Geometry
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A
- Affine geometryEuclidean geometry without distance and angles
- Affine transformationGeometric transformation that preserves lines but not angles nor the origin
- Aida YasuakiJapanese mathematician
- Analytic geometryStudy of geometry using a coordinate system
- ApothemSegment from the center of a polygon to the midpoint of one of its sides
- Arc lengthDistance along a curve
B
- Ball (mathematics)Volume space bounded by a sphere
- BaudhayanaIndian sage and mathematician
- Behrmann projectionThe Behrmann projection is a cylindrical equal-area map projection described by Walter Beh
- BisectionDivision of something into two equal or congruent parts
- Brachistochrone curveFastest curve descent without friction
- Brouwer fixed-point theoremTheorem in topology
C
- Cantor setSet of points on a line segment with certain topological properties
- CardioidType of plane curve
- Cartesian coordinate systemCoordinate system using perpendicular axes
- Cartesian ovalIn geometry, a Cartesian oval is a plane curve consisting of points that have the same lin
- CAT(k) spaceIn mathematics, a space, where is a real number, is a specific type of metric space. Intui
- Catalan solid13 polyhedra; duals of the Archimedean solids
- CatenaryCurve formed by a hanging chain
- Centre (geometry)In geometry, a centre (British English) or center (American English) (from Ancient Greek κ
- ChamferA chamfer ( SHAM-fər or CHAM-fər) is a transitional edge between two faces of an object. S
- CinsautCinsaut or Cinsault ( SAN-soh, French: ) is a red wine grape whose heat tolerance and prod
- Circular triangleTriangle with circular arc edges
- CircumferencePerimeter of a circle or ellipse
- Classification of Fatou componentsIn mathematics, Fatou components are components of the Fatou set. They were named after Pi
- Closeness (mathematics)Closeness is a basic concept in topology and related areas in mathematics. Intuitively, we
- CollineationIn projective geometry, a collineation is a one-to-one and onto map (a bijection) from one
- Compact spaceType of mathematical space
- ComparisonExamination of two or more entities to deduce their similarities and differences
- Compass equivalence theoremIn geometry, the compass equivalence theorem is an important statement in compass and stra
- Complex hyperbolic spaceIn mathematics, hyperbolic complex space is a Hermitian manifold which is the equivalent o
- ConeGeometric shape
- Congruence (geometry)Relationship between two figures of the same shape and size, or mirroring each other
- Conic sectionCurve from a cone intersecting a plane
- Connected spaceTopological space that is connected
- Constructive solid geometryCreating a complex 3D surface or object by combining primitive objects
- Convex setIn geometry, set whose intersection with every line is a single line segment
- Coordinate systemMethod for specifying point positions
- CoplanarityGeometric property of objects being in the same plane
- CubeSolid with six equal square faces
- CurvatureMathematical measure of how much a curve or surface deviates from flatness
- CurveMathematical idealization of the trace left by a moving point
- Curve orientationIn mathematics, an orientation of a curve is the choice of one of the two possible directi
- CycloidCurve traced by a point on a rolling circle
- CylinderThree-dimensional solid
- Cylindrical coordinate systemCoordinates comprising two distances and an angle
D
- DecagonShape with ten sides
- Deltoid curveIn geometry, a deltoid curve, also known as a tricuspoid curve or Steiner curve, is a hypo
- Differentiable manifoldManifold upon which it is possible to perform calculus
- Differential geometryBranch of mathematics
- Dihedral angleAngle between two planes in space
- DimensionProperty of a mathematical space
- Direction (geometry)Property shared by codirectional lines
- Discrete differential geometryArea of mathematics
- DistanceSeparation between two points
- Distance geometryDistance geometry is the branch of mathematics concerned with characterizing and studying
- DodecahedronPolyhedron with 12 faces
