# Outline of geometry > Mediated Wiki article. Canonical URL: https://mediated.wiki/source/Outline_of_geometry > Markdown URL: https://mediated.wiki/source/Outline_of_geometry.md > Source: https://en.wikipedia.org/wiki/Outline_of_geometry > Source revision: 1318177804 > License: Creative Commons Attribution-ShareAlike 4.0 International (https://creativecommons.org/licenses/by-sa/4.0/) {{Short description|1=Overview of and topical guide to geometry}} {{general geometry}} [Geometry](/source/Geometry) is a branch of [mathematics](/source/mathematics) concerned with questions of shape, size, relative position of figures, and the properties of space. Geometry is one of the oldest mathematical sciences. Modern geometry also extends into non-Euclidean spaces, topology, and fractal dimensions, bridging pure mathematics with applications in physics, computer science, and data visualization. {{TOC limit|limit=2}} == Types, methodologies, and terminologies of geometry. == * [Absolute geometry](/source/Absolute_geometry) * [Affine geometry](/source/Affine_geometry) * [Algebraic geometry](/source/Algebraic_geometry) * [Analytic geometry](/source/Analytic_geometry) * [Birational geometry](/source/Birational_geometry) * [Complex geometry](/source/Complex_geometry) * [Computational geometry](/source/Computational_geometry) * [Conformal geometry](/source/Conformal_geometry) * [Constructive solid geometry](/source/Constructive_solid_geometry) * [Contact geometry](/source/Contact_geometry) * [Convex geometry](/source/Convex_geometry) * [Descriptive geometry](/source/Descriptive_geometry) * [Differential geometry](/source/Differential_geometry) * [Digital geometry](/source/Digital_geometry) * [Discrete geometry](/source/Discrete_geometry) * [Distance geometry](/source/Distance_geometry) * [Elliptic geometry](/source/Elliptic_geometry) * [Enumerative geometry](/source/Enumerative_geometry) * [Epipolar geometry](/source/Epipolar_geometry) * [Euclidean geometry](/source/Euclidean_geometry) * [Finite geometry](/source/Finite_geometry) * [Fractal geometry](/source/Fractal_geometry) * [Geometry of numbers](/source/Geometry_of_numbers) * [Hyperbolic geometry](/source/Hyperbolic_geometry) * [Incidence geometry](/source/Incidence_geometry) * [Information geometry](/source/Information_geometry) * [Integral geometry](/source/Integral_geometry) * [Inversive geometry](/source/Inversive_geometry) * [Inversive ring geometry](/source/Inversive_ring_geometry) * [Klein geometry](/source/Klein_geometry) * [Lie sphere geometry](/source/Lie_sphere_geometry) * [Non-Euclidean geometry](/source/Non-Euclidean_geometry) * [Noncommutative algebraic geometry](/source/Noncommutative_algebraic_geometry) * [Noncommutative geometry](/source/Noncommutative_geometry) * [Ordered geometry](/source/Ordered_geometry) * [Parabolic geometry](/source/Parabolic_geometry_(differential_geometry)) * [Plane geometry](/source/Euclidean_plane_geometry) * [Projective geometry](/source/Projective_geometry) * [Quantum geometry](/source/Quantum_geometry) * [Riemannian geometry](/source/Riemannian_geometry) * [Ruppeiner geometry](/source/Ruppeiner_geometry) * [Solid geometry](/source/Solid_geometry) * [Spherical geometry](/source/Spherical_geometry) * [Symplectic geometry](/source/Symplectic_geometry) * [Synthetic geometry](/source/Synthetic_geometry) * [Systolic geometry](/source/Systolic_geometry) * [Taxicab geometry](/source/Taxicab_geometry) * [Toric geometry](/source/Toric_geometry) * [Transformation geometry](/source/Transformation_geometry) * [Tropical geometry](/source/Tropical_geometry) ==General geometry concepts== ===General