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searching for Parallel (geometry) 432 found (3929 total)

alternate case: parallel (geometry)

Parallel postulate (3,278 words) [view diff] no match in snippet view article find links to article

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

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

three-dimensional objects in two dimensions. Orthographic projection is a form of parallel projection in which all the projection lines are orthogonal to the projection

In Euclidean geometry, a translation is a geometric transformation that moves every point of a figure, shape or space by the same distance in a given direction

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

In affine geometry, uniform scaling (or isotropic scaling) is a linear transformation that enlarges (increases) or shrinks (diminishes) objects by a scale

curve or family of curves in a parallel and consistent manner. There are various kinds of connections in modern geometry, depending on what sort of data

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

learning, computational biology, computational economics, computational geometry, and computational number theory and algebra. Work in this field is often

In differential geometry, an affine connection is a geometric object on a smooth manifold which connects nearby tangent spaces, so it permits tangent vector

In differential geometry, a Riemannian manifold is a geometric space on which many geometric notions such as distance, angles, length, volume, and curvature

descriptive geometry and is a two-dimensional representation of a three-dimensional object. It is a parallel projection (the lines of projection are parallel both

In Riemannian or pseudo-Riemannian geometry (in particular the Lorentzian geometry of general relativity), the Levi-Civita connection is the unique affine

usual designation of the vertical coincides with the y-axis in co-ordinate geometry. This convention can cause confusion in the classroom. For the teacher

In the mathematical field of differential geometry, the Riemann curvature tensor or Riemann–Christoffel tensor (after Bernhard Riemann and Elwin Bruno

zigzag, tracing a path between two parallel lines; it can be described as both jagged and fairly regular. In geometry, this pattern is described as a skew

object are produced (called primary views), with each projection plane parallel to one of the coordinate axes of the object. The views are positioned relative

type of geometry that does not include the parallel postulate, called hyperbolic geometry. In this geometry, an infinite number of parallel lines pass

polygon with three corners and three sides, one of the basic shapes in geometry. The corners, also called vertices, are zero-dimensional points while the

Look up tesseract in Wiktionary, the free dictionary. In geometry, a tesseract or 4-cube is a four-dimensional hypercube, analogous to a two-dimensional

objects simultaneously. For example, in Euclidean geometry, when two lines in a plane are not parallel, their intersection is the point at which they meet

objects simultaneously. For example, in Euclidean geometry, when two lines in a plane are not parallel, their intersection is the point at which they meet

the names of the author who first published on the topic of hyperbolic geometry. Sometimes the qualificative "real" is added to distinguish it from complex

might or might not be self-evident in nature (e.g., the parallel postulate in Euclidean geometry). To axiomatize a system of knowledge is to show that its

D_{\text{KL}}(P\parallel Q)} does not equal D KL ( Q ∥ P ) {\displaystyle D_{\text{KL}}(Q\parallel P)} , and the asymmetry is an important part of the geometry. The

several fields of pure mathematics, including differential geometry, projective geometry, and manifolds. However, the term "map projection" refers specifically

of the point at infinity of a class of parallel lines is called their vanishing point. In hyperbolic geometry, points at infinity are typically named

superseded the fixed-function pipeline of the past that only allowed for common geometry transforming and pixel-shading functions; with shaders, customized effects

Descriptive geometry is the branch of geometry which allows the representation of three-dimensional objects in two dimensions by using a specific set of

In plane Euclidean geometry, a rhombus (pl.: rhombi or rhombuses) is a quadrilateral whose four sides all have the same length. Another name is equilateral

In geometry, the great dodecahedron is one of four Kepler–Poinsot polyhedra. It is composed of 12 pentagonal faces (six pairs of parallel pentagons), intersecting

In solid geometry, a wedge is a polyhedron defined by two triangles and three trapezoid faces. A wedge has five faces, nine edges, and six vertices. A

In geometry, a prismatoid is a polyhedron whose vertices all lie in two parallel planes. Its lateral faces can be trapezoids or triangles. If both planes

In geometry, a parallelepiped is a three-dimensional figure formed by six parallelograms (the term rhomboid is also sometimes used with this meaning).

intersect the surface. For example, when a rectangle is rotated around an axis parallel to one of its edges, then a hollow rectangle-section ring is produced.

equivalent to the parallel postulate, leading to Euclidean geometry. In hyperbolic geometry, arising from the negation of the parallel postulate, the summit

In geometry, coaxial means that several three-dimensional linear or planar forms share a common axis. The two-dimensional analog is concentric. Common

divided into: basic theorems and constructions of plane geometry and triangle congruence (1–26), parallel lines (27-34), the area of triangles and parallelograms

the motion of the distant stars to the local inertial frame Orientation (geometry) Point reflection Rolling – motion of two objects in contact with each-other

In geometry, Cavalieri's principle, a modern implementation of the method of indivisibles, named after Bonaventura Cavalieri, is as follows: 2-dimensional

In geometry, a geodesic (/ˌdʒiː.əˈdɛsɪk, -oʊ-, -ˈdiːsɪk, -zɪk/) is a curve representing in some sense the locally shortest path (arc) between two points

commercially by Parallel Quantum Solutions. There is a reduction in cost for academic users and a site license. Its strong points are geometry optimization

the total scene reflectance (planar albedo) for that specific incident geometry (say, Ω i {\displaystyle \Omega _{i}} ). Circular symmetry All pages with

In differential geometry, the holonomy of a connection on a smooth manifold is the extent to which parallel transport around closed loops fails to preserve

In geometry, a Johnson solid, sometimes also known as a Johnson–Zalgaller solid, is a convex polyhedron whose faces are regular polygons. They are sometimes

Spin(7). Spin(7)-manifolds are Ricci-flat and admit a parallel spinor. They also admit a parallel 4-form, known as the Cayley form, which is a calibrating

In mathematics, the differential geometry of surfaces deals with the differential geometry of smooth surfaces with various additional structures, most

In geometry, a hexagon (from Greek ἕξ, hex, meaning "six", and γωνία, gonía, meaning "corner, angle") is a six-sided polygon. The total of the internal

, and use the parallel axis theorem to derive the second moment of area with respect to the x ′ {\displaystyle x'} axis. The parallel axis theorem states

In projective geometry, Pascal's theorem (also known as the hexagrammum mysticum theorem, Latin for mystical hexagram) states that if six arbitrary points

In differential geometry, Riemann's minimal surface is a one-parameter family of minimal surfaces described by Bernhard Riemann in a posthumous paper published

principles. CASTEP permits geometry optimisation and finite temperature molecular dynamics with implicit symmetry and geometry constraints, as well as calculation

In differential geometry, a G2 manifold or Joyce manifold is a seven-dimensional Riemannian manifold with holonomy group contained in G2. The group G 2

of a quartic Cartesian coordinate system Caustic Cesàro equation Chord (geometry) Cissoid Circumference Closed timelike curve concavity Conchoid (mathematics)

In differential geometry, a G2 manifold or Joyce manifold is a seven-dimensional Riemannian manifold with holonomy group contained in G2. The group G 2

Levi-Civita connection Parallel transport Ricci calculus Tensor derivative (continuum mechanics) List of formulas in Riemannian geometry Einstein, Albert (1922)

