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This is list of geometry topics, by Wikipedia page. Table of Geometry, from the 1728 Cyclopaedia. ...
In geometry, two sets of points are of the same shape precisely if one can be transformed to another by dilating (i. ...
Following is a list of some mathematically well-defined shapes. ...
This is a list of differential geometry topics, by Wikipedia page. ...
A geometer is a mathematician whose area of study is geometry. ...
This is a list of curves, by Wikipedia page. ...
This is a list of curve topics in mathematics, by Wikipedia page. ...
Types, methodologies, and terminologies of geometry
Absolute geometry is a geometry that does not assume the parallel postulate or any of its alternatives. ...
In geometry, affine geometry occupies a place intermediate between Euclidean geometry and projective geometry. ...
Algebraic geometry is a branch of mathematics which, as the name suggests, combines abstract algebra, especially commutative algebra, with geometry. ...
Analytic geometry, also called coordinate geometry and earlier referred to as Cartesian geometry, is the study of geometry using the principles of algebra. ...
In mathematics, birational geometry is a part of the subject of algebraic geometry, that deals with the geometry of an algebraic variety that is dependent only on its function field. ...
In mathematics, complex geometry is the application of complex numbers to plane geometry. ...
Discrete geometry or combinatorial geometry may be loosely defined as study of geometrical objects and properties that are discrete or combinatorial, either by their nature or by their representation; the study that does not essentially rely on the notion of continuity. ...
In computer science, computational geometry is the study of algorithms to solve problems stated in terms of geometry. ...
In mathematics, conformal geometry is the study of the set of angle-preserving (conformal) transformations on a Euclidean-like space with a point added at infinity, or a Minkowski-like space with a couple of points added at infinity. That is, the setting is a compactification of a familiar space...
Constructive solid geometry (CSG) is a technique used in solid modeling. ...
In mathematics, contact geometry is the study of completely nonintegrable hyperplane fields on manifolds. ...
Convex Geometry is the branch of geometry studying convex bodies: compact, convex sets in Euclidean space. ...
Descriptive geometry builds on a practice, evolved over centuries, of displaying two images of an object, one as seen in one direction and a second image as seen from a direction 90° rotated (e. ...
In mathematics, differential topology is the field dealing with differentiable functions on differentiable manifolds. ...
Digital geometry deals with discrete sets (usually discrete point sets) considered to be digitized models or images of objects of the 2D or 3D Euclidean space. ...
Discrete geometry or combinatorial geometry may be loosely defined as study of geometrical objects and properties that are discrete or combinatorial, either by their nature or by their representation; the study that does not essentially rely on the notion of continuity. ...
Distance Geometry is the characterization and study of sets based only on given values of the distance between member pairs. ...
Elliptic geometry (sometimes known as Riemannian geometry) is a non-Euclidean geometry, in which, given a line L and a point p outside L, there exists no line parallel to L passing through p. ...
Euclid Euclidean geometry is a mathematical system due to the Hellenistic mathematician Euclid of Egypt. ...
A finite geometry is any geometric system that has only a finite number of points. ...
In number theory, the geometry of numbers is a topic and method arising from the work of Hermann Minkowski, on the relationship between convex sets and lattices in n-dimensional space. ...
The ancient Greek mathematician, physicist, and engineer Archimedes of Syracuse was the first mathematician to make explicit use of infinitesimals. ...
A triangle immersed in a saddle-shape plane (an hyperbolic paraboloid), as well as two diverging parallel lines. ...
In mathematics and especially in statistical inference, information geometry is the study of probability and information by way of differential geometry. ...
In mathematics, the term integral geometry in is used in two ways, which, although related, imply different views of the content of the subject. ...
In mathematics, inversive geometry is the geometry of circles and the set of transformations that map all circles into circles. ...
Behavior of lines with a common perpendicular in each of the three types of geometry The term non-Euclidean geometry (also spelled: non-Euclidian geometry) describes both hyperbolic and elliptic geometry, which are contrasted with Euclidean geometry. ...
In computer science, computational geometry is the study of algorithms to solve problems stated in terms of geometry. ...
In mathematics, Euclidean geometry is the familiar kind of geometry on the plane or in three dimensions. ...
In mathematics, Euclidean geometry is the familiar kind of geometry on the plane or in three dimensions. ...
Projective geometry is a non-metrical form of geometry that emerged in the early 19th century. ...
In mathematics, Riemannian geometry has at least two meanings, one of which is described in this article and another also called elliptic geometry. ...
Spherical geometry is the geometry of the two-dimensional surface of a sphere. ...
In mathematics, a symplectic manifold is a smooth manifold equipped with a closed, nondegenerate 2-form. ...
Synthetic geometry is a descriptive term that identifies a methodology of geometry which makes use of theorems and synthetic observations to create theorems or solve problems, as opposed to analytic geometry which uses algebra, numbers, computations to draw theorems or solve problems. ...
