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Parallel (geometry)

In geometry, parallel lines are lines in a plane which do not meet; that is, two lines in a plane that do not intersect or touch each other at any point are said to be parallel. 

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, ... 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.

Affine plane (incidence geometry)

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

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.

Augustus De Morgan

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

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.

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.

Coincident

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

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.

Curvature

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

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Elliptic geometry

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

Emil Artin

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

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.

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.

Equivalence relation

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

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".

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.

Euclidean geometry

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

Euclidean space

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

Geminus

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

Geodesic

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

Geometric Algebra

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

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.

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.

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

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.

Harold Scott MacDonald Coxeter

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

Hyperbolic geometry

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

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.

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.

Incidence geometry

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

Infinity

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

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).

John Wiley & Sons

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

Latitude

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

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.

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).

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.

Non-Euclidean geometry

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

Parallel curve

A parallel of a curve is the.

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.

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.

Plane (geometry)

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

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.

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.

Primitive notion

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

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).

Projective geometry

Projective geometry is a topic in mathematics.

Reflexive relation

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

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.

Skew lines

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

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").

Spherical geometry

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

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.

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.

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.

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).

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.

Transversal (geometry)

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

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.

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.

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.

Wilhelm Killing

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

References

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