concepts=== * [Chirality](/source/Chirality_(mathematics)) ** [Handedness](/source/Handedness) ** [Relative direction](/source/Relative_direction) ** [Mirror image](/source/Mirror_image) * [Coordinate-free treatment](/source/Coordinate-free_treatment) * [Four-dimensional space](/source/Four-dimensional_space) * [Infinitesimal transformation](/source/Infinitesimal_transformation) * [Geometric progression](/source/Geometric_progression) * [Geometric shape](/source/Geometric_shape) * [Pi](/source/Pi) * [Angular velocity](/source/Angular_velocity) * [Linear velocity](/source/velocity) * [De Moivre's theorem](/source/De_Moivre's_formula) * [Similar triangles](/source/Similar_triangles) * [Unit circle](/source/Unit_circle) * [Point](/source/point_(geometry)) * [Line](/source/line_(mathematics)) and [Ray](/source/line_(mathematics)) * [Plane](/source/plane_(mathematics)) ===Measurements=== * [Bearing](/source/bearing_(navigation)) * [Angle](/source/Angle) * [Degree](/source/degree_(angle)) * [Minute](/source/minute_of_arc) * [Radian](/source/Radian) * [Circumference](/source/Circumference) * [Diameter](/source/Diameter) ===Trigonometric functions=== * [Trigonometric function](/source/Trigonometric_function) ** [Asymptotes](/source/Asymptotes) ** [Circular functions](/source/Circular_functions) ** [Periodic functions](/source/Periodic_functions) ** [Law of cosines](/source/Law_of_cosines) ** [Law of sines](/source/Law_of_sines) ** [Polar sine](/source/Polar_sine) ===Vectors=== {{Main|Vector (geometric)}} * [Amplitude](/source/Amplitude) * [Dot product](/source/Dot_product) * [Norm (mathematics)](/source/Norm_(mathematics)) (also known as magnitude) * [Position vector](/source/Position_vector) * [Scalar multiplication](/source/Scalar_multiplication) * [Vector addition](/source/Vector_addition) * [Zero vector](/source/Zero_vector) ===Vector spaces and complex dimensions=== * [Complex plane](/source/Complex_plane) * [Imaginary axis](/source/Imaginary_axis) * [Linear interpolation](/source/Linear_interpolation) * [One-to-one](/source/bijection) * [Orthogonal](/source/Orthogonal) * [Polar coordinate system](/source/Polar_coordinate_system) * [Pole](/source/Pole_(complex_analysis)) * [Real axis](/source/Real_axis) * [Secant line](/source/Secant_line) * [Circular sector](/source/Circular_sector) or "sector" * [Semiperimeter](/source/Semiperimeter) === Symmetry, shape and pattern === * [Symmetry](/source/Symmetry) * [Shape](/source/Shape) * [Pattern](/source/Pattern) * [Crystal system](/source/Crystal_system) * [Frieze group](/source/Frieze_group) * [Isometry](/source/Isometry) * [Lattice](/source/Lattice_(group)) * [Point group](/source/Point_group) * [Point groups in two dimensions](/source/Point_groups_in_two_dimensions) * [Point groups in three dimensions](/source/Point_groups_in_three_dimensions) * [Space group](/source/Space_group) * [Symmetry group](/source/Symmetry_group) * [Translational symmetry](/source/Translational_symmetry) * [Wallpaper group](/source/Wallpaper_group) == Euclidean geometry foundations == {{Main|Euclidean geometry}} * [Hilbert's axioms](/source/Hilbert's_axioms) * [Locus](/source/Locus_(mathematics)) * [Line](/source/Line_(mathematics)) * [Line segment](/source/Line_segment) * [Parallel](/source/Parallel_(geometry)) * [Angle](/source/Angle) ** [Concurrent lines](/source/Concurrent_lines) ** [Adjacent angles](/source/Adjacent_angles) ** [Central angle](/source/Central_angle) ** [Complementary angles](/source/Complementary_angles) ** [Inscribed angle](/source/Inscribed_angle) ** [Internal angle](/source/Internal_angle) ** [Supplementary angles](/source/Supplementary_angles) ** [Angle