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Shape formed from points common to other shapes
In geometry, an intersection between geometric objects (seen as sets of points) is a point, line, or curve common to two or more objects (such as lines
Intersection_(geometry)
Common elements of two or more sets
simultaneously. For example, in Euclidean geometry, when two lines in a plane are not parallel, their intersection is the point at which they meet. More generally
Intersection
Common point(s) shared by two lines in Euclidean geometry
In Euclidean geometry, the intersection of a line and a line can be the empty set, a single point, or a line (if they coincide). Distinguishing these cases
Line–line_intersection
Two geometries based on axioms closely related to those specifying Euclidean geometry
geometry. As Euclidean geometry lies at the intersection of metric geometry and affine geometry, non-Euclidean geometry arises by either replacing the parallel
Non-Euclidean_geometry
Set of elements common to all of some sets
belong to A. The notion of intersection as an algebraic operation with sets as operands has been generalized from geometry, where it is encountered in
Intersection_(set_theory)
Study of geometry using a coordinate system
In mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts
Analytic_geometry
Geometrical problem
analytic geometry, a line and a sphere can intersect in three ways: no intersection at all, intersection at exactly one point, and intersection at two points
Line–sphere_intersection
In computational geometry, the multiple line segment intersection problem supplies a list of line segments in the Euclidean plane and asks whether any
Multiple line segment intersection
Multiple_line_segment_intersection
Type of geometry
(i.e. their point of intersection) show the same structure as propositions. Projective geometry can also be seen as a geometry of constructions with
Projective_geometry
Branch of algebraic geometry
In mathematics, intersection theory is one of the main branches of algebraic geometry, where it gives information about the intersection of two subvarieties
Intersection_theory
Type of metric geometry
Taxicab geometry or Manhattan geometry is geometry where the familiar Euclidean distance is ignored, and the distance between two points is instead defined
Taxicab_geometry
Topics referred to by the same term
Francisco Intersection in mathematics, including: Intersection (set theory), the set of elements common to some collection of sets Intersection (geometry) Intersection
Intersection_(disambiguation)
Intersection of two planes
In geometry, the intersection of two Euclidean planes in three-dimensional space is a line or the empty set for parallel planes. The line of intersection
Plane–plane_intersection
Geometrical concept
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
Cross_section_(geometry)
Method of calculating ray-triangle intersections in 3D space
ray-triangle intersection algorithm, named after its inventors Tomas Möller and Ben Trumbore, is a fast method for calculating the intersection of a ray and
Möller–Trumbore intersection algorithm
Möller–Trumbore_intersection_algorithm
Geometry calculation
Line-cylinder intersection is the calculation of any points of intersection, given an analytic geometry description of a line and a cylinder in 3D space
Line-cylinder_intersection
Branch of computer science
Computational geometry is a branch of computer science devoted to the study of algorithms that can be stated in terms of geometry. Some purely geometrical
Computational_geometry
Completion of the usual space with "points at infinity"
generally preferred. There are two classes of definitions. In synthetic geometry, point and line are primitive entities that are related by the incidence
Projective_space
Creating a complex 3D surface or object by combining primitive objects
Constructive solid geometry (CSG; formerly called computational binary solid geometry) is a technique used in solid modeling. Constructive solid geometry allows a
Constructive_solid_geometry
Point where two or more curves, lines, or edges meet
In geometry, a vertex (pl.: vertices or vertexes), also called a corner, is a point where two or more curves, lines, or line segments meet or intersect
Vertex_(geometry)
Topological model
Extended 9-Intersection Model (DE-9IM) is a topological model and a standard used to describe the spatial relations of two regions (two geometries in two-dimensions
DE-9IM
Branch of mathematics
varieties. Computational algebraic geometry is an area that has emerged at the intersection of algebraic geometry and computer algebra, with the rise
Algebraic_geometry
Set of points equidistant from a center
(sphaîra) 'ball') is a surface analogous to the circle, a curve. In solid geometry, a sphere is the set of points that are all at the same distance r from
Sphere
Branch of mathematics
geometry. As Euclidean geometry lies at the intersection of metric geometry and affine geometry, non-Euclidean geometry arises by either replacing the parallel
Geometry
Study of angle-preserving transformations
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
Inversive_geometry
Geometry of the surface of a sphere
