63 relations: Affine geometry, Affine plane (incidence geometry), Angle of parallelism, Augustus De Morgan, Binary relation, Clifford parallel, Coincident, Congruence (geometry), Curvature, D. Reidel, Elliptic geometry, Emil Artin, Equidistant, Equivalence class, Equivalence relation, Euclid, Euclid's Elements, Euclidean geometry, Euclidean space, Geminus, Geodesic, Geometric Algebra, Geometry, Gottfried Wilhelm Leibniz, Gradient, Great circle, Harold Scott MacDonald Coxeter, Hyperbolic geometry, Ideal point, If and only if, Incidence geometry, Infinity, Intersection (Euclidean geometry), John Wiley & Sons, Latitude, Lewis Carroll, Limiting parallel, Line (geometry), Non-Euclidean geometry, Parallel curve, Parallel postulate, Pencil (mathematics), Plane (geometry), Playfair's axiom, Posidonius, Primitive notion, Proclus, Projective geometry, Reflexive relation, Simplicius of Cilicia, ..., Skew lines, Sphere, Spherical geometry, Symmetric relation, Tangent, The College Mathematics Journal, Three-dimensional space, Transitive relation, Transversal (geometry), Ultraparallel theorem, Unicode, Wanda Szmielew, Wilhelm Killing. Expand index (13 more) »

## Affine geometry

In mathematics, affine geometry is what remains of Euclidean geometry when not using (mathematicians often say "when forgetting") the metric notions of distance and angle.

New!!: Parallel (geometry) and Affine geometry · See more »

## Affine plane (incidence geometry)

In geometry, an affine plane is a system of points and lines that satisfy the following axioms.

New!!: Parallel (geometry) and Affine plane (incidence geometry) · See more »

## Angle of parallelism

In hyperbolic geometry, the angle of parallelism \Pi(a), is the angle at one vertex of a right hyperbolic triangle that has two asymptotic parallel sides.

New!!: Parallel (geometry) and Angle of parallelism · See more »

## Augustus De Morgan

Augustus De Morgan (27 June 1806 – 18 March 1871) was a British mathematician and logician.

New!!: Parallel (geometry) and Augustus De Morgan · See more »

## Binary relation

In mathematics, a binary relation on a set A is a set of ordered pairs of elements of A. In other words, it is a subset of the Cartesian product A2.

New!!: Parallel (geometry) and Binary relation · See more »

## Clifford parallel

In elliptic geometry, two lines are Clifford parallel or paratactic lines if the perpendicular distance between them is constant from point to point.

New!!: Parallel (geometry) and Clifford parallel · See more »

## Coincident

In geometry, two points are called coincident when they are actually the same point as each other.

New!!: Parallel (geometry) and Coincident · See more »

## Congruence (geometry)

In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.

New!!: Parallel (geometry) and Congruence (geometry) · See more »

## Curvature

In mathematics, curvature is any of a number of loosely related concepts in different areas of geometry.

New!!: Parallel (geometry) and Curvature · See more »

## D. Reidel

D.

New!!: Parallel (geometry) and D. Reidel · See more »

## Elliptic geometry

Elliptic geometry is a geometry in which Euclid's parallel postulate does not hold.

New!!: Parallel (geometry) and Elliptic geometry · See more »

## Emil Artin

Emil Artin (March 3, 1898 – December 20, 1962) was an Austrian mathematician of Armenian descent.

New!!: Parallel (geometry) and Emil Artin · See more »

## Equidistant

A point is said to be equidistant from a set of objects if the distances between that point and each object in the set are equal.

New!!: Parallel (geometry) and Equidistant · See more »

## Equivalence class

In mathematics, when the elements of some set S have a notion of equivalence (formalized as an equivalence relation) defined on them, then one may naturally split the set S into equivalence classes.

New!!: Parallel (geometry) and Equivalence class · See more »

## Equivalence relation

In mathematics, an equivalence relation is a binary relation that is reflexive, symmetric and transitive.

New!!: Parallel (geometry) and Equivalence relation · See more »

## Euclid

Euclid (Εὐκλείδης Eukleidēs; fl. 300 BC), sometimes given the name Euclid of Alexandria to distinguish him from Euclides of Megara, was a Greek mathematician, often referred to as the "founder of geometry" or the "father of geometry".

New!!: Parallel (geometry) and Euclid · See more »

## Euclid's Elements

The Elements (Στοιχεῖα Stoicheia) is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid in Alexandria, Ptolemaic Egypt c. 300 BC.

New!!: Parallel (geometry) and Euclid's Elements · See more »

## Euclidean geometry

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

New!!: Parallel (geometry) and Euclidean geometry · See more »

## Euclidean space

In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces.

New!!: Parallel (geometry) and Euclidean space · See more »

## Geminus

Geminus of Rhodes (Γεμῖνος ὁ Ῥόδιος), was a Greek astronomer and mathematician, who flourished in the 1st century BC.