In mathematics, transformation geometry is a name for a pedagogic theory for teaching Euclidean geometry, based on the Erlangen programme. ...
Euclid Euclidean geometry is a mathematical system due to the Hellenistic mathematician Euclid of Egypt. ...
Hilberts axioms are a set of 20 assumptions (originally 21), David Hilbert proposed in 1899 as the foundation for a modern treatment of Euclidean geometry. ...
A spatial point is an entity with a location in space but no extent (volume, area or length). ...
In mathematics, a locus (Latin for place, plural loci) is a collection of points which share a common property. ...
A line, or straight line, can be described as an (infinitely) thin, (infinitely) long, perfectly straight curve (the term curve in mathematics includes straight curves). In Euclidean geometry, exactly one line can be found that passes through any two points. ...
Parallel is a term in geometry and in everyday life that refers to a property in Euclidean space of two or more lines or planes, or a combination of these. ...
This article is about angles in geometry. ...
It has been suggested that this article or section be merged into line. ...
In geometry, adjacent angles are angles that share a common vertex and edge, but which do not overlap. ...
A central angle is an angle whose vertex is the center of a circle, and whose sides pass through a pair of points on the circle, thereby subtending an arc between those two points whose angle is (by definition) equal to the central angle itself. ...
A pair of angles are complementary if the sum of their measures is 90 degrees. ...
In geometry, an inscribed angle is formed when two secant lines of a circle (or, in a degenerate case, when one secant line and one tangent line of that circle) intersect on the circle. ...
In geometry, an internal angle is an angle that 2 sides of a polygon form by touching. ...
A pair of angles are supplementary if their respective measures sum to 180 degrees. ...
Creating a regular hexagon with a ruler and compass Construction of a regular pentagon Compass and straightedge or ruler-and-compass construction is the construction of lengths or angles using only an idealized ruler and compass. ...
An example of congruence. ...
IT IS KNOWN AS MARK a lunitice insain int gw brain ...
Rotation of a plane, seen as the rotation of the terrain relative to the plane (exposure time 1. ...
In geometry, coordinate rotations and reflections are two kinds of isometry which are related to each to other. ...
In Euclidean geometry, translation is a transformation of Euclidean space which moves every point by a fixed distance in the same direction. ...
Example of a glide reflection In geometry, a glide reflection is a type of isometry of the Euclidean plane. ...
Several equivalence relations in mathematics are called similarity. ...
Several equivalence relations in mathematics are called similarity. ...
In mathematics, a homothety (or homothecy) is a transformation of space which dilates distances with respect to a fixed point called the origin. ...
In physics and mechanics, shear refers to a deformation that causes parallel surfaces to slide past one another (as opposed to compression and tension, which cause parallel surfaces to move towards or away from one another). ...
In mathematics, Euclidean geometry is the familiar kind of geometry on the plane or in three dimensions. ...
2D computer graphics is the computer-based generation of digital images—mostly from two-dimensional models (such as 2D geometric models, text, and digital images) and by techniques specific to them. ...
A 2D geometric model is a geometric model of an object as two-dimensional figure, usually on the Euclidean or Cartesian plane. ...
In geometry, an altitude of a triangle is a straight line through a vertex and perpendicular to (i. ...
In geometry, Brahmaguptas formula formula finds the area of any quadrilateral. ...
Creating a regular hexagon with a ruler and compass Construction of a regular pentagon Compass and straightedge or ruler-and-compass construction is the construction of lengths or angles using only an idealized ruler and compass. ...
This square and circle have the same area. ...
In mathematics, complex geometry is the application of complex numbers to plane geometry. ...
Types of conic sections Table of conics, Cyclopaedia, 1728 In mathematics, a conic section (or just conic) is a curve formed by intersecting a cone (more precisely, a right circular conical surface) with a plane. ...
In geometry, the focus (pl. ...
In Euclidean geometry, a circle is the set of all points in a plane at a fixed distance, called the radius, from a fixed point, the centre. ...
This list of circle topics is not intended for metaphorical circles, but rather for topics related to the geometric shape. ...
In geometry, Thales theorem (named after Thales of Miletus) states that if A, B and C are points on a circle where the line AC is a diameter of the circle, then the angle ABC is a right angle. ...
In geometry, a circumcircle of a given two-dimensional geometric shape is the smallest circle which contains the shape completely within it. ...
In geometry, a set of points is said to be concyclic if they lie on a common circle. ...
In geometry, the incircle or inscribed circle of a triangle is the largest circle contained in the triangle; it touches (is tangent to) the three sides. ...
In geometry, an orthocentric system is a set of four points in the plane where one point is the orthocenter of the triangle formed by the other three. ...
In geometry, the power center of three circles, also called the radical center, is the intersection point of the three radical lines. ...
In geometry, the nine-point circle is a circle that can be constructed for any given triangle. ...