In differential geometry, an Ehresmann connection (after the French mathematician Charles Ehresmann who first formalized this concept) is a version of

peptide bonds of parallel or antiparallel extended β-strands. However, Astbury did not have the necessary data on the bond geometry of the amino acids

In geometry, Max Dehn introduced two examples of planes, a semi-Euclidean geometry and a non-Legendrian geometry, that have infinitely many lines parallel

infinity, all the projectors are parallel, and the corresponding subset of planar projections are referred to as parallel projections. Mathematically, planar

In geometry, a base is a side of a polygon or a face of a polyhedron, particularly one oriented perpendicular to the direction in which height is measured

In geometry, a frustum (Latin for 'morsel'); (pl.: frusta or frustums) is the portion of a solid (normally a pyramid or a cone) that lies between two parallel

origin in a layer or body of rock that lacks visible or measurable movement parallel to the surface (plane) of the fracture ("Mode 1" Fracture). Although joints

approximate center of the Milky Way Galaxy, and the fundamental plane parallel to an approximation of the galactic plane but offset to its north. It uses

Solid geometry or stereometry is the geometry of three-dimensional Euclidean space (3D space). A solid figure is the region of 3D space bounded by a two-dimensional

In geometry, a cupola is a solid formed by joining two polygons, one (the base) with twice as many edges as the other, by an alternating band of isosceles

as detachment folds characterized by parallel geometries at the outer limbs and non-parallel interlimb geometries at stratigraphically distinct and lower

certain associated bundles, hence a notion of parallel transport. They have many applications in geometry and physics: see the method of moving frames

meridians of longitude, thus indicating true north (so they are not exactly parallel). Maps issued by the United Kingdom Ordnance Survey contain a diagram showing

spherical. In spatial (3D) geometry, as applied in astronomy, the equator of a rotating spheroid (such as a planet) is the parallel (circle of latitude) at

from an object intersect. Projection planes are used often in descriptive geometry and graphical representation. A picture plane in perspective drawing is

point P {\displaystyle P} on the diagonal A C {\displaystyle AC} , the parallel to A D {\displaystyle AD} through P {\displaystyle P} intersects the side

mathematics, the study of the circle has helped inspire the development of geometry, astronomy and calculus. Annulus: a ring-shaped object, the region bounded

David M. (1992). "A parallel algorithm for enclosed and enclosing triangles". International Journal of Computational Geometry & Applications. 2 (2):

In geometry, a cycloid is the curve traced by a point on a circle as it rolls along a straight line without slipping. A cycloid is a specific form of trochoid

In differential geometry, a caustic is the envelope of rays either reflected or refracted by a manifold. It is related to the concept of caustics in geometric

section of a large gear. A single pinion can simultaneously drive two racks, parallel but opposite; which will always be displaced by the same distance, only

Commutative rings are much better understood than noncommutative ones. Algebraic geometry and algebraic number theory, which provide many natural examples of commutative

intersection points for parallel lines. So, parallel and non-parallel lines must be studied separately in classical geometry, while they need not be distinguished

\mathbf {v} _{\parallel }} parallel to the axis will not change magnitude nor direction: v ∥ r o t = v ∥ ; {\displaystyle \mathbf {v} _{\parallel \mathrm {rot}

that shape that is equidistant from its boundaries. In Euclidean geometry, parallel lines (lines that never intersect) are equidistant in the sense that

In geometry, the great cubicuboctahedron is a nonconvex uniform polyhedron, indexed as U14. It has 20 faces (8 triangles, 6 squares and 6 octagrams), 48

Small circles on the sphere that are parallel to the equator are circles of latitude (or parallels). In geometry unrelated to astronomical bodies, geocentric

differential geometry, an affine connection can be defined without reference to a metric, and many additional concepts follow: parallel transport, covariant

In spherical geometry, a spherical circle (often shortened to circle) is the locus of points on a sphere at constant spherical distance (the spherical

twentieth century represented a major advance in differential geometry. The introduction of parallel transport, covariant derivatives and connection forms gave

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

the Theory of Parallels) The following passages define this pivotal concept in hyperbolic geometry: The angle HAD between the parallel HA and the perpendicular

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

space, a ball is a line segment. In other contexts, such as in Euclidean geometry and informal use, sphere is sometimes used to mean ball. In the field of

In geometry, a cone is a three-dimensional figure that tapers smoothly from a flat base (typically a circle) to a point not contained in the base, called

the product of the units of each vector. If two vectors are parallel or are anti-parallel (that is, they are linearly dependent), or if either one has

between the two, is aligned parallel with the axis of rotation, rather than radially as with the concentric cylindrical geometry of the more common radial

optical patterns of lines creates a real and visible pattern of roughly parallel dark and light bands, the moiré pattern, superimposed on the lines. The

In algebraic geometry and computational geometry, general position is a notion of genericity for a set of points, or other geometric objects. It means

In classical geometry, a radius (pl.: radii or radiuses) of a circle or sphere is any of the line segments from its center to its perimeter, and in more

by Robert Recorde, who considered that nothing could be more equal than parallel straight lines with the same length. An equation is written as two expressions

possibilities opened up by the exploration of such concepts as hypercube geometry. Some writers took the fourth dimension to be one of time, which is consistent

In geometry, the parabiaugmented truncated dodecahedron is one of the Johnson solids (J69). As its name suggests, it is created by attaching two pentagonal

In projective geometry, Desargues's theorem, named after Girard Desargues, states: Two triangles are in perspective axially if and only if they are in

JavaScript, Julia, Matlab, Perl, Python, R, and Visual Basic Tools for parallel programming The following code, which computes the factorial of a nonnegative

wide audience. Playfair's textbook Elements of Geometry made a brief expression of Euclid's parallel postulate known now as Playfair's axiom. In 1783

rigid bodies. Screw theory provides a mathematical formulation for the geometry of lines which is central to rigid body dynamics, where lines form the

In geometry, a pyramid is a polyhedron formed by connecting a polygonal base and a point, called the apex. Each base edge and apex form a triangle, called

In geometry, an n-gonal truncated trapezohedron is a polyhedron formed by a n-gonal trapezohedron with n-gonal pyramids truncated from its two polar axis

In Euclidean geometry, the medial triangle or midpoint triangle of a triangle △ABC is the triangle with vertices at the midpoints of the triangle's sides

In geometry, the 120-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol {5,3,3}. It is also called

derivative vanish. Surface normal Frenet–Serret formulas Differential geometry of surfaces § Tangent vectors and normal vectors Rojansky, Vladimir (1979)

In geometry, the biaugmented truncated cube is one of the Johnson solids (J67). As its name suggests, it is created by attaching two square cupolas (J4)

limiting parallel, and all converge asymptotically to a single ideal point called the centre of the horocycle. In some models of hyperbolic geometry, it looks

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

In geometry, an affine plane is a system of points and lines that satisfy the following axioms: Any two distinct points lie on a unique line. Given any

Euclidean geometry, the triangle postulate states that the sum of the angles of a triangle is two right angles. This postulate is equivalent to the parallel postulate

proper setting for this concept is in projective geometry where there will be no special cases due to parallel lines since all lines meet. Although stated