unlike coplanar lines in elliptic geometry. In the extrinsic 3-dimensional picture, a great circle is the intersection of the sphere with any plane through
Spherical_geometry
Branch of algebraic geometry concerned with counting solutions
enumerative geometry is the branch of algebraic geometry concerned with counting numbers of solutions to geometric questions, mainly by means of intersection theory
Enumerative_geometry
Geometric intersection of a line and plane in 3D space
In geometry, the intersection of a line and a plane in three-dimensional space can be the empty set, a point, or the line itself. It is the entire line
Line–plane_intersection
Skeletonized version of algebraic geometry
In mathematics, tropical geometry is the study of polynomials and their geometric properties when addition is replaced with minimization and multiplication
Tropical_geometry
Location of a discrete degeneracy between two electronic states
In quantum chemistry, a conical intersection of two or more potential energy surfaces is the set of molecular geometry points where the potential energy
Conical_intersection
Branch of mathematics
elements. Derived algebraic geometry can be thought of as an extension of this idea, and provides natural settings for intersection theory (or motivic homotopy
Derived_algebraic_geometry
Relation used in geometry
affine geometries and Euclidean geometry is a special instance of this type of geometry. In some other geometries, such as hyperbolic geometry, lines
Parallel_(geometry)
Generalized notion of counting curve intersections
In mathematics, and especially in algebraic geometry, the intersection number generalizes the intuitive notion of counting the number of times two curves
Intersection_number
Curve from a cone intersecting a plane
interesting and beautiful results in Euclidean geometry. A conic is the curve obtained as the intersection of a plane, called the cutting plane, with the
Conic_section
Line that intersects a curve at least twice
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
Secant_line
Analogs of homology groups for algebraic varieties
Complex Algebraic Geometry, v. 2, Theorem 10.1. Voisin, Hodge Theory and Complex Algebraic Geometry, v. 2, Ch. 11. Fulton, Intersection Theory, Chapter
Chow_group
Mathematical model of the physical space
Euclidean geometry is a mathematical system attributed to Euclid, an ancient Greek mathematician, which he described in his textbook on geometry, Elements
Euclidean_geometry
Property of points all lying on a single line
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
Collinearity
Intersection of cylinders
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
Steinmetz_solid
Convex polyhedron with regular faces
In geometry, a Johnson solid, sometimes also known as a Johnson–Zalgaller solid, is a convex polyhedron whose faces are regular polygons and that is not
Johnson_solid
Straight figure with zero width and depth
In geometry, a straight line, usually abbreviated line, is an infinitely long object with no width, depth, or curvature. It is a special case of a curve
Line_(geometry)
Branch of geometry
Descriptive geometry is a type of technical drawing and the branch of geometry which allows the representation of three-dimensional objects in two dimensions
Descriptive_geometry
Fundamental object of geometry
be determined by the intersection of two curves or three surfaces, called a vertex or corner. Since the advent of analytic geometry, points are often defined
Point_(geometry)
Subspace of n-space whose dimension is (n-1)
generated by the reflections. A convex polytope is the intersection of half-spaces. In non-Euclidean geometry, the ambient space might be the n-dimensional sphere
Hyperplane
Geometric axiom
at most one intersection point (i.e., only assumes the modern equivalent of the first four postulates) is known as an absolute geometry (or sometimes
Parallel_postulate
Traffic management concept
two phases. Many of the remaining 86 intersections with pedestrian scrambles are located where intersection geometry is skewed, requiring diagonal crossings
Pedestrian_scramble
One of eight divisions of a Euclidean 3D coordinate system
related to Octant (geometry). Octant (plane geometry) Octree Orthant Quadrant (plane geometry) Spherical octant, the intersection of an octant of space
Octant_(solid_geometry)
Non-Euclidean geometry
intersect: the point of intersection lies where the plane intersection meets σ or the line at infinity. Thus the axiom of projective geometry, requiring all pairs
Elliptic_geometry
Scheme in algebraic geometry
algebraic geometry, the normal cone of a subscheme of a scheme is a scheme analogous to the normal bundle or tubular neighborhood in differential geometry. The
Normal cone (algebraic geometry)
Normal_cone_(algebraic_geometry)
Theorem in plane geometry
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
Monge's_theorem
Type of non-Euclidean geometry
mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai–Lobachevskian geometry) is a non-Euclidean geometry. The parallel postulate
Hyperbolic_geometry
Mathematical theory
In mathematics, Arakelov theory (or Arakelov geometry) is an approach to Diophantine geometry, named for Suren Arakelov. It is used to study Diophantine