In geometry, the problem of dividing a circle into areas by means of an inscribed polygon with n sides, in such a way as to maximise the number of areas created by the edges and diagonals, has a solution by an inductive method. ...
Mrs. ...
Isoperimetry literally means having an equal perimeter. In mathematics, isoperimetry is the general study of geometric figures having equal boundaries. ...
An annulus In mathematics, an annulus (the Latin word for little ring, with plural annuli) is a ring-shaped geometric figure, or more generally, a term used to name a ring-shaped object. ...
In mathematics, Ptolemaios theorem is a relation in Euclidean geometry between the four sides and two diagonals or chords of a quadrilateral inscribed in circle. ...
(This page refers to eccentricity in mathematics. ...
The ellipse and some of its mathematical properties. ...
The semi-major axis of an ellipse In geometry, the term semi-major axis (also semimajor axis) is used to describe the dimensions of ellipses and hyperbolae. ...
A graph of a hyperbola, where h = k = 0 and a = b = 2. ...
Wikisource has an original article from the 1911 Encyclopædia Britannica about: Parabola A parabola The parabola (from the Greek: παÏαβολή) is a conic section generated by the intersection of a right circular conical surface and a plane parallel to a generating straight line of that surface. ...
In mathematics, the matrix representation of conic sections is one way of studying a conic section, its axis, vertices, foci, tangents, and the relative position of a given point. ...
Dandelin Spheres—graphics by Hop David In geometry, a nondegenerate conic section formed by a plane intersecting a cone has one or two Dandelin spheres characterized thus: Each Dandelin sphere touches, but does not cross, both the plane and the cone. ...
For closed convex planar bodies whose boundary is a smooth curve, one notes that there are exactly two parallel tangent lines to the boundary curve in any given direction. ...
In geometry, a cyclic quadrilateral is a quadrilateral whose vertices all lie on a single circle. ...
In geometry, Eulers line (red line in the image), named after Leonhard Euler, is the line passing through the orthocenter (blue), the circumcenter (green), the centroid (yellow), and the center of the nine-point circle (red point) of any triangle. ...
For alternate meanings, such as the musical instrument, see triangle (disambiguation). ...
A frieze group is an infinite discrete symmetry group for a pattern on a strip (infinitely wide rectangle). ...
In geometry, the golden angle is the angle created by dividing the circumference c of a circle into a section a and a smaller section b such that and and taking the angle of arc subtended by the length of circumference equal to b as the golden angle. ...
In geometry, Herons formula (also called Heros formula) states that the area of a triangle whose sides have lengths a, b and c is where s is the triangles semiperimeter: (see also square root). ...
A Heronian triangle is a triangle whose side lengths and area are all rational numbers. ...
Interactive geometry software (IGS, also called dynamic geometry environments, DGEs) are computer programs which allow one to create and then manipulate geometric constructions, primary in plane geometry. ...
Pappus of Alexandria (Greek Πάππος ὠἈλεξανδÏεÏÏ‚) is one of the most important Hellenistic mathematicians of antiquity, known for his work Synagoge or Collection (c. ...
a and b are parallel, the transversal t produces congruent angles. ...
In geometry, given a triangle and a point, the pedal triangle is given thus: Let the triangle be ABC, and the point P. Drop perpendiculars from P to the three sides of the triangle (these may need to be produced, ie extended). ...
Look up Polygon in Wiktionary, the free dictionary. ...
In geometry, a star polygon is a complex, equilateral equiangular polygon, so named for its starlike appearance, created by connecting one vertex of a simple, regular, n-sided polygon to another, non-adjacent vertex and continuing the process until the original vertex is reached again. ...
Given a simple polygon constructed on a grid of equal-distanced points (i. ...
In mathematics, shape dissection is a theory about subdivision, especially of polygons and polyhedra and in relation to fundamental questions on area and volume. ...
In geometry, the Bolyai-Gerwien theorem states that if two simple polygons of equal area are given, one can cut the first into finitely many polygonal pieces and rearrange the pieces to obtain the second polygon. ...
In geometry, the Poncelet-Steiner theorem on ruler-and-compass constructions states that whatever can be constructed by straightedge with compass, can be constructed by straightedge alone, if you are given a single circle and the location of its centre. ...
Polygon triangulation is a topic in computational geometry. ...
Pons Asinorum (Latin for Bridge of Donkeys) is the name given to Euclids fifth proposition in Book 1 of his Elements of geometry, namely that in an isosceles triangle, the angles at the base are equal, and if the equal length sides are extended then the angles beyond the...
In mathematics, the Pythagorean theorem or Pythagorass theorem, is a relation in Euclidean geometry between the three sides of a right triangle. ...
Sangaku or San Gaku (ç®—é¡; lit. ...
A straightedge is a tool similar to a ruler, but without markings. ...
In geometry, three special lines are associated with every triangle, the triangles symmedians. ...