In geometry, a zonohedron is a convex polyhedron that is centrally symmetric, every face of which is a polygon that is centrally symmetric (a zonogon)

out using geometrical construction techniques which rely on projection geometry, or by calculation using the known formulas and trigonometric tables usually

In the mathematical field of differential geometry, a calibrated manifold is a Riemannian manifold (M,g) of dimension n equipped with a differential p-form

Snyder in 1987 to be the same projection as Mercator's. However, given the geometry of a sundial, these maps may well have been based on the similar central

In geometry, an axis-aligned object (axis-parallel, axis-oriented) is an object in n-dimensional space whose shape is aligned with the coordinate axes

especially differential geometry and gauge theory, a connection on a fiber bundle is a device that defines a notion of parallel transport on the bundle;

gene in question and downstream is toward the 3' end. Due to the anti-parallel nature of DNA, this means the 3' end of the template strand is upstream

In differential geometry, the torsion tensor is a tensor that is associated to any affine connection. The torsion tensor is a bilinear map of two input

searching, data structures, computational geometry, and linear programming, VLSI, distributed computing, parallel processing, computer aided design, robotics

In geometry, the parabiaugmented hexagonal prism is one of the Johnson solids (J55). As the name suggests, it can be constructed by doubly augmenting a

dictionary. In painting, photography, graphical perspective and descriptive geometry, a picture plane is an image plane located between the "eye point" (or

In geometry, an arrangement of lines is the subdivision of the Euclidean plane formed by a finite set of lines. An arrangement consists of bounded and

interests include computational geometry, parallel algorithms, and geographic information systems. SUN–NSERC Chair in Applied Parallel Computing, Carleton University

physics, zonal flow connotes a tendency of flux to conform to a pattern parallel to the equator of a sphere. In meteorological term regarding atmospheric

and Ziegler on the subject, as well as in many other texts in discrete geometry, convex polytopes are often simply called "polytopes". Grünbaum points

In geometry, a dodecagon, or 12-gon, is any twelve-sided polygon. A regular dodecagon is a figure with sides of the same length and internal angles of

interests include computational geometry, parallel algorithms, and geographic information systems. SUN–NSERC Chair in Applied Parallel Computing, Carleton University

the pilot's left to right in piloted aircraft, and parallel to the wings of a winged aircraft, parallel to the buttock line. Longitudinal axis, or roll axis —

two-dimensional polar coordinate system in the plane through the point, parallel to the reference plane. The third coordinate may be called the height or

part of algebra which is relevant to real algebraic (and semialgebraic) geometry. It is mostly concerned with the study of ordered fields and ordered rings

descriptions. Poem and Book on Tape (Stand-Up Tragedy 2011) "Protective Geometry" Ed Pinsent and Bryan Lewis Saunders. Comic Book. (2012) "Episode 5: Recent

especially in the special theory of relativity. Spacetime diagrams can show the geometry underlying phenomena like time dilation and length contraction without

5D Chess with Multiverse Time Travel is a 2020 chess variant video game developed by Conor Petersen at American studio Thunkspace, released for Microsoft

transformations are also isometries of the hyperbolic plane, so in hyperbolic geometry all Apollonian gaskets are congruent. In a sense, there is therefore only

absolute geometry—a geometry that includes both Euclidean geometry and hyperbolic geometry. The discovery of a consistent alternative geometry that might

In geometry, an n-agonal bifrustum is a polyhedron composed of three parallel planes of n-agons, with the middle plane largest and usually the top and

In geometry, a convex curve is a plane curve that has a supporting line through each of its points. There are many other equivalent definitions of these

hyperbolic geometry (Lobachevsky's celebrated non-Euclidean geometry), hyperbolic functions (sinh, cosh, tanh, etc.), and gyrovector spaces (a geometry proposed

all the axioms that lead to Euclidean geometry with the exception of the axiom that is equivalent to the parallel postulate of Euclid. The theorem is named

makes with the longitudinal axis of the vehicle, as a function of static geometry, and kinematic and compliant effects. This can be contrasted with steer

Graham Bell from 1898 to 1908 developed space frames based on tetrahedral geometry. Bell's interest was primarily in using them to make rigid frames for nautical

In geometry, the hyperplane separation theorem is a theorem about disjoint convex sets in n-dimensional Euclidean space. There are several rather similar

attempts to prove or disprove Euclid's parallel line postulate spurred the development of non-Euclidean geometry. The Greek word mathēmatikē (μαθηματική)

In geometry, two lines l 1 {\displaystyle l_{1}} and l 2 {\displaystyle l_{2}} are antiparallel with respect to a given line m {\displaystyle m} if they

In geometry, the Minkowski sum of two sets of position vectors A and B in Euclidean space is formed by adding each vector in A to each vector in B: A +

differences in each direction, a new shape of three dimensional Cartesian geometry would need to be used. The development of the OSA-UCS took place during

asymptotes parallel to the non-primed coordinate axes. The following completion (see Möbius and Laguerre planes) homogenizes the geometry of hyperbolas:

Axonometry is a graphical procedure belonging to descriptive geometry that generates a planar image of a three-dimensional object. The term "axonometry"

mathematics, transformation geometry (or transformational geometry) is the name of a mathematical and pedagogic take on the study of geometry by focusing on groups

pins-and-string construction of ellipsoids and hyperboloids is contained in the book Geometry and the imagination written by D. Hilbert & S. Vossen, too. Choose an ellipse

constructibility Rank-into-rank Kripke–Platek axioms Diamond principle Parallel postulate Birkhoff's axioms (4 axioms) Hilbert's axioms (20 axioms) Tarski's

In geometry, a Euclidean plane isometry is an isometry of the Euclidean plane, or more informally, a way of transforming the plane that preserves geometrical

Rotational symmetry, also known as radial symmetry in geometry, is the property a shape has when it looks the same after some rotation by a partial turn

game is far larger than what could fit into memory at once. The geometry step (with Geometry pipeline), which is responsible for the majority of the operations

satisfy AP·PB = CP·PD (power of a point theorem). The midpoints of a set of parallel chords of a conic are collinear (midpoint theorem for conics). Chords were

In neutral or absolute geometry, and in hyperbolic geometry, there may be many lines parallel to a given line l {\displaystyle l} through a point P {\displaystyle

symmetry about every point. This can be studied with the tools of Riemannian geometry, leading to consequences in the theory of holonomy; or algebraically through

In geometry, the minimum bounding box or smallest bounding box (also known as the minimum enclosing box or smallest enclosing box) for a point set S in

mathematician Bernhard Riemann developed Elliptic geometry, another non-Euclidean geometry where no parallel can be found and the sum of angles in a triangle

the Euclidean parallel postulate could be proved as a theorem. It is now known that the type of the fourth angle depends upon the geometry in which the

spacetime geometry around the star onto 3-dimensional space. A curve is a geodesic if the tangent vector of the curve at any point is equal to the parallel transport