Arakelov_theory
Relationship between two lines that meet at a right angle
In geometry, two geometric objects are perpendicular if they intersect at right angles, i.e. at an angle of 90 degrees or π/2 radians. The condition of
Perpendicular
Multivariate generalization of the median
In statistics and computational geometry, the notion of centerpoint is a generalization of the median to data in higher-dimensional Euclidean space. Given
Centerpoint_(geometry)
Shared independent set of two matroids
In combinatorial optimization, the matroid intersection problem is to find a largest common independent set in two matroids over the same ground set. If
Matroid_intersection
Database of data representing objects in geometric space
boolean ST_Length(geometry) : number ST_Area(geometry) : number ST_Centroid(geometry) : geometry ST_Intersection(geometry, geometry) : geometry Thus, a spatial
Spatial_database
Point on a line segment which is equidistant from both endpoints
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
Midpoint
In geometry, a centre (Commonwealth English) or center (American English) (from Ancient Greek κέντρον (kéntron) 'pointy object') of an object is a point
Centre_(geometry)
Shape with three sides
three sides connected at three corners. It is one of the basic shapes in geometry and the simplest of polygons. The corners, also called vertices, are zero-dimensional
Triangle
Property shared by codirectional lines
In geometry, direction, also known as spatial direction, vector direction or relative direction, is the common characteristic of all rays which coincide
Direction_(geometry)
Curve that is common to two geometric objects
In geometry, an intersection curve is a curve that is common to two geometric objects. In the simplest case, the intersection of two non-parallel planes
Intersection_curve
Isomorphism of projective spaces in geometry
In projective geometry, a homography is an isomorphism of projective spaces, induced by an isomorphism of the vector spaces from which the projective spaces
Homography
2004 geometry book
99 Points of Intersection: Examples—Pictures—Proofs is a book on constructions in Euclidean plane geometry in which three or more lines or curves meet
99_Points_of_Intersection
Convex quadrilateral with at least one pair of parallel sides
In geometry, a trapezoid (/ˈtræpəzɔɪd/) in North American English or trapezium (/trəˈpiːziəm/) in British English is a quadrilateral that has at least
Trapezoid
Theorem in projective geometry
In projective geometry, Pascal's theorem (also known as the hexagrammum mysticum theorem, Latin for mystical hexagram) states that if six arbitrary points
Pascal's_theorem
Branch of differential geometry and differential topology
Symplectic geometry is a branch of differential geometry and differential topology that studies symplectic manifolds; that is, differentiable manifolds
Symplectic_geometry
Simple curve of Euclidean geometry
mathematics, the study of the circle has helped inspire the development of geometry, astronomy and calculus. Annulus: a ring-shaped object, the region bounded
Circle
Euclidean geometry without distance and angles
In mathematics, affine geometry is what remains of Euclidean geometry when ignoring (mathematicians often say "forgetting") the metric notions of distance
Affine_geometry
in intersection theory that appear in symplectic geometry as they do not naturally fit into other lists such as the glossary of algebraic geometry. Contents:
Glossary of symplectic geometry
Glossary_of_symplectic_geometry
US highway network
clearances and load limits, traffic volumes and vehicle mix, and intersection geometry. The route consists of lanes designed to be a width of 12 feet (3
National_Network
In projective geometry, an intersection theorem or incidence theorem is a statement concerning an incidence structure – consisting of points, lines, and
Intersection_theorem
Number of intersection points of algebraic curves and hypersurfaces
In algebraic geometry, Bézout's theorem is a statement concerning the number of common zeros of n polynomials in n indeterminates. In its original form
Bézout's_theorem
Lines which intersect at a single point
In geometry, lines in a plane or higher-dimensional space are concurrent if they intersect at a single point. The set of all lines through a point is called
Concurrent_lines
Term in computer science
although a hierarchy over deformable geometry must be updated as the geometry changes. Because exact intersection tests are deferred to the leaves, BVHs
Collision_detection
Geometric shape
geometry, cones are assumed to be right circular, i.e., with a circle base perpendicular to the axis. If the cone is right circular the intersection of
Cone
Figure formed by two rays meeting at a common point
In geometry, an angle is formed by two lines that meet at a point. Each line is called a side of the angle, and the point they share is called the vertex
Angle
Hyperbolic geometry is a non-Euclidean geometry where the first four axioms of Euclidean geometry are kept but the fifth axiom, the parallel postulate
Constructions in hyperbolic geometry
Constructions_in_hyperbolic_geometry
Study of complex manifolds and several complex variables