In geometry, a tiling (also called tessellation, mosaic or dissection) of a given shape S consists of a collection of other shapes which precisely cover S. Often the shape S to be tiled is the Euclidean plane, but other shapes and three-dimensional objects are considered as well. ...
In a given set S={A} of shapes (e. ...
A tessellated plane seen in street pavement. ...
An aperiodic tiling is a tiling of the plane by a set of prototiles that can only be tiled in a non-repeating (non-periodic) pattern. ...
Wang tiles (or Wang dominoes), first proposed by Hao Wang in 1961, are equal-sized squares with a color on each edge which give rise to a simple undecidable decision problem. ...
A Penrose tiling A Penrose tiling is pattern of tiles, discovered by Roger Penrose and Robert Ammann, which could completely cover an infinite plane, but only in a pattern which is non-repeating (aperiodic). ...
In acrobatics, the trapeze is a certain acrobatic device that is shaped like a trapezoid. ...
The term trapezium can mean more than one thing: In human anatomy, trapezium is a bone in the hand In geometry, a trapezium is also a name for a class of quadrilaterals. ...
An isosceles trapezoid. ...
For alternate meanings, such as the musical instrument, see triangle (disambiguation). ...
In mathematics, the Pythagorean theorem or Pythagorass theorem is a relation in Euclidean geometry between the three sides of a right triangle. ...
In mathematics, triangle inequality is the theorem stating that for any triangle, the measure of a given side must be less than the sum of the other two sides but greater than the difference between the two sides. ...
In geometry, Pedoes inequality, named after Dan Pedoe, states that if a, b, and c are the lengths of the sides of a triangle with area f, and A, B, and C are the lengths of the sides of a triangle with area F, then with equality if and...
Wikibooks has more about this subject: Trigonometry Trigonometry (from the Greek trigonon = three angles and metro = measure) is a branch of mathematics dealing with angles, triangles and trigonometric functions such as sine, cosine and tangent. ...
This is a list of trigonometry topics, by Wikipedia page. ...
Example of an Egyptian design with wallpaper group p4m A wallpaper group (or plane crystallographic group) is a mathematical concept to classify repetitive designs on two-dimensional surfaces, such as walls, based on the symmetries in the pattern. ...
3-dimensional Euclidean geometry (solid geometry) In mathematics, solid geometry was the traditional name for the geometry of three-dimensional Euclidean space — for practical purposes the kind of space we live in. ...
This article or section does not cite its references or sources. ...
The rewrite of this article is being devised at Talk:3D computer graphics/Temp. ...
Binary space partitioning (BSP) is a method for recursively subdividing a space into convex sets by hyperplanes. ...
A ray traced scene. ...
The Graham scan, named after Ronald Graham, is a method of computing the convex hull of a given set of points in the plane with time complexity O(n log n). ...
In mathematics, the Borromean rings consist of three topological circles which are linked despite the fact that no two of them are linked, i. ...
Quartz crystal In chemistry and mineralogy, a crystal is a solid in which the constituent atoms, molecules, or ions are packed in a regularly ordered, repeating pattern extending in all three spatial dimensions. ...
Cuisenaire rods are rods used in elementary school as well as other levels of learning and even with adults. ...
In projective geometry, Desargues theorem, named in honor of Girard Desargues, states: In a projective space, two triangles are in perspective axially if and only if they are in perspective centrally. ...
A right circular cone In geometry, a right circular cone is a cone whose base is a circle and whose apex is on a line perpendicular to the plane containing the base. ...
Hyperboloid of one sheet Hyperboloid of two sheets In mathematics, a hyperboloid is a quadric, a type of surface in three dimensions, described by the equation: (hyperboloid of one sheet), or (hyperboloid of two sheets) If, and only if, , it is a hyperboloid of revolution. ...
Paraboloid of revolution Hyperbolic paraboloid In mathematics, a paraboloid is a quadric, a type of surface in three dimensions, described by the equation: (elliptic paraboloid), or (hyperbolic paraboloid). ...
This article is about the geometric shape. ...
In geometry, the defect of a vertex of a polyhedron is the amount by which the sum of the angles of the faces at the vertex falls short of a full circle. ...
In geometry, a prism is a polyhedron made of two parallel copies of some polygonal base joined by faces that are rectangles or parallelograms. ...
A prismatoid is a polyhedron where all vertices lie in two parallel planes. ...
Honeycomb on a Langstroth frame A honeycomb is a mass of hexagonal wax cells built by honeybees in their nests to contain their larvae and stores of honey and pollen. ...
Geometric shape created by connecting a polygonal base to an apex For other versions including architectural Pyramids, see Pyramid (disambiguation). ...
In geometry, a parallelepiped (pronounced ; meaning of parallel planes) or parallelopipedon is a three-dimensional figure like a cube, except that its faces are not squares but parallelograms. ...