In geometry, the trilinear coordinates x : y : z of a point relative to a given triangle describe the relative directed distances from the three sidelines

under the term Computational Engineering, including using computational geometry and virtual design for engineering tasks, often coupled with a simulation-driven

to hang in front of (over) or behind (under) the roll when it is placed parallel to the wall. This divides opinions about which orientation is better. Arguments

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

In geometry, a Cartesian coordinate system (UK: /kɑːrˈtiːzjən/, US: /kɑːrˈtiːʒən/) in a plane is a coordinate system that specifies each point uniquely

In geometry, a Cartesian coordinate system (UK: /kɑːrˈtiːzjən/, US: /kɑːrˈtiːʒən/) in a plane is a coordinate system that specifies each point uniquely

under the term Computational Engineering, including using computational geometry and virtual design for engineering tasks, often coupled with a simulation-driven

In geometry, the Whitney umbrella or Whitney's umbrella, named after American mathematician Hassler Whitney, and sometimes called a Cayley umbrella, is

compressor Rutter, J.W. (2000). Geometry of Curves. CRC Press. pp. 204. ISBN 9781584881667. McCleary, John (2013). Geometry from a Differentiable Viewpoint

In geometry, bisection is the division of something into two equal or congruent parts (having the same shape and size). Usually it involves a bisecting

In non-Euclidean geometry, the Poincaré half-plane model is a way of representing the hyperbolic plane using points in the familiar Euclidean plane. Specifically

In mathematics, specifically Riemannian geometry, Synge's theorem is a classical result relating the curvature of a Riemannian manifold to its topology

In physics and geometry, a catenary (US: /ˈkætəˌnɛri/ KAT-ə-nerr-ee, UK: /kəˈtiːnəri/ kə-TEE-nər-ee) is the curve that an idealized hanging chain or cable

In Euclidean geometry, Varignon's theorem holds that the midpoints of the sides of an arbitrary quadrilateral form a parallelogram, called the Varignon

⁠T2/T1⁠ = r = ⁠N2/N1⁠, and ⁠ω2/ω1⁠ = ⁠1/r⁠ = ⁠N1/N2⁠. Depending on the geometry of the pair, the sense of rotation may also be inverted (from clockwise

topic, he brought them to the state prior to the invention of analytic geometry. His definitions of the terms ellipse, parabola, and hyperbola are the

the plane, while the points on the plane through the sphere's center and parallel to the image plane project to points at infinity; often the projection

plane as the two types of objects and ignore all the properties of this geometry except for the relation of which points are incident on which lines for

introduced to allow user level parallel programming on heterogeneous clusters and multiprocessor systems and in 2008 parallel computing technology was included

In geometry, an infinite skew polygon or skew apeirogon is an infinite 2-polytope with vertices that are not all colinear. Infinite zig-zag skew polygons

In hyperbolic geometry, two lines are said to be ultraparallel if they do not intersect and are not limiting parallel. The ultraparallel theorem states

noted for his work on parallel coordinates (||-coords), which he proposed in 1959, for the visualization of multidimensional geometries (as in linear algebra)

In three-dimensional geometry, the girth of a geometric object, in a certain direction, is the perimeter of its parallel projection in that direction

{\left(y-y_{\circ }\right)^{2}}{b^{2}}}=1\ .} The axes are still parallel to the x- and y-axes. In analytic geometry, the ellipse is defined as a quadric: the set of

axiom has is 2. Thus compass and straightedge geometry solves second-degree equations, while origami geometry, or origametry, can solve third-degree equations

alternatives, leading to non-Euclidean geometries. Nagel and Newman consider the question raised by the parallel postulate to be "...perhaps the most significant

the Miller indices. They are written (hkℓ), and denote the family of (parallel) lattice planes (of the given Bravais lattice) orthogonal to g h k ℓ =

In geometry, a secant is a line that intersects a curve at a minimum of two distinct points. The word secant comes from the Latin word secare, meaning

In geometry, a rhombicuboctahedral prism is a convex uniform polychoron (four-dimensional polytope). It is one of 18 convex uniform polyhedral prisms created

In geometry, the Pappus chain is a ring of circles between two tangent circles investigated by Pappus of Alexandria in the 3rd century AD. The arbelos

the paradigms of object-oriented programming. In Euclidean geometry, a translation (geometry) moves every point a constant distance in a specified direction

general relativity, if two objects are set in motion along two initially parallel trajectories, the presence of a tidal gravitational force will cause the

Symplectic geometry is a branch of differential geometry and differential topology that studies symplectic manifolds; that is, differentiable manifolds

In geometry, the hexagonal prism is a prism with hexagonal base. Prisms are polyhedrons; this polyhedron has 8 faces, 18 edges, and 12 vertices. If faces

In geometry, inversive geometry is the study of inversion, a transformation of the Euclidean plane that maps circles or lines to other circles or lines

switch-less network topology for connecting processing nodes in a parallel computer system. In geometry, a torus is created by revolving a circle about an axis

mathematics, and especially differential geometry and gauge theory, a connection is a device that defines a notion of parallel transport on the bundle; that is

In computational geometry, the method of rotating calipers is an algorithm design technique that can be used to solve optimization problems including finding

Squaring the circle is a problem in geometry first proposed in Greek mathematics. It is the challenge of constructing a square with the area of a given

SWAT and WADS – SWAT and WADS conferences Conferences on computational geometry, graph drawing, and other application areas of geometric computing: GD

In geometry a conoid (from Greek κωνος  'cone' and -ειδης  'similar') is a ruled surface, whose rulings (lines) fulfill the additional conditions: (1)

In geometry, a real projective line is a projective line over the real numbers. It is an extension of the usual concept of a line that has been historically

he was formulating his theories on n-dimensional non-Euclidean geometry. The geometry of the novel's universe contains six dimensions – the three spatial

rendering pipeline can be divided into conceptual stages: application, geometry and rasterization. The application stage is responsible for generating

\phi ,\,\sin \phi ,\,0)} , the expression of the rotation in reflection geometry is δ β {\displaystyle \delta \beta } is: δ β r = 2 Δ n n 0 2 − 1 sin ⁡

The pitch of a helix is the height of one complete helix turn, measured parallel to the axis of the helix. A double helix consists of two (typically congruent)

their depth. Finding matches in stereo vision is restricted by epipolar geometry: Each pixel's match in another image can only be found on a line called

In geometry, a slab is a region between two parallel lines in the Euclidean plane, or between two parallel planes in three-dimensional Euclidean space

In geometry, the 600-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol {3,3,5}. It is also known

at Brown University. He is best known for his 1985 book "Computational Geometry: An Introduction" into which he blended salient parts of M. I. Shamos'

rendering pipeline can be divided into conceptual stages: application, geometry and rasterization. The application stage is responsible for generating

In the mathematical theory of Riemannian geometry, there are two uses of the term Fermi coordinates. In one use they are local coordinates that are adapted

In geometry, Monge's theorem, named after Gaspard Monge, states that for any three circles in a plane, none of which is completely inside one of the others

sequence alignment, especially in bioinformatics Affine geometry, a geometry characterized by parallel lines Affine group, the group of all invertible affine

