of non-Euclidean geometries and then draw some comparisons with Euclidean concepts. See also: Differential geometry; Euclidean geometry; Projective geometry; Riemannian geometry
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