A tetrahedron (plural: tetrahedra) is a polyhedron composed of four triangular faces, three of which meet at each vertex. ...
A Heronian tetrahedron is a tetrahedron whose sides, faces and volume are all rational numbers. ...
In solid geometry and some ancient physical theories, a Platonic solid is a convex polyhedron with: All its faces being congruent regular polygons The same number of faces meeting at each of its vertices These are in contrast to: The Kepler-Poinsot solids, which are not convex The Archimedean and...
In geometry an Archimedean solid or semi-regular solid is a semi-regular convex polyhedron composed of two or more types of regular polygon meeting in identical vertices. ...
A Kepler solid (also called Kepler-Poinsot solid) is a regular non-convex polyhedron, all the faces of which are identical regular polygons and which has the same number of faces meeting at all its vertices (compare to Platonic solids). ...
The elongated square gyrobicupola (J37), a Johnson solid In geometry, a Johnson solid is a convex polyhedron, each face of which is a regular polygon, which is not a Platonic solid, Archimedean solid, prism, or antiprism. ...
A uniform polyhedron is a polyhedron with regular polygons as faces and identical vertices. ...
A polyhedral compound is a polyhedron which is itself composed of several other polyhedra sharing a common centre, the three-dimensional analogs of polygonal compounds such as the hexagram. ...
The third on Hilberts list of mathematical problems, presented in 1900, is the easiest one. ...
The triaugmented triangular prism, a convex deltahedron A deltahedron (plural deltahedra) is a polyhedron whose faces are all equilateral triangles. ...
A surface normal, or just normal to a flat surface is a three-dimensional vector which is perpendicular to that surface. ...
In mathematics, a 3-sphere is a higher-dimensional analogue of a sphere. ...
In mathematics, a spheroid is a quadric surface in three dimensions obtained by rotating an ellipse about one of its principal axes. ...
3D rendering of an ellipsoid In mathematics, an ellipsoid is a type of quadric that is a higher dimensional analogue of an ellipse. ...
A parabolic microphone uses a parabolic reflector to collect and focus sound waves onto a microphone receiver, in much the same way that a parabolic antenna (e. ...
A parabolic reflector (also known as a parabolic dish or a parabolic mirror) is a reflective device formed in the shape of a paraboloid of revolution. ...
Cross section may refer to the following In geometry, Cross section is the intersection of a 3-dimensional body with a plane. ...
The sphericon is a 3D shape with one side and two edges, discovered by Colin Roberts, of Hertfordshire, England. ...
Stereographic projection of a circle of radius R onto the x axis. ...
In mathematics, solid geometry was the traditional name for the geometry of three-dimensional Euclidean space — for practical purposes the kind of space we live in. ...
n-dimensional Euclidean geometry The solid interior of a sphere or circle; in mathematics, latter terms refer specifically to the (n-1)-dimensional surface of an n-dimensional solid ball. ...
Look up convex in Wiktionary, the free dictionary. ...
Convex Hull: Elastic band analogy // Alternative definitions In mathematics, the convex hull or convex envelope for a set of points X in a real vector space V is the minimal convex set containing X. (Note that X may be the union of any set of objects made of points). ...
In mathematics, a Coxeter group is a group with a presentation of the form where mi,j ≥ 2; the condition mi,j = ∞ means no relation of the form (xixj)m should be imposed. ...
In mathematics the Euclidean distance or Euclidean metric is the ordinary distance between the two points that one would measure with a ruler, which can be proven by repeated application of the Pythagorean theorem. ...
A hyperplane is a concept in geometry. ...
See lattice for other meanings of this term, both within and without mathematics. ...
In mathematics, integral polytopes have associated Ehrhart polynomials which encode some geometrical information about them. ...
In mathematics, the Leech lattice is a lattice Λ in R24 discovered John Leech ( 16 (1964), 657--682). ...
In mathematics, Minkowskis theorem in the geometry of numbers applies to convex symmetric sets and lattices; it relates the number of contained lattice points to the volume of such a set. ...
In mathematics, sphere packing problems are problems concerning arrangements of non-overlapping identical spheres which fill a space. ...
In mathematics, sphere packing problems are problems concerning arrangements of non-overlapping identical spheres which fill a space. ...
In mathematics, the Kepler conjecture is a conjecture about sphere packing in three dimensional Euclidean space. ...
In geometry, the kissing number problem is to find the maximum number of spheres of radius 1 that can simultaneously touch the unit sphere in n-dimensional Euclidean space (or, with the restriction for their centres to be in a particular lattice). ...
In geometry, a tiling (also called tessellation, mosaic or dissection) of a given shape S consists of a collection of other shapes which precisely cover S. Often the shape S to be tiled is the Euclidean plane, but other shapes and three-dimensional objects are considered as well. ...
In geometry, the Andreini tessellations are the complete set of 28 uniform (space-filling) honeycombs of 3-space. ...