In physics and geometry, isotropy (from Ancient Greek ἴσος (ísos) 'equal' and τρόπος (trópos) 'turn, way') is uniformity in all orientations. Precise definitions

and the introduction of logarithms to Italy. Cavalieri's principle in geometry partially anticipated integral calculus. Born in Milan, Cavalieri joined

In geometry, a set of points is convex if it contains every line segment between two points in the set. For example, a solid cube is a convex set, but

lattices). A family of lattice planes is a collection of equally spaced parallel lattice planes that, taken together, intersect all lattice points. Every

apparent separation. Angular distance appears in mathematics (in particular geometry and trigonometry) and all natural sciences (e.g., kinematics, astronomy

electric circuit. The capacitance between two conductors depends only on the geometry; the opposing surface area of the conductors and the distance between them;

einander he laid the foundation of modern synthetic geometry. In projective geometry even parallel lines have a point in common: a point at infinity. Thus

the topic has split into two topics with different emphases. Integral geometry sprang from the principle that the mathematically natural probability models

representation of one metric space as a subset of another. Like congruence in geometry. Isometry (disambiguation) Isometric video game (disambiguation) This disambiguation

Hamiltonian Systems and of Gravitation, Gauge Theories, and Differential Geometry, which attempted to bridge the gap between theoretical physicists and mathematicians

in parallel. Unlike an anti-roll bar, a de Dion tube is not directly connected to the chassis, and is not intended to flex. In suspension geometry it

generator is a line parallel to the y-axis (plane model) or a line on the cylinder (space model). The connection to linear geometry is given by the following

In analytic geometry, the intersection of a line and a plane in three-dimensional space can be the empty set, a point, or a line. It is the entire line

In geometry, a hyperplane is a generalization of a two-dimensional plane in three-dimensional space to mathematical spaces of arbitrary dimension. Like

system of coordinates used in projective geometry, just as Cartesian coordinates are used in Euclidean geometry. They have the advantage that the coordinates

In geometry, a prismatic uniform polyhedron is a uniform polyhedron with dihedral symmetry. They exist in two infinite families, the uniform prisms and

Wallis's postulate and is logically equivalent to Euclid's parallel postulate. In hyperbolic geometry (where Wallis's postulate is false) similar triangles

General of the École Polytechnique. He is considered a reviver of projective geometry, and his work Traité des propriétés projectives des figures is considered

In the differential geometry of curves, the evolute of a curve is the locus of all its centers of curvature. That is to say that when the center of curvature

on Mathworld Wolfram Sommerville, D. M. Y. (1909). "Classification of Geometries with Projective Metric". Proceedings of the Edinburgh Mathematical Society

are parallel, and "closed" otherwise. In 1993, Thierry Valet and Albert Fert presented a model for the giant magnetoresistance in the CPP geometry, based

In geometry, a skew polygon is a closed polygonal chain in Euclidean space. It is a figure similar to a polygon except its vertices are not all coplanar

In geometry, a decagon (from the Greek δέκα déka and γωνία gonía, "ten angles") is a ten-sided polygon or 10-gon. The total sum of the interior angles

which is parallel to the normal line. For other differential invariants of surfaces, in the neighborhood of a point, see Differential geometry of surfaces

hyperplane H, the width of C parallel to H, w(C,H), is the distance between the two supporting hyperplanes of C that are parallel to H. The smallest such distance

In geometry, a Wythoff construction, named after mathematician Willem Abraham Wythoff, is a method for constructing a uniform polyhedron or plane tiling

classifications of folds, based on their geometry. The most commonly used terms to describe and classify folds, based on their geometry, are the terms antiforms and

e12, e123). The element e123 is a trivector and the pseudoscalar for the geometry. Bivectors in three dimensions are sometimes identified with pseudovectors

of the 20th century, the assumption had been that the three-dimensional geometry of the universe (its description in terms of locations, shapes, distances

Mangione, Milano, Bompiani, 2011. Saccheri–Legendre theorem Hyperbolic geometry Parallel postulate Giordano Vitale List of Jesuit scientists List of Roman

The fundamental theorem of Riemannian geometry states that on any Riemannian manifold (or pseudo-Riemannian manifold) there is a unique affine connection

shifting the ski or snowboard onto its edges. When edged, the sidecut geometry causes the ski (in the following, snowboard is implicit and not mentioned)

language semantics Type theory Algorithms Computational geometry Distributed algorithms Parallel algorithms Randomized algorithms Artificial intelligence

In geometry, a tetrahedral prism is a convex uniform 4-polytope. This 4-polytope has 6 polyhedral cells: 2 tetrahedra connected by 4 triangular prisms

care that the numerical solution respects the underlying structure or geometry of these classes. Quantized state systems methods are a family of ODE integration

In geometry, a tetrahedral prism is a convex uniform 4-polytope. This 4-polytope has 6 polyhedral cells: 2 tetrahedra connected by 4 triangular prisms

In geometry, a triangular prism or trigonal prism is a prism with 2 triangular bases. If the edges pair with each triangle's vertex and if they are perpendicular

that develops downstream). This is present in curved surfaces and general geometry changes like a convex surface. A unique example of severe geometric changes

In geometry, a normal is an object (e.g. a line, ray, or vector) that is perpendicular to a given object. For example, the normal line to a plane curve

ancient Greek mathematicians Euclid and Pythagoras. In the Greek deductive geometry exemplified by Euclid's Elements, distances were not represented as numbers

In geometry, the heptagonal antiprism is the fifth in an infinite set of antiprisms formed by two parallel polygons separated by a strip of triangles

refract light. At least one surface must be angled — elements with two parallel surfaces are not prisms. The most familiar type of optical prism is the

In the mathematical field of differential geometry, the Levi-Civita parallelogramoid is a quadrilateral in a curved space whose construction generalizes

segment, the solid defined by cutting a sphere with a pair of parallel planes Arc (geometry), a closed segment of a differentiable curve Segment (handwriting)

with 0° at the Equator. Lines of constant latitude, or parallels, run east-west as circles parallel to the equator. Latitude and longitude are used together

point. In projective geometry every line has a point at infinity or "figurative point" where it crosses all the lines that are parallel to it. The ellipse

directions to magnetize the material, which are a 180° rotation apart. The line parallel to these directions is called the easy axis. In other words, the easy axis

In geometry, an octahedron (pl.: octahedra or octahedrons) is a polyhedron with eight faces. One special case is the regular octahedron, a Platonic solid

cylindrical and conical surfaces depending on whether or not the line is parallel to the axis. A circle that is rotated around any diameter generates a sphere

complementary algebra and analytic geometry. Bellavitis married in 1842 and had one son who also taught geometry at the University of Padua. Bellavitis

the stereographic plane is an alternative setting for spherical analytic geometry instead of spherical polar coordinates or three-dimensional cartesian coordinates

the maximum resolution of the optical system. Lens-reflector artifacts, geometry and other imperfections determine the actual diameter of the focal cloud

in the slip-parallel direction than the slip-perpendicular direction and is commonly a result of slickenside formation. The unique geometry of a slickenside

forces and movement. The movement of a body, or link, is studied using geometry so the link is considered to be rigid. The connections between links are

theory of relativity where the geometry included not only space but also time. The basic entity of this new geometry is four-dimensional spacetime. The