trisection](/source/Angle_trisection) * [Congruence](/source/Congruence_(geometry)) ** [Reflection](/source/Reflection_(mathematics)) ** [Rotation](/source/Rotation_(mathematics)) ** [Coordinate rotations and reflections](/source/Coordinate_rotations_and_reflections) ** [Translation](/source/Translation_(geometry)) ** [Glide reflection](/source/Glide_reflection) * [Similarity](/source/Similarity_(geometry)) ** [Similarity transformation](/source/Similarity_transformation_(geometry)) ** [Homothety](/source/Homothetic_transformation) * [Shear mapping](/source/Shear_mapping) === Euclidean plane geometry === {{Main|Plane geometry}} * [2D computer graphics](/source/2D_computer_graphics) * [2D geometric model](/source/2D_geometric_model) * [Altitude](/source/Altitude_(triangle)) * [Brahmagupta's formula](/source/Brahmagupta's_formula) * [Bretschneider's formula](/source/Bretschneider's_formula) * [Compass and straightedge constructions](/source/Compass_and_straightedge_constructions) ** [Squaring the circle](/source/Squaring_the_circle) * [Complex geometry](/source/Complex_geometry) * [Conic section](/source/Conic_section) ** [Focus](/source/Focus_(geometry)) ** [Circle](/source/Circle) *** [List of circle topics](/source/List_of_circle_topics) *** [Thales' theorem](/source/Thales'_theorem) *** [Circumcircle](/source/Circumcircle) *** [Concyclic](/source/Concyclic) *** [Incircle and excircles of a triangle](/source/Incircle_and_excircles_of_a_triangle) *** [Orthocentric system](/source/Orthocentric_system) *** [Monge's theorem](/source/Monge's_theorem) *** [Power center](/source/Power_center_(geometry)) *** [Nine-point circle](/source/Nine-point_circle) *** [Circle points segments proof](/source/Circle_points_segments_proof) *** [Mrs. Miniver's problem](/source/Mrs._Miniver's_problem) *** [Isoperimetric theorem](/source/Isoperimetric_theorem) *** [Annulus](/source/Annulus_(mathematics)) *** [Ptolemaios' theorem](/source/Ptolemaios'_theorem) *** [Steiner chain](/source/Steiner_chain) ** [Eccentricity](/source/Eccentricity_(mathematics)) ** [Ellipse](/source/Ellipse) *** [Semi-major axis](/source/Semi-major_axis) ** [Hyperbola](/source/Hyperbola) ** [Parabola](/source/Parabola) ** [Matrix representation of conic sections](/source/Matrix_representation_of_conic_sections) ** [Dandelin spheres](/source/Dandelin_spheres) * [Curve of constant width](/source/Curve_of_constant_width) ** [Reuleaux triangle](/source/Reuleaux_triangle) * [Frieze group](/source/Frieze_group) * [Golden angle](/source/Golden_angle) * [Holditch's theorem](/source/Holditch's_theorem) * [Interactive geometry software](/source/Interactive_geometry_software) * [Involutes](/source/Involute) ** [Goat grazing problem](/source/Goat_grazing_problem) * [Parallel postulate](/source/Parallel_postulate) * [Polygon](/source/Polygon) ** [Star polygon](/source/Star_polygon) ** [Pick's theorem](/source/Pick's_theorem) ** [Shape dissection](/source/Shape_dissection) ** [Bolyai–Gerwien theorem](/source/Bolyai%E2%80%93Gerwien_theorem) ** [Poncelet–Steiner theorem](/source/Poncelet%E2%80%93Steiner_theorem) ** [Polygon triangulation](/source/Polygon_triangulation) * [Pons asinorum](/source/Pons_asinorum) * [Quadrilateral](/source/Quadrilateral) ** [Bicentric quadrilateral](/source/Bicentric_quadrilateral) ** [Cyclic quadrilateral](/source/Cyclic_quadrilateral) ** [Equidiagonal quadrilateral](/source/Equidiagonal_quadrilateral) ** [Kite (geometry)](/source/Kite_(geometry)) ** [Orthodiagonal quadrilateral](/source/Orthodiagonal_quadrilateral) *** [Rhombus](/source/Rhombus) ** [Rectangle](/source/Rectangle) *** [Square](/source/Square) ** [Tangential