algebraic geometry falls in this category, together with more geometric aspects of complex analysis. Complex geometry sits at the intersection of algebraic
Complex_geometry
Set of points that satisfy some specified conditions
In geometry, a locus (plural: loci; Latin for 'place, location') is a set of all points (commonly, a line, a line segment, a curve or a surface), whose
Locus_(mathematics)
Operation that cuts polytope vertices, creating a new facet in place of each vertex
In geometry, a truncation is an operation in any dimension that cuts polytope vertices, creating a new facet in place of each vertex. The term originates
Truncation_(geometry)
Topics referred to by the same term
Intersection theory may refer to: Intersection theory, especially in algebraic geometry Intersection (set theory) This disambiguation page lists articles
Intersection theory (disambiguation)
Intersection_theory_(disambiguation)
Term in mathematics
mathematics, an algebraic variety V in projective space is a complete intersection if the ideal of V is generated by exactly codim V elements. That is,
Complete_intersection
On triangles inscribed in a circle with a diameter as an edge
In geometry, Thales's theorem states that if A, B, and C are distinct points on a circle where the line AC is a diameter, the angle ∠ ABC is a right angle
Thales's_theorem
Property of objects which are scaled or mirrored versions of each other
In Euclidean geometry, two objects are similar if they have the same shape, or if one has the same shape as the mirror image of the other. More precisely
Similarity_(geometry)
The terminology of algebraic geometry changed drastically during the twentieth century, with the introduction of the general methods, initiated by David
Glossary of classical algebraic geometry
Glossary_of_classical_algebraic_geometry
Planar surface that forms part of the boundary of a solid object
In solid geometry, a face is a flat surface (a planar region) that forms part of the boundary of a solid object. For example, a cube has six faces in this
Face_(geometry)
90° angle (π/2 radians)
In geometry and trigonometry, a right angle is an angle of exactly 90 degrees or π {\displaystyle \pi } /2 radians corresponding to a quarter turn.
Right_angle
1946 book by André Weil
Foundations of Algebraic Geometry is a book by André Weil (1946, 1962) that develops algebraic geometry over fields of any characteristic. In particular
Foundations of Algebraic Geometry
Foundations_of_Algebraic_Geometry
Geometric point from which certain types of curves are constructed
In geometry, focuses or foci (/ˈfoʊsaɪ/ or /ˈfoʊkaɪ/; sing.: focus) are special points with reference to which any of a variety of curves is constructed
Focus_(geometry)
In the theory of analytic geometry for real three-dimensional space, the curve formed from the intersection between a sphere and a cylinder can be a circle
Sphere–cylinder_intersection
Geometry without the parallel postulate
Corollary 1.8, p. 11. Indeed, absolute geometry is in fact the intersection of hyperbolic geometry and Euclidean geometry when these are regarded as sets of
Absolute_geometry
Flat surface
In Euclidean geometry, a plane is a flat two-dimensional surface that extends indefinitely. Euclidean planes often arise as subspaces of three-dimensional
Euclidean planes in three-dimensional space
Euclidean_planes_in_three-dimensional_space
Geometric object with flat sides
In elementary geometry, a polytope is a geometric object with flat sides (faces). Polytopes are the generalization of three-dimensional polyhedra to any
Polytope
This is a list of algebraic geometry topics, by Wikipedia page. Affine space Projective space Projective line, cross-ratio Projective plane Line at infinity
List of algebraic geometry topics
List_of_algebraic_geometry_topics
Line intersecting 2 coplanar lines at 2 points
In geometry, a transversal is a line that passes through two lines in the same plane at two distinct points. Transversals play a role in establishing whether
Transversal_(geometry)
Affine subspace of a Euclidean space
In geometry, a flat is an affine subspace, i.e. a subset of an affine space that is itself an affine space. Particularly, in the case the parent space
Flat_(geometry)
Spherical geometry analog of a straight line
circle, and is the intersection of the sphere with a plane not passing through its center. Small circles are the spherical-geometry analog of circles in
Great_circle
Property of a mathematical space
back to René Descartes, substantial development of a higher-dimensional geometry only began in the 19th century, via the work of Arthur Cayley, William
Dimension
In geometry, set whose intersection with every line is a single line segment
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
Convex_set
from intersection theory in algebraic geometry, for the case of subvarieties of projective space with codimension large enough to make the intersection have
Fulton–Hansen connectedness theorem
Fulton–Hansen_connectedness_theorem
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INTERSECTION GEOMETRY
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INTERSECTION GEOMETRY
INTERSECTION GEOMETRY
INTERSECTION GEOMETRY
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