The triaugmented triangular prism, in geometry, is a convex polyhedron with 14 equilateral triangles as its faces. It can be constructed from a triangular

same projection. Ordinary cusps appear when the tangent to the curve is parallel to the direction of projection (that is when the tangent projects on a

In geometry, a spherical cap or spherical dome is a portion of a sphere or of a ball cut off by a plane. It is also a spherical segment of one base, i

structure could be modeled using the hexastix cylinder packing geometry. Hexastix geometry has also found use in architecture, being used to construct a

In geometry, a tetrahedron (pl.: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six

In projective geometry, a plane at infinity is the hyperplane at infinity of a three dimensional projective space or to any plane contained in the hyperplane

1648, the Savilian Professors of Geometry and Astronomy. In 1649 Wallis was appointed as Savilian Professor of Geometry. Wallis seems to have been chosen

In geometry, the perpendicular distance between two objects is the distance from one to the other, measured along a line that is perpendicular to one or

the same scene from the same distance will exhibit identical perspective geometry, regardless of lens used. However, since wide-angle lenses have a wider

vary). Partial derivatives are used in vector calculus and differential geometry. The partial derivative of a function f ( x , y , … ) {\displaystyle f(x

In geometry, the small cubicuboctahedron is a uniform star polyhedron, indexed as U13. It has 20 faces (8 triangles, 6 squares, and 6 octagons), 48 edges

rotates about it and a translation parallel to the axis is included in the screw displacement. Euclidean geometry is expressed in the complex plane by

from the fundamentals of crystal structure to the mathematics of crystal geometry, including those that are not periodic or quasicrystals. At the atomic

In geometry, a Steinmetz solid is the solid body obtained as the intersection of two or three cylinders of equal radius at right angles. Each of the curves

essential torus may be defined geometrically, as an embedded, non-boundary parallel, incompressible torus, or it may be defined algebraically, as a subgroup

In geometry, a bigon, digon, or a 2-gon, is a polygon with two sides (edges) and two vertices. Its construction is degenerate in a Euclidean plane because

{\displaystyle \nabla T=\omega \otimes T.\,} An example for recurrent tensors are parallel tensors which are defined by ∇ A = 0 {\displaystyle \nabla A=0} with respect

In geometry, an icositetragon (or icosikaitetragon) or 24-gon is a twenty-four-sided polygon. The sum of any icositetragon's interior angles is 3960 degrees

Bicycle and motorcycle geometry is the collection of key measurements (lengths and angles) that define a particular bike configuration. Primary among these

here under more than one heading. This is particularly so for variable geometry and combined (closed) wing types. Most of the configurations described

In geometry, Villarceau circles (/viːlɑːrˈsoʊ/) are a pair of circles produced by cutting a torus obliquely through its center at a special angle. Given

It is an example of an injective metric. In two dimensions, i.e. plane geometry, if the points p and q have Cartesian coordinates ( x 1 , y 1 ) {\displaystyle

definition is preferable: a rectilinear polygon is a polygon with sides parallel to the axes of Cartesian coordinates. The distinction becomes crucial when

if no part of γ is part of some parallel of S, then γ is a geodesic. — Andrew Pressley: Elementary Differential Geometry, p. 183 Pressley (p. 185) explains

In geometry, Villarceau circles (/viːlɑːrˈsoʊ/) are a pair of circles produced by cutting a torus obliquely through its center at a special angle. Given

definition is preferable: a rectilinear polygon is a polygon with sides parallel to the axes of Cartesian coordinates. The distinction becomes crucial when

the RF source equally between the elements. This often has the circuit geometry of a tree structure. When a radio signal passes a conductor, it induces

synonym for "reflection". In a plane (or, respectively, 3-dimensional) geometry, to find the reflection of a point drop a perpendicular from the point

Epipolar geometry is the geometry of stereo vision. When two cameras view a 3D scene from two distinct positions, there are a number of geometric relations

Mathieu (2019). "Parallel Transport Unfolding: A Connection-Based Manifold Learning Approach". SIAM Journal on Applied Algebra and Geometry. 3 (2): 266–291

In geometry, a supporting line L of a curve C in the plane is a line that contains a point of C, but does not separate any two points of C. In other words

constructs line segments BL and CM over BC, such that BL and CM are a parallel and equal in length to AH. The following identity then holds for the areas

involved in thin-skinned style of deformation, have a so-called ramp-flat geometry. Thrusts mainly propagate along zones of weakness within a sedimentary

In geometry, a polyhedron (pl.: polyhedra or polyhedrons; from Greek πολύ (poly-)  'many' and ἕδρον (-hedron)  'base, seat') is a three-dimensional figure

In geometry, the snub disphenoid is a convex polyhedron with 12 equilateral triangles as its faces. It is an example of deltahedron and Johnson solid.

In geometry, a Catalan surface, named after the Belgian mathematician Eugène Charles Catalan, is a ruled surface all of whose generators are parallel to

In geometry, Apollonius's theorem is a theorem relating the length of a median of a triangle to the lengths of its sides. It states that the sum of the

In geometry, the midpoint is the middle point of a line segment. It is equidistant from both endpoints, and it is the centroid both of the segment and

Posamentier, Alfred S.; Salkind, Charles T. (1996). Challenging Problems in Geometry (Second ed.). Dover. p. 172. ISBN 0-486-69154-3. Voles, Roger, "Integer

weight – there is no requirement for edge lengths to obey normal rules of geometry such as the triangle inequality. A spanning tree for that graph would be

In Euclidean plane geometry, a tangent line to a circle is a line that touches the circle at exactly one point, never entering the circle's interior. Tangent

molecular orbitals. Anti-periplanar geometry will put a bonding orbital and an anti-bonding orbital approximately parallel to each other, or syn-periplanar

because of the difficulty of aligning them to the needed precision. The geometry (resonator type) must be chosen so that the beam remains stable, i.e. the

of two scientific computing disciplines: computational geometry and parallel computing. Parallel mesh generation methods decompose the original mesh generation

of Geometry, 95 (1–2): 165–171, doi:10.1007/s00022-009-0018-2, S2CID 121123017 Grabiner, Judith V. (2009), "Why did Lagrange "prove" the parallel postulate

line will not intersect the plane is if the ray's direction vector is parallel to the plane. When this happens, the dot product between the ray's direction

metamorphism in the region between the trench and the volcanic arc. The geometry of a slab window depends primarily on the angle the ridge intersects the

which is therefore discounted). The second is a matter of geometry, on the model of parallel lines; it is something that can be discussed for linear problems

In differential geometry, the Ricci curvature tensor, named after Gregorio Ricci-Curbastro, is a geometric object which is determined by a choice of Riemannian

Pedoe: Geometry: A Comprehensive Course. Dover, 1970, pp. 35–36, 114–115 Daniel Pedoe: "On (what should be) a Well-Known Theorem in Geometry." The American

washer or disc integration method is used when integrating by an axis parallel to the axis of rotation. The general equation can be written as: V = π

Hyperbolic geometry is a non-Euclidean geometry where the first four axioms of Euclidean geometry are kept but the fifth axiom, the parallel postulate

the “tile mosaic” due to the development of arithmetic calculation and geometry—the girih tiles. Girih are lines (strapwork) that decorate the tiles. The