In mathematics, a uniform tessellation is a tessellation of a d-dimensional space, or a (hyper)surface, such that all its vertices are identical, i. ...
This is the Voronoi diagram of a random set of points in the plane (all points lie within the image). ...
In mathematics, and computational geometry, the Delaunay triangulation or Delone triangularization for a set P of points in the plane is the triangulation DT(P) of P such that no point in P is inside the circumcircle of any triangle in DT(P). ...
Quasicrystals are a peculiar form of solid in which the atoms are arranged in a seemingly regular, yet non-repeating structure. ...
// The parallelogram law in elementary geometry In elementary geometry, the parallelogram law states that the sum of the squares of the lengths of the four sides of a parallelogram equals the sum of the squares of the lengths of the two diagonals. ...
In geometry polytope means, first, the generalization to any dimension of polygon in two dimensions, and polyhedron in three dimensions. ...
In mathematics, the Schläfli symbol is a simple notation that gives a summary of some important properties of a particular regular polytope. ...
A dodecahedron, one of the five Platonic solids. ...
A sphere (< Greek σφαίÏα) is a perfectly symmetrical geometrical object. ...
Ellipsoid Elliptic Paraboloid Hyperbolic Paraboloid Hyperboloid of One Sheet Hyperboloid of Two Sheets Cone Elliptic Cylinder Hyperbolic Cylinder Parabolic Cylinder In mathematics a quadric, or quadric surface, is any D-dimensional (hyper-)surface represented by a second-order equation in spatial variables (coordinates). ...
In mathematics, a hypersphere is a sphere which has dimension 3 or higher. ...
A sphere (< Greek σφαίÏα) is a perfectly symmetrical geometrical object. ...
In mathematics, a spheroid is a quadric surface in three dimensions obtained by rotating an ellipse about one of its principal axes. ...
3D rendering of an ellipsoid In mathematics, an ellipsoid is a type of quadric that is a higher dimensional analogue of an ellipse. ...
Hyperboloid of one sheet Hyperboloid of two sheets In mathematics, a hyperboloid is a quadric, a type of surface in three dimensions, described by the equation: (hyperboloid of one sheet), or (hyperboloid of two sheets) If, and only if, , it is a hyperboloid of revolution. ...
Paraboloid of revolution Hyperbolic paraboloid In mathematics, a paraboloid is a quadric, a type of surface in three dimensions, described by the equation: (elliptic paraboloid), or (hyperbolic paraboloid). ...
In common usage and elementary geometry, a cone (Greek: κώνος) is a solid object obtained by rotating a right triangle around one of its two short sides, the cones axis. ...
A torus. ...
In mathematics, a root system is a configuration of vectors in a Euclidean space satisfying certain geometrical properties. ...
Several equivalence relations in mathematics are called similarity. ...
A zonohedron is a convex polyhedron where every face is a polygon with point symmetry, or equivalently, symmetry under rotations through 180°. The regular polygons with such symmetry are those with an even number of sides, so the zonohedra with regular polygons for sides are easily enumerated: Of the Platonic...
Non-Euclidean geometry Projective geometry is a non-metrical form of geometry that emerged in the early 19th century. ...
In projective geometry, Desargues theorem, named in honor of Girard Desargues, states: In a projective space, two triangles are in perspective axially if and only if they are in perspective centrally. ...
Girard Desargues (1591 - 1661) was a French mathematician and one of the founders of projective geometry. ...
In geometry and topology, the line at infinity is a line which is added to the real (affine) plane in order to give closure to, and remove the exceptional cases from, the incidence properties of the resulting projective plane. ...
The point at infinity, also called ideal point, is a point which when added to the real number line yields a closed curve called the real projective line, . Nota Bene: The real projective line is not equivalent to the extended real number line. ...
In projective geometry, the plane at infinity is a projective plane which is added to the affine 3-space in order to give it closure of incidence properties. ...
In mathematics, in particular projective geometry, the hyperplane at infinity, also called ideal hyperplane, is a projective (n − 1) -space added to Euclidean n-space — — in order to give it closure of incidence properties, thereby converting into the projective n-space . ...
In mathematics, a projective line is a one-dimensional projective space. ...
Projective plane - Wikipedia, the free encyclopedia /**/ @import /skins-1. ...
The Roman surface (so called because Jakob Steiner was in Rome when he thought of it) is a self-intersecting immersion of the real projective plane into three-dimensional space, with an unusually high degree of symmetry. ...
In mathematics, a projective space is a fundamental construction from any vector space. ...
In mathematics, the Riemann sphere is the unique simply-connected, compact, Riemann surface. ...
In mathematics, the complex projective plane, usually denoted CP2, is the two-dimensional complex projective space. ...
In mathematics, the fundamental theorem of projective geometry states that if Pn is a projective space and F and F′ are frames of Pn, then there exists a unique projective transformation sending F to F′. In case n = 1 this comes down to saying that given two ordered triples of...
