In geometry, parallel lines are coplanar infinite straight lines that do not intersect at any point. Parallel planes are planes in the same three-dimensional...

In geometry, the parallel postulate is the fifth postulate in Euclid's Elements and a distinctive axiom in Euclidean geometry. It states that, in two-dimensional...

at the intersection of metric geometry and affine geometry, non-Euclidean geometry arises by either replacing the parallel postulate with an alternative...

mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai–Lobachevskian geometry) is a non-Euclidean geometry. The parallel postulate of Euclidean...

Absolute geometry is a geometry based on an axiom system for Euclidean geometry without the parallel postulate or any of its alternatives. Traditionally...

notion of parallel lines is one of the main properties that is independent of any metric, affine geometry is often considered as the study of parallel lines...

exception of the parallel postulate) that theorems proved from them were deemed absolutely true, and thus no other sorts of geometry were possible. Today...

In differential geometry, parallel transport (or parallel translation) is a way of transporting geometrical data along smooth curves in a manifold. If...

Elliptic geometry is an example of a geometry in which Euclid's parallel postulate does not hold. Instead, as in spherical geometry, there are no parallel lines...

and Riemannian geometry. Later in the 19th century, it appeared that geometries without the parallel postulate (non-Euclidean geometries) can be developed...

between two parallel lines Distance from a point to a line Flat (geometry) Incidence (geometry) Line segment Generalised circle Locus Plane (geometry) Polyline...

for projective geometry was indeed the theory of perspective. Another difference from elementary geometry is the way in which parallel lines can be said...

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 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...

hyperbolic geometry; each of these new geometries makes a different change to the parallel postulate. The principles of any of these geometries can be extended...

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

Look up parallel in Wiktionary, the free dictionary. Parallel may refer to: Parallel (geometry), two lines in the Euclidean plane which never intersect...

In three-dimensional geometry, a parallel projection (or axonometric projection) is a projection of an object in three-dimensional space onto a fixed plane...

Absolute geometry Affine geometry Algebraic geometry Analytic geometry Birational geometry Complex geometry Computational geometry Conformal geometry Constructive...

In geometry and science, a cross section is the non-empty intersection of a solid body in three-dimensional space with a plane, or the analog in higher-dimensional...

computation Parallel evolution, the independent emergence of a similar trait in different unrelated species Parallel (geometry), the property of parallel lines...

Taxicab geometry or Manhattan geometry is geometry where the familiar Euclidean distance is ignored, and the distance between two points is instead defined...

century American geometry textbooks define a trapezium as having no parallel sides, a trapezoid as having exactly one pair of parallel sides, and a parallelogram...

intersect at a unique point, so parallel lines do not exist. Both finite affine plane geometry and finite projective plane geometry may be described by fairly...

A parallel of a curve is the envelope of a family of congruent circles centered on the curve. It generalises the concept of parallel (straight) lines....

space; this parallels developments in topology, differential and complex geometry. One key achievement of this abstract algebraic geometry is Grothendieck's...

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

foundations of motion planning, computational biology, computational geometry and parallel computing. Amato is the Abel Bliss Professor of Engineering and...

In mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts...

one of the most basic of curvilinear geometric shapes. In elementary geometry, it is considered a prism with a circle as its base. A cylinder may also...