"Binary space partitions for axis-parallel segments, rectangles, and hyperrectangles". Discrete & Computational Geometry. 31 (2): 207–227. doi:10.1007/s00454-003-0729-3

chemistry, energy minimization (also called energy optimization, geometry minimization, or geometry optimization) is the process of finding an arrangement in

called Deferred Geometry Pipeline seeks to minimize leakage in fixed-function geometry units by utilizing an imbalance between geometry and fragment computation

an equal length along each longer side, and an imaginary fourth line parallel to the short side. The process of mentally rotating the short sides onto

"Variable-Geometry Turbochargers". Coursework for Physics 240. Retrieved 17 April 2012. Tan, Paul (16 August 2006). "How does Variable Turbine Geometry work

functions. In this geometry, there are significant differences from Euclidean geometry; in particular, there are infinitely many parallels to a straight line

is essentially geometrical in character (making use of non-Euclidean geometries), suggested that general relativity be formulated using the language of

900 mi) long. About 25 giant dike swarms are known on Earth. The primary geometry of most giant dike swarms is poorly known due to their old age and subsequent

geometry, where uniqueness of parallels no longer holds. In this geometry the sum of angles in a triangle add up to less than 180°. Elliptic geometry

in movies. Oblique projection is a type of parallel projection: it projects an image by intersecting parallel rays (projectors) from the three-dimensional

Robot kinematics applies geometry to the study of the movement of multi-degree of freedom kinematic chains that form the structure of robotic systems.

including experimental design, finite geometry, physical chemistry, software testing, cryptography, and algebraic geometry. Without further specifications the

In Riemannian geometry, Gauss's lemma asserts that any sufficiently small sphere centered at a point in a Riemannian manifold is perpendicular to every

Quadrature of the Parabola (Greek: Τετραγωνισμὸς παραβολῆς) is a treatise on geometry, written by Archimedes in the 3rd century BC and addressed to his Alexandrian

mid-19th century, flaws in Euclid's axioms for geometry became known. In addition to the independence of the parallel postulate, established by Nikolai Lobachevsky

This is a glossary of some terms used in Riemannian geometry and metric geometry — it doesn't cover the terminology of differential topology. The following

in movies. Oblique projection is a type of parallel projection: it projects an image by intersecting parallel rays (projectors) from the three-dimensional

Rehmeyer, Julie, "Sacred Geometry", Science News, March 21, 2008. Rothman, Tony; Fugakawa, Hidetoshi (May 1998). "Japanese Temple Geometry". Scientific American

preventing security vulnerabilities. Computer graphics and computational geometry address the generation of images. Programming language theory considers

In differential geometry, a hyperkähler manifold is a Riemannian manifold ( M , g ) {\displaystyle (M,g)} endowed with three integrable almost complex

metric space is the hyperbolic plane. In terms of the models of hyperbolic geometry, this model is frequently designated the Poincaré half-plane model. Mathematicians

thrust-fold belts. Fold and thrust belts are formed of a series of sub-parallel thrust sheets, separated by major thrust faults. As the total shortening

mid-19th century, flaws in Euclid's axioms for geometry became known. In addition to the independence of the parallel postulate, established by Nikolai Lobachevsky

water. It is also a concept in geometry and can be used as a conceptualization process for 3D structures. In geometry, the mirror image of an object or

In mathematics, contact geometry is the study of a geometric structure on smooth manifolds given by a hyperplane distribution in the tangent bundle satisfying

In geometry, a plane of rotation is an abstract object used to describe or visualize rotations in space. The main use for planes of rotation is in describing

In Euclidean geometry, oblique reflections generalize ordinary reflections by not requiring that reflection be done using perpendiculars. If two points

In Euclidean geometry, the AA postulate states that two triangles are similar if they have two corresponding angles congruent. The AA postulate follows

benefit over anti-lag systems in race cars is reliability. A variable-geometry turbocharger provides an improved response at varying engine speeds. With

a much wider class of problems in algebraic geometry. See also algebraic geometry and analytic geometry for a more general theory. Using the intrinsic

In Euclidean geometry, an angle can refer to a number of concepts relating to the intersection of two straight lines at a point. Formally, an angle is

In geometry, an octagon (from Ancient Greek ὀκτάγωνον (oktágōnon) 'eight angles') is an eight-sided polygon or 8-gon. A regular octagon has Schläfli symbol

finite element method, values are calculated at discrete places on a meshed geometry. "Finite volume" refers to the small volume surrounding each node point

under it along the Hellenic subduction zone. The Hellenic Trench trends parallel to its southern side. The Aegean Sea plate, a microplate, is often considered

In geometry, the Bilinski dodecahedron is a convex polyhedron with twelve congruent golden rhombus faces. It has the same topology as the face-transitive

In geometry, given a triangle ABC and a point P on its circumcircle, the three closest points to P on lines AB, AC, and BC are collinear. The line through

meaningful in Euclidean geometry but meaningless in projective geometry. A different situation appeared in the 19th century: in some geometries the sum of the

a wood saw that is specially designed for making a rip cut, a cut made parallel to the direction of the wood grain. The cutting edge of each tooth has

{L}}} , and these complex dimensions appear in formulae which describe the geometry of the fractal. For fractal strings associated with sets like Cantor sets

doi:10.1007/BF01181172. S2CID 120768630. Falconer, K. J. (1985). The Geometry of Fractal Sets. Cambridge University Press. pp. 96–99. The Kakeya Problem

Karmarkar, Narendra (1991). "A new parallel architecture for sparse matrix computation based on finite projective geometries". Proceedings of the 1991 ACM/IEEE

In geometry, a skew apeirohedron is an infinite skew polyhedron consisting of nonplanar faces or nonplanar vertex figures, allowing the figure to extend

orientable. Cartesian coordinate system – Most common coordinate system (geometry) Chirality (mathematics) – Property of an object that is not congruent

"Spaces of geodesics". In Del Riego, L. (ed.). Differential Geometry Workshop on Spaces of Geometry (Guanajuato, 1992). Aportaciones Mat. Notas Investigación

Publications (September 1990), link to Google books Hunt, K. H., Kinematic Geometry of Mechanism, Oxford University Press, 1990 R.S. Ball, A Treatise on the

comprising periodically repeating opaque parallel lines as shown in Figure 1. The lines of one layer are parallel to the lines of the second layer. The superposition

isometric view can be obtained in a 3D scene. Starting with the camera aligned parallel to the floor and aligned to the coordinate axes, it is first rotated horizontally

needed to complete a proof in plane geometry. Other common auxiliary constructs in elementary plane synthetic geometry are the helping circles. As an example

many metamaterials, these fields are not necessarily parallel. When one set of the fields are parallel, and one set are not, the material is called anisotropic

Computing (Old City Publishing; 2011) Computational Geometry (Elsevier; 1993) International Journal of Parallel, Emergent, and Distributed Systems (Taylor and

mathematics, intersection theory is one of the main branches of algebraic geometry, where it gives information about the intersection of two subvarieties

fundamental contributions to data structures, computational geometry, computer algebra, parallel computing, VLSI design, computational complexity, combinatorial