A projective transformation is a transformation used in projective geometry: it is the composition of a pair of perspective projections. ...
In mathematics, a Möbius transformation is a bijective conformal mapping of the extended complex plane (i. ...
In mathematics, the cross-ratio cr( w, x, y, z ) of an ordered quadruple of complex numbers (which may be real numbers) is Cross-ratios are preserved by linear fractional transformations, i. ...
Duality in the projective plane refers to the interchangeability between points and lines which preserves incidence properties. ...
In mathematics, homogeneous coordinates, introduced by August Ferdinand Möbius, allow affine transformations to be easily represented by a matrix. ...
WTF!?!? WTF!?!? WTF!?!? WTF!?!? WTF!?!? WTF!?!? WTF!?!? Pappuss hexagon theorem (attributed to Pappus of Alexandria) states that given one set of collinear points A, B, C, and another set of collinear points a, b, c, then the intersection points x, y, z of line pairs Ab and aB, Ac...
In geometry, the relations of incidence are those such as lies on between points and lines (as in point P lies on line L), and intersects (as in line L1 intersects line L2, in three-dimensional space). ...
In projective geometry, Pascals theorem states that if a hexagon is inscribed in any circle and opposite pairs of sides are extended until they meet. ...
In geometry, affine geometry occupies a place intermediate between Euclidean geometry and projective geometry. ...
In mathematics, an affine space is an abstract structure that generalises the affine-geometric properties of Euclidean space. ...
In geometry, an affine transformation or affine map (from the Latin, affinis, connected with) between two vector spaces consists of a linear transformation followed by a translation: In the finite-dimensional case each affine transformation is given by a matrix A and a vector b, which can be written as...
A finite geometry is any geometric system that has only a finite number of points. ...
In mathematics, differential topology is the field dealing with differentiable functions on differentiable manifolds. ...
In mathematics, contact geometry is the study of completely nonintegrable hyperplane fields on manifolds. ...
In mathematics, Riemannian geometry has at least two meanings, one of which is described in this article and another also called elliptic geometry. ...
In mathematics, a symplectic manifold is a smooth manifold equipped with a closed, nondegenerate 2-form. ...
Behavior of lines with a common perpendicular in each of the three types of geometry The term non-Euclidean geometry (also spelled: non-Euclidian geometry) describes both hyperbolic and elliptic geometry, which are contrasted with Euclidean geometry. ...
Angle excess is the amount by which the sum of the angles of a polygon on a sphere exceeds the sum of the angles of a polygon with the same number of sides in a plane. ...
A triangle immersed in a saddle-shape plane (an hyperbolic paraboloid), as well as two diverging parallel lines. ...
In geometry, a pseudosphere or tractricoid in the traditional usage, is the result of revolving a tractrix about its asymptote. ...
In geometry, a pseudosphere or tractricoid is the result of revolving a tractrix about its asymptote. ...
Elliptic geometry (sometimes known as Riemannian geometry) is a non-Euclidean geometry, in which, given a line L and a point p outside L, there exists no line parallel to L passing through p. ...
Spherical geometry is the geometry of the two-dimensional surface of a sphere. ...
In physics and mathematics, Minkowski space (or Minkowski spacetime) is the mathematical setting in which Einsteins theory of special relativity is most conveniently formulated. ...
The geometrization conjecture, also known as Thurstons geometrization conjecture, concerns the geometric structure of compact 3-manifolds. ...
Numerical geometry In mathematics, the differential geometry of curves provides definitions and methods to analyze smooth curves in Riemannian manifolds and Pseudo-Riemannian manifolds (and in particular in Euclidean space) using differential and integral calculus. ...
In the mathematical subfield of numerical analysis a Bézier curve is a parametric curve important in computer graphics. ...
One type of spline, a bézier curve In the mathematical subfield of numerical analysis, a spline is a special function defined piecewise by polynomials. ...
In the mathematical subfield of numerical analysis a Hermite spline is a spline curve where each polynomial of the spline is in Hermite form. ...
In the mathematical subfield of numerical analysis a B-spline is a spline function which has minimal support with respect to a given degree, smoothness, and domain partition. ...
NURBS, short for nonuniform rational B-spline, is a computer graphics technique for drawing curves. ...
A parametric surface is a surface defined by a parametric equation, involving two parameters. ...
Geometric algorithms Convex Hull: Elastic band analogy // Alternative definitions In mathematics, the convex hull or convex envelope for a set of points X in a real vector space V is the minimal convex set containing X. (Note that X may be the union of any set of objects made of points). ...
In computational geometry, the point in polygon (also point-in-polygon or PIP) problem asks whether a given point in the plane lies inside, outside, or on the boundary of a simple polygon. ...
The point location problems and algorithms are a fundamental topic of computational geometry. ...
Hidden line removal is an extension of wireframe rendering where lines (or segments of lines) covered by surfaces are not drawn. ...