New!!: Parallel (geometry) and Geminus · See more »

## Geodesic

In differential geometry, a geodesic is a generalization of the notion of a "straight line" to "curved spaces".

New!!: Parallel (geometry) and Geodesic · See more »

## Geometric Algebra

Geometric Algebra is a book written by Emil Artin and published by Interscience Publishers, New York, in 1957.

New!!: Parallel (geometry) and Geometric Algebra · See more »

## Geometry

Geometry (from the γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.

New!!: Parallel (geometry) and Geometry · See more »

## Gottfried Wilhelm Leibniz

Gottfried Wilhelm (von) Leibniz (or; Leibnitz; – 14 November 1716) was a German polymath and philosopher who occupies a prominent place in the history of mathematics and the history of philosophy.

New!!: Parallel (geometry) and Gottfried Wilhelm Leibniz · See more »

## Gradient

In mathematics, the gradient is a multi-variable generalization of the derivative.

New!!: Parallel (geometry) and Gradient · See more »

## Great circle

A great circle, also known as an orthodrome, of a sphere is the intersection of the sphere and a plane that passes through the center point of the sphere.

New!!: Parallel (geometry) and Great circle · See more »

## Harold Scott MacDonald Coxeter

Harold Scott MacDonald "Donald" Coxeter, FRS, FRSC, (February 9, 1907 – March 31, 2003) was a British-born Canadian geometer.

New!!: Parallel (geometry) and Harold Scott MacDonald Coxeter · See more »

## Hyperbolic geometry

In mathematics, hyperbolic geometry (also called Bolyai–Lobachevskian geometry or Lobachevskian geometry) is a non-Euclidean geometry.

New!!: Parallel (geometry) and Hyperbolic geometry · See more »

## Ideal point

In hyperbolic geometry, an ideal point, omega point or point at infinity is a well defined point outside the hyperbolic plane or space.

New!!: Parallel (geometry) and Ideal point · See more »

## If and only if

In logic and related fields such as mathematics and philosophy, if and only if (shortened iff) is a biconditional logical connective between statements.

New!!: Parallel (geometry) and If and only if · See more »

## Incidence geometry

In mathematics, incidence geometry is the study of incidence structures.

New!!: Parallel (geometry) and Incidence geometry · See more »

## Infinity

Infinity (symbol) is a concept describing something without any bound or larger than any natural number.

New!!: Parallel (geometry) and Infinity · See more »

## Intersection (Euclidean geometry)

In geometry, an intersection is a point, line, or curve common to two or more objects (such as lines, curves, planes, and surfaces).

New!!: Parallel (geometry) and Intersection (Euclidean geometry) · See more »

## John Wiley & Sons

John Wiley & Sons, Inc., also referred to as Wiley, is a global publishing company that specializes in academic publishing.

New!!: Parallel (geometry) and John Wiley & Sons · See more »

## Latitude

In geography, latitude is a geographic coordinate that specifies the north–south position of a point on the Earth's surface.

New!!: Parallel (geometry) and Latitude · See more »

## Lewis Carroll

Charles Lutwidge Dodgson (27 January 1832 – 14 January 1898), better known by his pen name Lewis Carroll, was an English writer, mathematician, logician, Anglican deacon, and photographer.

New!!: Parallel (geometry) and Lewis Carroll · See more »

## Limiting parallel

In neutral or absolute geometry, and in hyperbolic geometry, there may be many lines parallel to a given line l through a point P not on line R; however, in the plane, two parallels may be closer to l than all others (one in each direction of R).

New!!: Parallel (geometry) and Limiting parallel · See more »

## Line (geometry)

The notion of line or straight line was introduced by ancient mathematicians to represent straight objects (i.e., having no curvature) with negligible width and depth.

New!!: Parallel (geometry) and Line (geometry) · See more »

## Non-Euclidean geometry

In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those specifying Euclidean geometry.

New!!: Parallel (geometry) and Non-Euclidean geometry · See more »

## Parallel curve

A parallel of a curve is the.

New!!: Parallel (geometry) and Parallel curve · See more »

## Parallel postulate

In geometry, the parallel postulate, also called Euclid's fifth postulate because it is the fifth postulate in Euclid's ''Elements'', is a distinctive axiom in Euclidean geometry.

New!!: Parallel (geometry) and Parallel postulate · See more »

## Pencil (mathematics)

In projective geometry, a pencil is a family of geometric objects with a common property, for example the set of lines that pass through a given point in a projective plane.

New!!: Parallel (geometry) and Pencil (mathematics) · See more »

## Plane (geometry)

In mathematics, a plane is a flat, two-dimensional surface that extends infinitely far.

New!!: Parallel (geometry) and Plane (geometry) · See more »

## Playfair's axiom

In geometry, Playfair's axiom is an axiom that can be used instead of the fifth postulate of Euclid (the parallel postulate): In a plane, given a line and a point not on it, at most one line parallel to the given line can be drawn through the point.

