Foundations of geometry is the study of geometries as axiomatic systems. There are several sets of axioms which give rise to Euclidean geometry or to non-Euclidean geometries. These are fundamental to the study and of historical importance, but there are a great many modern geometries that are not Euclidean which can be studied from this viewpoint. The term axiomatic geometry can be applied to any geometry that is developed from an axiom system, but is often used to mean Euclidean geometry studied from this point of view. The completeness and independence of general axiomatic systems are important mathematical considerations, but there are also issues to do with the teaching of geometry which come into play.
and 20 Related for: Foundations of geometry information
Foundationsof Differential Geometry is an influential 2-volume mathematics book on differential geometry written by Shoshichi Kobayashi and Katsumi Nomizu...
mathematics, affine geometry is what remains of Euclidean geometry when ignoring (mathematicians often say "forgetting") the metric notions of distance and angle...
Foundationsof Algebraic Geometry is a book by André Weil (1946, 1962) that develops algebraic geometry over fields of any characteristic. In particular...
Foundationsof mathematics is the study of the philosophical and logical and/or algorithmic basis of mathematics, or, in a broader sense, the mathematical...
Considered the "father ofgeometry", he is chiefly known for the Elements treatise, which established the foundationsofgeometry that largely dominated...
Euclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry, Elements...
theory, the calculus of variations, commutative algebra, algebraic number theory, the foundationsofgeometry, spectral theory of operators and its application...
Gerard A. (2006), FoundationsofGeometry, Pearson/Prentice-Hall, p. 229, ISBN 978-0-13-143700-5 Jacobs, Harold R. (1974), Geometry, W. H. Freeman & Co...
converse is not true. Affine geometry Erlangen program Foundationsofgeometry Incidence geometry Non-Euclidean geometry Faber 1983, pg. 131 In "Appendix...
Synthetic geometry (sometimes referred to as axiomatic geometry or even pure geometry) is geometry without the use of coordinates. It relies on the axiomatic...
statement. When a complete set of axioms for Euclidean geometry is used (see Foundationsofgeometry) this assertion of Euclid can be proved. The exterior...
(today Târgu-Mureş), where he spent the rest of his life. Bolyai's main interests were the foundationsofgeometry and the parallel axiom. His main work, Tentamen...
different geometries. A geometry where the parallel postulate does not hold is known as a non-Euclidean geometry. Geometry that is independent of Euclid's...
Differential geometry is a mathematical discipline that studies the geometryof smooth shapes and smooth spaces, otherwise known as smooth manifolds. It...
Trinity. In 1897, he wrote An Essay on the FoundationsofGeometry (submitted at the Fellowship Examination of Trinity College) which discussed the Cayley–Klein...
relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers (arithmetic). Classic geometry was focused...
Geometry (from Ancient Greek γεωμετρία (geōmetría) 'land measurement'; from γῆ (gê) 'earth, land', and μέτρον (métron) 'a measure') is a branch of mathematics...
geometric solutions of cubic equations and laid the foundations for the development of analytic geometry and non-Euclidean geometry. He also extracted...
Global Information