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...

Foundations of Differential Geometry is an influential 2-volume mathematics book on differential geometry written by Shoshichi Kobayashi and Katsumi Nomizu...

Foundations of Algebraic Geometry is a book by André Weil (1946, 1962) that develops algebraic geometry over fields of any characteristic. In particular...

theory, the calculus of variations, commutative algebra, algebraic number theory, the foundations of geometry, spectral theory of operators and its application...

Euclidean geometry is a mathematical system attributed to Euclid, an ancient Greek mathematician, which he described in his textbook on geometry, Elements...

axioms are a set of 20 assumptions proposed by David Hilbert in 1899 in his book Grundlagen der Geometrie (tr. The Foundations of Geometry) as the foundation...

converse is not true. Affine geometry Erlangen program Foundations of geometry Incidence geometry Non-Euclidean geometry Faber 1983, pg. 131 In "Appendix...

Considered the "father of geometry", he is chiefly known for the Elements treatise, which established the foundations of geometry that largely dominated...

In geometry, a point is an abstract idealization of an exact position, without size, in physical space, or its generalization to other kinds of mathematical...

for teaching high school geometry, known as SMSG axioms. A few other textbooks in the foundations of geometry use variants of Birkhoff's axioms. The distance...

"Polytope Edge". From Wolfram MathWorld. Wylie Jr., C.R. (1964), Foundations of Geometry, New York: McGraw-Hill, p. 64, ISBN 0-07-072191-2 {{citation}}:...

(today Târgu-Mureş), where he spent the rest of his life. Bolyai's main interests were the foundations of geometry and the parallel axiom. His main work, Tentamen...

mathematics, affine geometry is what remains of Euclidean geometry when ignoring (mathematicians often say "forgetting") the metric notions of distance and angle...

Foundations of mathematics are the logical and mathematical framework that allows the development of mathematics without generating self-contradictory...

Synthetic geometry (sometimes referred to as axiomatic geometry or even pure geometry) is geometry without the use of coordinates. It relies on the axiomatic...

collection in 13 books of definitions, postulates, propositions and mathematical proofs that covers plane and solid Euclidean geometry, elementary number...

Pasch's theorem as an axiom in his modern treatment of Euclidean geometry in The Foundations of Geometry (1899). However, it was found by E. H. Moore in 1902...

de B. Robinson (1959) Foundations of Geometry, 4th ed., p. 8, University of Toronto Press Mary Tiles (2004) The Philosophy of Set Theory, p. 99 Phil...

The Foundations of Geometry (PDF), translated by Townsend, E. J., LaSalle, IL: Open Court Publishing Hilbert, David (1999) [1971], Foundations of Geometry...

Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It...

Gerard A. (2006), Foundations of Geometry, Pearson/Prentice-Hall, p. 229, ISBN 978-0-13-143700-5 Jacobs, Harold R. (1974), Geometry, W. H. Freeman & Co...

non-Archimedean geometry is any of a number of forms of geometry in which the axiom of Archimedes is negated. An example of such a geometry is the Dehn plane...

of all external experience. When David Hilbert wrote his book, Foundations of Geometry (1899), providing a new set of axioms for Euclidean geometry,...

In geometry, a straight line, usually abbreviated line, is an infinitely long object with no width, depth, or curvature, an idealization of such physical...

(1st ed.), London: Macmillan and Co. Wylie, C. R. Jr. (1964), Foundations of Geometry, McGraw–Hill Papadopoulos, Athanase; Théret, Guillaume (2014),...

and Non-Euclidean Geometries: Development and History, 3rd edition, W. H. Freeman, 1994. George E. Martin, The Foundations of Geometry and the Non-Euclidean...

statement. When a complete set of axioms for Euclidean geometry is used (see Foundations of geometry) this assertion of Euclid can be proved. The exterior...

projective and algebraic geometry. His work in the foundations of geometry predates the similar, but more popular, work of David Hilbert by about a decade...

Geometry (from Ancient Greek γεωμετρία (geōmetría) 'land measurement'; from γῆ (gê) 'earth, land' and μέτρον (métron) 'a measure') is a branch of mathematics...

In Euclidean geometry, two objects are similar if they have the same shape, or if one has the same shape as the mirror image of the other. More precisely...