New!!: Parallel (geometry) and Playfair's axiom · See more »

## Posidonius

Posidonius (Ποσειδώνιος, Poseidonios, meaning "of Poseidon") "of Apameia" (ὁ Ἀπαμεύς) or "of Rhodes" (ὁ Ῥόδιος) (c. 135 BCE – c. 51 BCE), was a Greek Stoic philosopher, politician, astronomer, geographer, historian and teacher native to Apamea, Syria.

New!!: Parallel (geometry) and Posidonius · See more »

## Primitive notion

In mathematics, logic, and formal systems, a primitive notion is an undefined concept.

New!!: Parallel (geometry) and Primitive notion · See more »

## Proclus

Proclus Lycaeus (8 February 412 – 17 April 485 AD), called the Successor (Greek Πρόκλος ὁ Διάδοχος, Próklos ho Diádokhos), was a Greek Neoplatonist philosopher, one of the last major classical philosophers (see Damascius).

New!!: Parallel (geometry) and Proclus · See more »

## Projective geometry

Projective geometry is a topic in mathematics.

New!!: Parallel (geometry) and Projective geometry · See more »

## Reflexive relation

In mathematics, a binary relation R over a set X is reflexive if every element of X is related to itself.

New!!: Parallel (geometry) and Reflexive relation · See more »

## Simplicius of Cilicia

Simplicius of Cilicia (Σιμπλίκιος ὁ Κίλιξ; c. 490 – c. 560) was a disciple of Ammonius Hermiae and Damascius, and was one of the last of the Neoplatonists.

New!!: Parallel (geometry) and Simplicius of Cilicia · See more »

## Skew lines

In three-dimensional geometry, skew lines are two lines that do not intersect and are not parallel.

New!!: Parallel (geometry) and Skew lines · See more »

## Sphere

A sphere (from Greek σφαῖρα — sphaira, "globe, ball") is a perfectly round geometrical object in three-dimensional space that is the surface of a completely round ball (viz., analogous to the circular objects in two dimensions, where a "circle" circumscribes its "disk").

New!!: Parallel (geometry) and Sphere · See more »

## Spherical geometry

Spherical geometry is the geometry of the two-dimensional surface of a sphere.

New!!: Parallel (geometry) and Spherical geometry · See more »

## Symmetric relation

In mathematics and other areas, a binary relation R over a set X is symmetric if it holds for all a and b in X that a is related to b if and only if b is related to a. In mathematical notation, this is: Symmetry, along with reflexivity and transitivity, are the three defining properties of an equivalence relation.

New!!: Parallel (geometry) and Symmetric relation · See more »

## Tangent

In geometry, the tangent line (or simply tangent) to a plane curve at a given point is the straight line that "just touches" the curve at that point.

New!!: Parallel (geometry) and Tangent · See more »

## The College Mathematics Journal

The College Mathematics Journal, published by the Mathematical Association of America, is an expository journal aimed at teachers of college mathematics, particular those teaching the first two years.

New!!: Parallel (geometry) and The College Mathematics Journal · See more »

## Three-dimensional space

Three-dimensional space (also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called parameters) are required to determine the position of an element (i.e., point).

New!!: Parallel (geometry) and Three-dimensional space · See more »

## Transitive relation

In mathematics, a binary relation over a set is transitive if whenever an element is related to an element and is related to an element then is also related to.

New!!: Parallel (geometry) and Transitive relation · See more »

## Transversal (geometry)

In geometry, a transversal is a line that passes through two lines in the same plane at two distinct points.

New!!: Parallel (geometry) and Transversal (geometry) · See more »

## Ultraparallel theorem

In hyperbolic geometry, the ultraparallel theorem states that every pair of ultraparallel lines (lines that are not intersecting and not limiting parallel) has a unique common perpendicular hyperbolic line.

New!!: Parallel (geometry) and Ultraparallel theorem · See more »

## Unicode

Unicode is a computing industry standard for the consistent encoding, representation, and handling of text expressed in most of the world's writing systems.

New!!: Parallel (geometry) and Unicode · See more »

## Wanda Szmielew

Wanda Montlak Szmielew (1918–1976) was a Polish mathematical logician (of Jewish descent) who first proved the decidability of the first-order theory of abelian groups.

New!!: Parallel (geometry) and Wanda Szmielew · See more »

## Wilhelm Killing

Wilhelm Karl Joseph Killing (10 May 1847 – 11 February 1923) was a German mathematician who made important contributions to the theories of Lie algebras, Lie groups, and non-Euclidean geometry.

New!!: Parallel (geometry) and Wilhelm Killing · See more »

## Redirects here:

Non parallel, Non-parallel, Nonparallel, Not parallel, Parallel Line, Parallel line, Parallel lines, Parallel lines (geometry), Parallel lines and parallel planes, Parallel lines in hyperbolic geometry, Parallel plane, Parallel planes, Parallel propagation, Parallela, Parallelism (geometry), Parellel lines, ∥, ∦, ⋕, ⦷.

## References

[1] https://en.wikipedia.org/wiki/Parallel_(geometry)