- Dual polygonPolygon constructed from another
E
- EllipsePlane curve
- EllipsisTriple-dot punctuation mark
- Elliptic curveAlgebraic curve in mathematics
- Elliptic geometryNon-Euclidean geometry
- Equilateral polygonPolygon in which all sides have equal length
- Equilateral triangleShape with three equal sides
- Euclidean geometryMathematical model of the physical space
- Euclidean planeGeometric model of the planar projection of the physical universe
- Euclidean spaceFundamental space of geometry
- Euler characteristicTopological invariant in mathematics
- Euler classIn mathematics, specifically in algebraic topology, the Euler class is a characteristic cl
- Exact trigonometric valuesTrigonometric values in terms of square roots and fractions
F
- Face (geometry)Planar surface that forms part of the boundary of a solid object
- FacetingStella octangula as a faceting of the cube
- Field lineVisual aid to depiction of a vector field
- Finite subdivision ruleIn mathematics, a finite subdivision rule is a recursive way of dividing a polygon or othe
- Flat (geometry)Affine subspace of a Euclidean space
- Focus (geometry)Geometric point from which certain types of curves are constructed
- Four-dimensional spaceGeometric space with four dimensions
- FractalInfinitely detailed mathematical structure
- Fractal curveMathematical curve whose shape is a fractal
- FrustumPortion of a solid that lies between two parallel planes cutting the solid
- Fundamental domainTopological space
G
- Gaston JuliaGaston Maurice Julia (3 February 1893 – 19 March 1978) was a French mathematician who devi
- Gaussian curvatureProduct of the principal curvatures of a surface
- General topologyBranch of topology
- Generalised circleIn geometry, a generalized circle, sometimes called a cline or circline, is a straight lin
- Generalized trigonometryStudy of triangles in other spaces than the Euclidean plane
- Gosper curveThe Gosper curve, named after Bill Gosper, also known as the Peano-Gosper Curve and the fl
- Graph paperWriting paper with a grid
- Great circleSpherical geometry analog of a straight line
- Grégoire de Saint-VincentGrégoire de Saint-Vincent (French pronunciation: ) - in Latin : Gregorius a Sancto Vincent
H
- Hanner polytopeConvex polytope constructed recursively
- HeadlampLamp mounted in the front of a vehicle
- Headlamp (outdoor)A headlamp, headlight, or head torch (UK) is a light source affixed to the head typically
- HeightMeasure of vertical distance
- Henry John Stephen SmithHenry John Stephen Smith (2 November 1826 – 9 February 1883) was an Irish mathematician an
- HexagonShape with six sides
- HomeomorphismMapping which preserves all topological properties of a given space
- HomographyIsomorphism of projective spaces in geometry
- Homology (mathematics)Algebraic structure associated with a topological space
- HomotopyContinuous deformation between two continuous functions
- Honeycomb (geometry)In geometry, a honeycomb is a space filling or close packing of polyhedral or higher-dimen
- HyperbolaPlane curve: conic section
- HyperboleRhetorical device
- Hyperbolic 3-manifoldIn mathematics, more precisely in topology and differential geometry, a hyperbolic 3-manif
- Hyperbolic angleArgument of the hyperbolic functions
- Hyperbolic functionsHyperbolic analogues of trigonometric functions
- Hyperbolic geometryType of non-Euclidean geometry
- Hyperbolic spaceNon-Euclidean geometry
- Hyperbolic triangleTriangle in hyperbolic geometry
- HyperboloidUnbounded quadric surface
- HypercubeConvex polytope, the n-dimensional analogue of a square and a cube
- HyperplaneSubspace of n-space whose dimension is (n-1)
- HyperspaceFaster-than-light travel in science fiction
I
- Icosahedral symmetry3D symmetry group
- IcosahedronPolyhedron with 20 faces
- Ideal polyhedronShape in hyperbolic geometry
- Ideal triangleType of hyperbolic triangle
- Implicit curveIn mathematics, an implicit curve is a plane curve defined by an implicit equation relatin
- Incidence geometryField of mathematics which studies incidence structures
- Integer latticeIn mathematics, the n-dimensional integer lattice (or cubic lattice), denoted , is the l