quadrilateral](/source/Tangential_quadrilateral) ** [Trapezoid](/source/Trapezoid) *** [Isosceles trapezoid](/source/Isosceles_trapezoid) * [Sangaku](/source/Sangaku) * [Straightedge](/source/Straightedge) * [Symmedian](/source/Symmedian) * [Tessellation](/source/Tessellation) ** [Prototile](/source/Prototile) ** [Aperiodic tiling](/source/Aperiodic_tiling) *** [Wang tile](/source/Wang_tile) *** [Penrose tiling](/source/Penrose_tiling) * [Trapezoid](/source/Trapezoid) (trapezium) ** [Isosceles trapezoid](/source/Isosceles_trapezoid) * [Triangle](/source/Triangle) ** [Acute and obtuse triangles](/source/Acute_and_obtuse_triangles) ** [Equilateral triangle](/source/Equilateral_triangle) ** [Euler's line](/source/Euler's_line) ** [Heron's formula](/source/Heron's_formula) ** [Integer triangle](/source/Integer_triangle) *** [Heronian triangle](/source/Heronian_triangle) ** [Isosceles triangle](/source/Isosceles_triangle) ** [List of triangle inequalities](/source/List_of_triangle_inequalities) ** [List of triangle topics](/source/List_of_triangle_topics) ** [Pedal triangle](/source/Pedal_triangle) ** [Pedoe's inequality](/source/Pedoe's_inequality) ** [Pythagorean theorem](/source/Pythagorean_theorem) ** [Pythagorean triangle](/source/Pythagorean_triangle) ** [Right triangle](/source/Right_triangle) ** [Triangle inequality](/source/Triangle_inequality) * [Trigonometry](/source/Trigonometry) ** [List of trigonometry topics](/source/List_of_trigonometry_topics) * [Wallpaper group](/source/Wallpaper_group) === 3-dimensional Euclidean geometry === {{Main|Solid geometry}} * [3D projection](/source/3D_projection) * [3D computer graphics](/source/3D_computer_graphics) ** [Binary space partitioning](/source/Binary_space_partitioning) ** [Ray tracing](/source/Ray_tracing_(graphics)) ** [Graham scan](/source/Graham_scan) * [Borromean rings](/source/Borromean_rings) * [Cavalieri's principle](/source/Cavalieri's_principle) * [Cross section](/source/Cross_section_(geometry)) * [Crystal](/source/Crystal) * [Cuisenaire rods](/source/Cuisenaire_rods) * [Desargues' theorem](/source/Desargues'_theorem) * [Right circular cone](/source/Right_circular_cone) * [Hyperboloid](/source/Hyperboloid) * [Napkin ring problem](/source/Napkin_ring_problem) * [Pappus's centroid theorem](/source/Pappus's_centroid_theorem) * [Paraboloid](/source/Paraboloid) * [Polyhedron](/source/Polyhedron) ** [Defect](/source/Defect_(geometry)) ** [Dihedral angle](/source/Dihedral_angle) ** [Prism](/source/Prism_(geometry)) ** [Prismatoid](/source/Prismatoid) ** [Honeycomb](/source/Honeycomb_(geometry)) ** [Pyramid](/source/Pyramid_(geometry)) ** [Parallelepiped](/source/Parallelepiped) ** [Tetrahedron](/source/Tetrahedron) *** [Heronian tetrahedron](/source/Heronian_tetrahedron) ** [Platonic solid](/source/Platonic_solid) ** [Archimedean solid](/source/Archimedean_solid) ** [Kepler-Poinsot polyhedra](/source/Kepler-Poinsot_polyhedra) ** [Johnson solid](/source/Johnson_solid) ** [Uniform polyhedron](/source/Uniform_polyhedron) ** [Polyhedral compound](/source/Polyhedral_compound) ** [Hilbert's third problem](/source/Hilbert's_third_problem) ** [Deltahedron](/source/Deltahedron) ** [Surface normal](/source/Surface_normal) * [3-sphere](/source/3-sphere), [spheroid](/source/spheroid), [ellipsoid](/source/ellipsoid) ** [Parabolic microphone](/source/Parabolic_microphone) ** [Parabolic reflector](/source/Parabolic_reflector) * [Soddy's hexlet](/source/Soddy's_hexlet) * [Sphericon](/source/Sphericon) * [Stereographic projection](/source/Stereographic_projection) * [Stereometry](/source/Stereometry) === ''n''-dimensional Euclidean geometry === * [Ball](/source/Ball_(mathematics)) * [Convex](/source/%3ACategory%3AConvex_geometry) ** [Convex