Bernard H. Lavenda, (2012) " A New Perspective on Relativity : An Odyssey In Non-Euclidean Geometries", World Scientific, pp.
Euclidean geometry, where Euclidean space is viewed as the natural representation space of the group of Euclidean motions
Rytz’s construction is a classical construction of Euclidean geometry, in which only compass and ruler are allowed as aids.
Its five chapters concern Euclidean and non-Euclidean geometry, and literalist and non-literalist views on the meaning of numbers.
geometry | Euclidean space | Geometry | Euclidean vector | Euclidean geometry | algebraic geometry | non-Euclidean geometry | Cylinder (geometry) | cylinder (geometry) | Taxicab geometry | prism (geometry) | parallel (geometry) | Noncommutative geometry | Geometry Wars: Galaxies | Euclidean group | Euclidean distance | Euclidean | Diophantine geometry | Whitehead's point-free geometry | Wedge (geometry) | Variable Geometry | Variable geometry | Triangulation (geometry) | Translation (geometry) | translation (geometry) | Table of Geometry, from the 1728 ''Cyclopaedia, or an Universal Dictionary of Arts and Sciences | Stochastic geometry | Square pyramidal molecular geometry | Square (geometry) | Reciprocation (geometry) |
Daniel Pedoe named it the most elementary theorem in Euclidean geometry since it only concerns straight lines and distances.
Later in the 19th century, the German mathematician Bernhard Riemann developed Elliptic geometry, another non-Euclidean geometry where no parallel can be found and the sum of angles in a triangle is more than 180°.
Martin Gardner, Non-Euclidean Geometry, Chapter 14 of The Colossal Book of Mathematics, W. W.Norton & Company, 2001, ISBN 0-393-02023-1
He received his Ph.D. in 1927 from Johns Hopkins University, under the supervision of Frank Morley; his dissertation was titled Lagrange Resolvents in Euclidean Geometry.
Edwin Bidwell Wilson & Gilbert N. Lewis (1912) "The space-time manifold of relativity. The non-Euclidean geometry of mechanics and electromagnetics", Proceedings of the American Academy of Arts and Sciences 48:387–507.