- Integral curveIn mathematics, an integral curve is a parametric curve that represents a specific solutio
- Internal and external anglesSupplementary pair of angles at each vertex of a polygon
- Intersection (geometry)Shape formed from points common to other shapes
- Intersection curveIn geometry, an intersection curve is a curve that is common to two geometric objects. In
- Invariant (mathematics)Property that is not changed by mathematical transformations
- Inverse curveIn inversive geometry, an inverse curve of a given curve C is the result of applying an in
- Inversive geometryStudy of angle-preserving transformations
- Isogonal figurePolytope or tiling whose vertices are identical
- Isohedral figureIn geometry, a tessellation of dimension 2 (a plane tiling) or higher, or a polytope of di
- IsometryDistance-preserving mathematical transformation
- Isosceles triangleTriangle with at least two sides congruent
- Isotoxal figurePolytope or tiling with one type of edge
J
K
- Kakutani fixed-point theoremIn mathematical analysis, the Kakutani fixed-point theorem is a fixed-point theorem for se
- Kepler–Poinsot polyhedronAny of 4 regular star polyhedra
- Kite (geometry)Quadrilateral symmetric across a diagonal
- Knot groupIn mathematics, a knot is an embedding of a circle into 3-dimensional Euclidean space. The
- Knot tabulationEver since Sir William Thomson's vortex theory, mathematicians have tried to classify and
- Knot theoryStudy of mathematical knots
- Koch snowflakeFractal curve
L
- Lattice (group)Periodic set of points
- Law of cosinesGeneralization of Pythagorean theorem
- Law of cotangentsTrigonometric identity relating the sides and angles of a triangle
- Law of sinesProperty of all triangles on a Euclidean plane
- Law of tangentsRelates tangents of two angles of a triangle and the lengths of the opposing sides
- LemniscateFigure-eight-shaped curve
- LengthMeasure of distance in physical space
- Line (graphics)In graphics, narrow field between two points
- Line segmentPart of a straight line that is bounded by two distinct end points
- Line–line intersectionCommon point(s) shared by two lines in Euclidean geometry
- Local propertyIn mathematics, a mathematical object is said to satisfy a property locally, if the proper
- Locus (mathematics)Set of points that satisfy some specified conditions
- Louis PoinsotLouis Poinsot (French pronunciation: ; 3 January 1777 – 5 December 1859) was a French math
M
- Mandelbrot setFractal named after mathematician Benoit Mandelbrot
- ManifoldTopological space that locally resembles Euclidean space
- Mathematical Models (Cundy and Rollett)Mathematical Models is a book on the construction of physical models of mathematical objec
- Mathematical tileMathematical tiles are tiles which were used extensively as a building material in the sou
- Metric spaceMathematical space with a notion of distance
- MinggatuMongolian astronomer and mathematician
- Minimal surfaceSurface that locally minimizes its area
- Minimal surface of revolutionIn mathematics, a minimal surface of revolution or minimum surface of revolution is a surf
- Minkowski's theoremEvery symmetric convex set in R^n with volume > 2^n contains a non-zero integer point
- Möbius stripNon-orientable surface with one edge
- Motion (geometry)Transformation of a geometric space preserving structure
- Multilinear algebraMultilinear algebra is the study of functions with multiple vector-valued arguments, with
- Multilinear formIn abstract algebra and multilinear algebra, a multilinear form on a vector space over a f
- Multilinear mapVector-valued function of multiple vectors, linear in each argument
- Mysterium CosmographicumMysterium Cosmographicum (lit. The Cosmographic Mystery, alternately translated as Cosmic
N
- N-skeletonIn mathematics, particularly in algebraic topology, the n-skeleton of a topological space
- N-sphereGeneralized sphere of dimension n (mathematics)
- Neighbourhood (mathematics)Open set containing a given point
- Neoclassical compoundCompound words composed from Latin or ancient Greek
- Net (polyhedron)Edge-joined polygons which fold into a polyhedron