hull](/source/Convex_hull) * [Coxeter group](/source/Coxeter_group) * [Euclidean distance](/source/Euclidean_distance) * [Homothetic center](/source/Homothetic_center) * [Hyperplane](/source/Hyperplane) * [Lattice](/source/Lattice_(group)) ** [Ehrhart polynomial](/source/Ehrhart_polynomial) ** [Leech lattice](/source/Leech_lattice) ** [Minkowski's theorem](/source/Minkowski's_theorem) * [Packing](/source/Packing_problems) ** [Sphere packing](/source/Sphere_packing) *** [Kepler conjecture](/source/Kepler_conjecture) *** [Kissing number problem](/source/Kissing_number_problem) ** [Honeycomb](/source/Honeycomb_(geometry)) *** [Andreini tessellation](/source/Andreini_tessellation) *** [Uniform tessellation](/source/Uniform_tiling) *** [Voronoi tessellation](/source/Voronoi_tessellation) *** [Delaunay triangulation](/source/Delaunay_triangulation) *** [Quasicrystal](/source/Quasicrystal) * [Parallelogram law](/source/Parallelogram_law) * [Polytope](/source/Polytope) ** [Schläfli symbol](/source/Schl%C3%A4fli_symbol) ** [Regular polytope](/source/Regular_polytope) ** ''[Regular Polytopes](/source/Regular_Polytopes_(book))'' * [Sphere](/source/Sphere) * [Quadric](/source/Quadric) ** [Hypersphere](/source/Hypersphere), [sphere](/source/sphere) ** [Spheroid](/source/Spheroid) ** [Ellipsoid](/source/Ellipsoid) ** [Hyperboloid](/source/Hyperboloid) ** [Paraboloid](/source/Paraboloid) ** [Cone](/source/Cone_(geometry)) * [Torus](/source/Torus) * [Root system](/source/Root_system) * [Similarity](/source/Similarity_(geometry)) * [Zonotope](/source/Zonotope) == Other geometries (not Euclidean) == {{Main|Non-Euclidean Geometry}} * [Projective geometry](/source/Projective_geometry) ** [Arc (projective geometry)](/source/Arc_(projective_geometry)) ** [Desargues' theorem](/source/Desargues'_theorem) ** [Girard Desargues](/source/Girard_Desargues) ** [Desarguesian plane](/source/Desarguesian_plane) ** [Line at infinity](/source/Line_at_infinity) ** [Point at infinity](/source/Point_at_infinity) ** [Plane at infinity](/source/Plane_at_infinity) ** [Hyperplane at infinity](/source/Hyperplane_at_infinity) ** [Projective line](/source/Projective_line) ** [Projective plane](/source/Projective_plane) *** [Oval (projective plane)](/source/Oval_(projective_plane)) *** [Roman surface](/source/Roman_surface) ** [Projective space](/source/Projective_space) ** [Complex projective line](/source/Complex_projective_line) ** [Complex projective plane](/source/Complex_projective_plane) ** [Fundamental theorem of projective geometry](/source/Fundamental_theorem_of_projective_geometry) ** [Projective transformation](/source/Projective_transformation) *** [Möbius transformation](/source/M%C3%B6bius_transformation) ** [Cross-ratio](/source/Cross-ratio) ** [Duality](/source/Duality_(projective_geometry)) ** [Homogeneous coordinates](/source/Homogeneous_coordinates) ** [Pappus's hexagon theorem](/source/Pappus's_hexagon_theorem) ** [Incidence](/source/Incidence_(geometry)) ** [Pascal's theorem](/source/Pascal's_theorem) * [Affine geometry](/source/Affine_geometry) ** [Affine space](/source/Affine_space) ** [Affine transformation](/source/Affine_transformation) * [Finite geometry](/source/Finite_geometry) * [Differential geometry](/source/Differential_geometry) ** [Contact geometry](/source/Contact_geometry) ** [Riemannian geometry](/source/Riemannian_geometry) ** [Symplectic geometry](/source/Symplectic_geometry) * [Non-Euclidean plane geometry](/source/Non-Euclidean_geometry) * [Angle excess](/source/Angle_excess) * [Hyperbolic geometry](/source/Hyperbolic_geometry) ** [Pseudosphere](/source/Pseudosphere) ** [Tractricoid](/source/Tractricoid) * [Elliptic