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...

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

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...

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...

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...

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

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

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

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

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

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

Foundations of mathematics is the study of the philosophical and logical and/or algorithmic basis of mathematics, or, in a broader sense, the mathematical...

Raymond (1964), Foundations of Geometry, New York: McGraw-Hill, ISBN 978-0-070-72191-3 Wylie, Jr., C.R. (2009) [1964], Foundations of Geometry, Mineola, New...

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...

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

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...

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

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...

constructions), and mathematical proofs of the propositions. The books cover plane and solid Euclidean geometry, elementary number theory, and incommensurable...

relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers (arithmetic). Classic geometry was focused...

Trinity. In 1897, he wrote An Essay on the Foundations of Geometry (submitted at the Fellowship Examination of Trinity College) which discussed the Cayley–Klein...

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...

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

subjects: use of infinitesimal analysis in geometry, analytic geometry of planes, analytical mechanics, optics, physical foundations of mechanics); Hermann...

the support in exactly three points – vertices of a triangle. Euclid's Elements Foundations of geometry Hilbert's axioms Saccheri quadrilateral (considered...

In geometry, a locus (plural: loci) (Latin word for "place", "location") is a set of all points (commonly, a line, a line segment, a curve or a surface)...

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

(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...

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...