- Neusis constructionGeometric construction used in Ancient Greek mathematics
- Non-Euclidean geometryTwo geometries based on axioms closely related to those specifying Euclidean geometry
- Noncommutative algebraic geometryBranch of mathematics
- Noncommutative geometryBranch of mathematics
- Nowhere dense setIn mathematics, a subset of a topological space is called nowhere dense or rare if its clo
O
- OctagonPolygon shape with eight sides
- Octahedral symmetry3D symmetry group
- OctahedronPolyhedron with eight triangular faces
- One-dimensional spaceSpace with one dimension
- Open setBasic subset of a topological space
- OrientabilityPossibility of a consistent definition of "clockwise" in a mathematical space
- OrthogonalityVarious meanings of the terms
- Outer billiardsOuter billiards is a dynamical system based on a convex shape in the plane. Classically, t
P
- ParabolaPlane curve: conic section
- ParaboloidQuadric surface with one axis of symmetry and no center of symmetry
- Parallel (geometry)Relation used in geometry
- Parallel postulateGeometric axiom
- Parallel projectionProjection of a 3D object onto a plane via parallel rays
- ParallelepipedHexahedron with parallelogram faces
- ParallelogramQuadrilateral with two pairs of parallel sides
- PentagonShape with five sides
- PentagramFive-pointed star polygon
- PerimeterPath that surrounds an area
- PerpendicularRelationship between two lines that meet at a right angle
- PhiTwenty-first letter in the Greek alphabet
- Plane (mathematics)2D surface which extends indefinitely
- Plane cubic curveType of mathematical curve
- Plane curveMathematical concept
- Plane–plane intersectionIn analytic geometry, the intersection of two planes in three-dimensional space is a line.
- Platonic solidAny of the five regular polyhedra
- Playfair's axiomModern formulation of Euclid's parallel postulate
- Poincaré conjectureTheorem in geometric topology
- Point (geometry)Fundamental object of geometry
- Point reflectionGeometric symmetry operation
- Polar coordinate systemCoordinates comprising a distance and an angle
- Polygram (geometry)In geometry, a generalized polygon can be called a polygram, and named specifically by its
- Polyhedra (software)Polyhedra is a family of relational database management systems offered by ENEA AB, a Swed
- PolyhedronFlat-sided three-dimensional shape
- PolytopeGeometric object with flat sides
- Polytope compound3D shape made of polyhedra sharing a common center
- Prism (geometry)Solid with 2 parallel n-gonal bases connected by n parallelograms
- Projective geometryType of geometry
- Projective lineLine with a point at infinity added
- Projective planeGeometric concept of a 2D space with "points at infinity" adjoined
- Projective spaceCompletion of the usual space with "points at infinity"
- Pyramid (geometry)Conic solid with a polygonal base
- Pythagorean theoremRelation between sides of a right triangle
- Pythagorean tripleInteger side lengths of a right triangle
Q
R
- RadiusLine segment in a circle or sphere from its center to its perimeter or surface
- RectangleQuadrilateral with four right angles
- Rectilinear polygonA rectilinear polygon is a polygon all of whose sides meet at right angles. Thus the inter
- Reflection (mathematics)Mapping from a Euclidean space to itself
- Regular dodecahedronSolid with 12 equal pentagonal faces
- Regular icosahedronSolid with twenty equal triangular faces
- Regular octahedronSolid with eight equal triangular faces
- Regular polygonShape with equal angles and equal sides
- Regular polyhedronPolyhedron with regular congruent polygons as faces
- Reuleaux tetrahedronShape formed by intersecting four balls
- Reuleaux triangleCurved triangle with constant width
- RhombusQuadrilateral with sides of equal length
- Riemannian geometryBranch of differential geometry
- Riemannian manifoldSmooth manifold with an inner product on each tangent space
- Right angle90° angle (π/2 radians)
- Right circular cylinderCylinder whose generatrices are perpendicular to the bases
- Right triangleTriangle containing a 90-degree angle
- Rotation (mathematics)Motion of a certain space that preserves at least one point