geometry](/source/Elliptic_geometry) ** [Spherical geometry](/source/Spherical_geometry) * [Minkowski space](/source/Minkowski_space) * [Thurston's conjecture](/source/Thurston's_conjecture) == Numerical geometry == * [Parametric curve](/source/Parametric_curve) ** [Bézier curve](/source/B%C3%A9zier_curve) ** [Spline](/source/Spline_(mathematics)) *** [Hermite spline](/source/Hermite_spline) **** [B-spline](/source/B-spline) *** [NURBS](/source/NURBS) * [Parametric surface](/source/Parametric_surface) == Geometric algorithms == * [Convex hull](/source/Convex_hull) construction * [Euclidean shortest path](/source/Euclidean_shortest_path) * [Point in polygon](/source/Point_in_polygon) * [Point location](/source/Point_location) * [Hidden line removal](/source/Hidden_line_removal) == History of geometry == [History of geometry](/source/History_of_geometry) * [Timeline of geometry](/source/Timeline_of_geometry) * [Babylonian geometry](/source/Babylonian_geometry) * [Egyptian geometry](/source/Egyptian_geometry) * Ancient Greek geometry ** [Euclidean geometry](/source/Euclidean_geometry) *** [Pythagorean theorem](/source/Pythagorean_theorem) *** [Euclid's ''Elements''](/source/Euclid's_Elements) *** ''[Measurement of a Circle](/source/Measurement_of_a_Circle)'' * [Indian mathematics](/source/Indian_mathematics) ** [Bakhshali manuscript](/source/Bakhshali_manuscript) * Modern geometry ** [History of analytic geometry](/source/History_of_analytic_geometry) *** [History of the Cartesian coordinate system](/source/History_of_the_Cartesian_coordinate_system) ** [History of non-Euclidean geometry](/source/History_of_non-Euclidean_geometry) ** [History of topology](/source/History_of_topology) ** [History of algebraic geometry](/source/History_of_algebraic_geometry) ** [Erlangen program](/source/Erlangen_program) * == Generalizations == * [Noncommutative geometry](/source/Noncommutative_geometry) * [Topology](/source/Topology) == Connections to other fields == * [Mathematics and fiber arts](/source/Mathematics_and_fiber_arts) * [Van Hiele model](/source/Van_Hiele_model) - Prevailing theory of how children learn to reason in geometry * [Astronomy](/source/Astronomy) * [Computer graphics](/source/Computer_graphics) * [Image analysis](/source/Image_analysis) * [Robot control](/source/Robot_control) * The [Strähle construction](/source/Str%C3%A4hle_construction) is used in the design of some musical instruments. * [Burmester's theory](/source/Burmester's_theory) for the design of mechanical linkages ==Lists== * [List of mathematical shapes](/source/List_of_mathematical_shapes) * [List of geometers](/source/List_of_geometers) * [List of curves](/source/List_of_curves) * [List of curves topics](/source/List_of_curves_topics) * [List of trigonometric identities](/source/List_of_trigonometric_identities) ==See also== * [List of basic mathematics topics](/source/List_of_basic_mathematics_topics) * [List of mathematics articles](/source/List_of_mathematics_articles) * [Table of mathematical symbols](/source/Table_of_mathematical_symbols) ==Further reading== *{{cite book | last = Rich | first = Barnett | title = Schaum's Outline of Geometry |edition= 4th | publisher = McGraw-Hill | location = New York | year = 2009 | isbn = 978-0-07-154412-2 }} ==External links== {{Outline footer}} Geometry Geometry Category:Geometry Geometry --- Adapted from the Wikipedia article [Outline of geometry](https://en.wikipedia.org/wiki/Outline_of_geometry) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Outline_of_geometry?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.