Mathematical morphology (MM) is a theoretical model for digital images built upon lattice theory and topology. ...
Minkowski sum A + B B A In geometry, the Minkowski sum of two sets A and B in Euclidean space is the result of adding every element of A to every element of B, i. ...
Generalizations In mathematics, there is a close relationship between spaces, which are geometric in nature, and the numerical functions on them. ...
Topology (Greek topos, place and logos, study) is a branch of mathematics concerned with spatial properties preserved under bicontinuous deformation (stretching without tearing or gluing); these are the topological invariants. ...
Various In geometry, a figure is chiral (and said to have chirality) if it is not identical to its mirror image, or more particularly if it cannot be mapped to its mirror image by rotations and translations alone. ...
It has been suggested that this article or section be merged into Laterality. ...
A right-handed Cartesian coordinate system, presenting the z (up) vector and y (forward) vector, the right is defined to be the positive x vector. ...
This article is about the Twilight Zone episode. ...
An influential research programme and manifesto was published in 1872 by Felix Klein, under the title Vergleichende Betrachtungen über neuere geometrische Forschungen. ...
Four dimensions refers to adding a fourth dimension to our current three dimensions. ...
In mathematics, a symmetry group describes all symmetries of objects. ...
Invariant may have meanings invariant (computer science), such as a combination of variables not altered in a loop invariant (mathematics), something unaltered by a transformation invariant (music) invariant (physics) conserved by system symmetry This is a disambiguation page — a navigational aid which lists other pages that might otherwise share the...
In integral geometry (otherwise called geometric probability theory), Hadwigers theorem states that the space of translation-invariant, finitely additive, not-necessarily-nonnegative set functions defined on finite unions of compact convex sets in Rn consists (up to scalar multiples) of one measure that is homogeneous of degree k for...
To meet Wikipedias quality standards and make it more accessible, this article may require cleanup. ...
Borg cube ship Cubane Cube farm Cube puzzle Cube Rooms of the Queens House, Greenwich, and Wilton House, Wiltshire Cube root Cubic Cubic curve Cubic spline Bicubic spline Cubic equation Cubic function Cubic polynomial Cubicle Cubism Gelatinous cube Hilbert cube Ice Cube Impossible cube Magic cube Semiperfect magic cube...
Lower-case π (the lower case letter is usually used for the constant) The mathematical constant π is an irrational number, approximately equal to 3. ...
Square with symmetry group D4 Symmetry is a characteristic of geometrical shapes, equations, and other objects; we say that such an object is symmetric with respect to a given operation if this operation, when applied to the object, does not appear to change it. ...
In geometry, two sets have the same shape if one can be transformed to another by a combination of translations, rotations and uniform scalings. ...
A pattern is a form, template, or model (or, more abstractly, a set of rules) which can be used to make or to generate things or parts of a thing, especially if the things that are generated have enough in common for the underlying pattern to be inferred or discerned...
In mineralogy and crystallography, a crystal structure is a unique arrangement of atoms in a crystal. ...
A frieze group is an infinite discrete symmetry group for a pattern on a strip (infinitely wide rectangle). ...
In mathematics, an isometry, isometric isomorphism or congruence mapping is a distance-preserving isomorphism between metric spaces. ...
The ordinary meaning of lattice is the basis for several technical usages A cherry lattice pastry A mathematical lattice that is a type of partially ordered set. ...
In mathematics, point group is a group of geometric symmetries (isometries) leaving a point fixed. ...
In geometry, a point group in two dimensions is an isometry group in two dimensions that leaves the origin fixed, or correspondingly, an isometry group of a circle. ...
A discrete point group in 3D is a finite symmetry group in 3D that leaves the origin fixed. ...
The space group of a crystal is a mathematical description of the symmetry inherent in the structure. ...
The symmetry group of an object (e. ...
A translation slides an object by a vector a: Ta(p) = p + a. ...
Example of an Egyptian design with wallpaper group p4m A wallpaper group (or plane crystallographic group) is a mathematical concept to classify repetitive designs on two-dimensional surfaces, such as walls, based on the symmetries in the pattern. ...
Applications Radio telescopes are among many different tools used by astronomers Astronomy (Greek: αστÏονομία = άστÏον + νόμος, astronomia = astron + nomos, literally, law of the stars) is the science of celestial objects (such as stars, planets, comets, and galaxies) and phenomena that originate outside the Earths atmosphere (such as auroras and cosmic background radiation). ...
Computer graphics (CG) is the field of visual computing, where one utilizes computers both to generate visual images synthetically and to integrate or alter visual and spatial information sampled from the real world. ...
Image analysis is the extraction of useful information from images; mainly from digital images by means of digital image processing techniques. ...
Robot control is the theory of how to model and control robots. ...
Strähles construction is a geometric means of approximating the placement of lute, viol, and guitar frets. ...
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