- Rotations in 4-dimensional Euclidean spaceSpecial orthogonal group
- Rubber scienceRubber science is a science fiction term describing a quasi-scientific explanation for an
S
- Sakabe KōhanJapanese mathematician
- Scaling (geometry)Geometric transformation
- Schläfli symbolNotation for polytopes and tessellations
- ShapeForm of an object
- Shear mappingType of geometric transformation
- Sierpiński carpetThe Sierpiński carpet is a plane fractal first described by Wacław Sierpiński in 1916. The
- Sierpiński triangleFractal composed of triangles
- Similarity (geometry)Property of objects which are scaled or mirrored versions of each other
- SizeMagnitude or dimension of a thing
- Skew apeirohedronIn geometry, a skew apeirohedron is an infinite skew polyhedron consisting of nonplanar fa
- Skew linesLines not in the same plane
- Small stellated dodecahedronKepler–Poinsot polyhedron
- Solid angleMeasure in 3-dimensional geometry
- Solid geometryField of mathematics dealing with three-dimensional Euclidean spaces
- Solid of revolutionType of three-dimensional shape
- Solid torusIn mathematics, a solid torus is the topological space formed by sweeping a disk around a
- SphereSet of points equidistant from a center
- Spherical coordinate systemCoordinates comprising a distance and two angles
- Spherical geometryGeometry of the surface of a sphere
- SquareShape with four equal sides and angles
- Square latticeIn mathematics, the square lattice is a type of lattice in a two-dimensional Euclidean spa
- Squaring the circleProblem of constructing equal-area shapes
- Squeeze mappingIn linear algebra, a squeeze mapping, also called a squeeze transformation, is a type of l
- Star polygonRegular non-convex polygon
- Star polyhedronPolyhedron with some pattern of nonconvexity
- StellationExtending the elements of a polytope to form a new figure
- Stereographic projectionParticular mapping that projects a sphere onto a plane
- Straightedge and compass constructionMethod of drawing geometric objects
- Sub-Riemannian manifoldIn mathematics, a sub-Riemannian manifold is a certain type of generalization of a Riemann
- Surface (mathematics)Mathematical idealization of the surface of a body
- Surface (topology)Two-dimensional manifold
- Surface areaMeasure of a two-dimensional surface
- Surface of revolutionSurface created by rotating a curve about an axis
- SymmetryMathematical invariance under transformations
- Symmetry (geometry)Geometrical property
- Symmetry in mathematicsSymmetry occurs not only in geometry, but also in other branches of mathematics. Symmetry
- Systolic geometryForm of differential geometry
T
- TangentIn mathematics, straight line touching a plane curve without crossing it
- Tautochrone curveCurve for which the time to roll to the end is equal for all starting points
- TensorAlgebraic object with geometric applications
- TessellationCovering by shapes without overlaps or gaps
- TesseractFour-dimensional analogue of the cube
- TetrahedronPolyhedron with four faces
- Theorema EgregiumResult of differential geometry proved by Gauss
- ThetaEighth letter of the Greek alphabet
- Topological propertyIn topology and related areas of mathematics, a topological property or topological invari
- Topological spaceMathematical space with a notion of closeness
- Toroidal polyhedronPartition of a toroidal surface into polygons
- TorusDoughnut-shaped surface of revolution
- Transformation (function)Function that applies a set to itself
- Translation (geometry)Planar movement within a Euclidean space without rotation
- TrapezoidConvex quadrilateral with at least one pair of parallel sides
- Triangle centerPoint in a triangle that can be seen as its middle under some criteria
- Trigonometric functionsFunctions of an angle
- Trigonometric seriesInfinite sum of sines and cosines
- Trigonometric tableLists of values of mathematical functions
- Truncation (geometry)Operation that cuts polytope vertices, creating a new facet in place of each vertex
- Twisted cubicIn mathematics, a twisted cubic is a smooth, rational curve C of degree three in projectiv
- Two-dimensional spaceMathematical space with two coordinates