This is a list of differential geometry topics. See also glossary of differential and metric geometry and list of Lie group topics. List of curves topics

part of a degenerate polyhedron. An angle of 180° means the faces are parallel, as in a tiling. An angle greater than 180° exists on concave portions

two-dimensional geometry, the infinite dihedral group represents the frieze group symmetry, p1m1, seen as an infinite set of parallel reflections along

have pitch angles of exactly 90 degrees have teeth that point outward parallel with the axis and resemble the points on a crown, whence the name crown

different proof that does not presuppose the parallel postulate and is therefore valid in non-Euclidean geometry as well. By its help, the mapping that maps

schedule instructions on the CPU to minimize latency. The geometry processor contains a Geometry Assembler, a Tesselator, and a Vertex Assembler. The Tesselator

Files have angled ridges or teeth and cannot be resharpened. Floats have parallel teeth and they can be resharpened as many times as the thickness of the

In geometry, a hemipolyhedron is a uniform star polyhedron some of whose faces pass through its center. These "hemi" faces lie parallel to the faces of

In geometry, a hemipolyhedron is a uniform star polyhedron some of whose faces pass through its center. These "hemi" faces lie parallel to the faces of

geometry of general relativity, and attempted to incorporate electromagnetic fields into a more general geometry, since ordinary Riemannian geometry seemed

On the Moving Sphere and On Risings and Settings, both about spherical geometry. Autolycus was born in Pitane, a town of Aeolis within Ionia, Asia Minor

two-dimensional geometry, the infinite dihedral group represents the frieze group symmetry, p1m1, seen as an infinite set of parallel reflections along

William F. Osgood & William C. Graustein (1922) Plane and Solid Analytic Geometry, page 307, link from University of Michigan Historical Math Collection

downwards into the fault at the base of the cover sequence with a helicoidal geometry. In detail, many strike-slip faults at surface consist of en echelon or

Ordered geometry is a form of geometry featuring the concept of intermediacy (or "betweenness") but, like projective geometry, omitting the basic notion

In differential geometry, the two principal curvatures at a given point of a surface are the maximum and minimum values of the curvature as expressed by

the grain and is thus differentiated from a groove which is cut with, or parallel to the grain. Dados are often used to affix shelves to cabinetry bodies

relativity, and differential geometry more generally, Schild's ladder is a first-order method for approximating parallel transport of a vector along a

the parallel postulate was significant for the further development of geometry, as it clearly shows the possibility of non-Euclidean geometries. The

across the wave face, or "down the line," that is, parallel to the wave crest and beach – riding parallel to the crest (perpendicular to the pull of gravity

A sheeted dyke complex, or sheeted dike complex, is a series of sub-parallel intrusions of igneous rock, forming a layer within the oceanic crust. At mid-ocean

Because its two threads run straight and parallel, a straight stitch is not natively stretchable. Zigzag stitch geometry is produced when the needle moves rhythmically

{\displaystyle \cos \alpha x+\sin \alpha y=p} then the vector (cos α, sin α) is parallel to the segment PX, and the length of PX, which is the distance from the

end points of one diameter are parallel to the other diameter !). This is a standard situation in descriptive geometry: From an ellipse the center C {\displaystyle

plane of an optical system (such as a camera) when the lens plane is not parallel to the image plane. It is applicable to the use of some camera movements

a major fault that cuts across an area of steeply folded bedrock. The geometry of a trellis drainage system is similar to that of a common garden trellis

Quadrics in "Geometry Formulas and Facts", excerpted from 30th Edition of CRC Standard Mathematical Tables and Formulas, CRC Press, from The Geometry Center

characteristics code with arbitrary geometry modeling, developed for EPRI by TransWare Enterprises Inc. RAPTOR-M3G – A proprietary parallel radiation transport code

seat tube. In a traditional-geometry diamond frame, the top tube is horizontal (parallel to the ground). In a compact-geometry frame, the top tube is normally

In geometry, the relation of hyperbolic orthogonality between two lines separated by the asymptotes of a hyperbola is a concept used in special relativity

affine plane: in analytic geometry this results in division by zero, while in synthetic geometry the lines A1A2, B1B2 are parallel to the line of centers

articles about curves used in different fields: mathematics (including geometry, statistics, and applied mathematics), physics, engineering, economics

Look up collinearity or collinear in Wiktionary, the free dictionary. In geometry, collinearity of a set of points is the property of their lying on a single

acting parallel to the plane of the crack and perpendicular to the crack front), and Mode III – Tearing mode (a shear stress acting parallel to the plane

In hyperbolic geometry, a horosphere (or parasphere) is a specific hypersurface in hyperbolic n-space. It is the boundary of a horoball, the limit of a

based ATMOL program, which, unlike GAMESS, lacked analytical gradients for geometry optimisation. GAMESS-UK can perform many general computational chemistry

Non-Euclidean geometry, systems of points, lines, and planes analogous to Euclidean geometry but without uniquely determined parallel lines Euclidean

to convey information about an object. A common use is to specify the geometry necessary for the construction of a component and is called a detail drawing

In geometry, the truncated octahedron is the Archimedean solid that arises from a regular octahedron by removing six pyramids, one at each of the octahedron's

In joinery, a groove is a slot or trench cut into a member which runs parallel to the grain. A groove is thus differentiated from a dado, which runs across

known as anode and cathode. The electrodes may be in the form of parallel plates (Parallel Plate Ionization Chambers: PPIC), or a cylinder with a coaxially

In geometry, a transversal plane is a plane that intersects (not contains) two or more lines or planes. A transversal plane may also form dihedral angles

Bézout's theorem is a statement in algebraic geometry concerning the number of common zeros of n polynomials in n indeterminates. In its original form

parallel postulate yield Euclidean geometry, and with the parallel postulate negated, yields non-Euclidean geometry. For examples, elliptic geometry (no

In geometry, Plücker coordinates, introduced by Julius Plücker in the 19th century, are a way to assign six homogeneous coordinates to each line in projective

of surface energy at various times within the canyon depends on canyon geometry and orientation. Canyons with north–south orientation were found to have

of the other two. Constant width means that the separation of every two parallel supporting lines is the same, independent of their orientation. Because

(S-S)=\operatorname {span} (S-S)} is always a linear subspace of X {\displaystyle X} parallel to aff ⁡ S {\displaystyle \operatorname {aff} S} if S ≠ ∅ {\displaystyle

Möbius geometry, where lines and circles can be mapped to each other, but neither can be mapped to points. Both Möbius geometry and Laguerre geometry are

Einstein's field equation. The term pp stands for plane-fronted waves with parallel propagation, and was introduced in 1962 by Jürgen Ehlers and Wolfgang Kundt

In differential geometry, a quaternionic manifold is a quaternionic analog of a complex manifold. The definition is more complicated and technical than

author of New Foundations of Geometry (1835–1838). He also wrote Geometrical Investigations on the Theory of Parallels (1840) and Pangeometry (1855)

that the scope of axonometric projection could encompass every type of parallel projection, including not only orthographic projection (and multiview projection)