Geometry is a branch of 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.
Types, methodologies, and terminologies of geometry. Absolute geometry Affine geometry Algebraic geometry Analytic geometry Birational geometry Complex geometry Computational geometry Conformal geometry Constructive solid geometry Contact geometry Convex geometry Descriptive geometry Differential geometry Digital geometry Discrete geometry Distance geometry Elliptic geometry Enumerative geometry Epipolar geometry Euclidean geometry Finite geometry Fractal geometry Geometry of numbers Hyperbolic geometry Incidence geometry Information geometry Integral geometry Inversive geometry Inversive ring geometry Klein geometry Lie sphere geometry Non-Euclidean geometry Noncommutative algebraic geometry Noncommutative geometry Ordered geometry Parabolic geometry Plane geometry Projective geometry Quantum geometry Riemannian geometry Ruppeiner geometry Solid geometry Spherical geometry Symplectic geometry Synthetic geometry Systolic geometry Taxicab geometry Toric geometry Transformation geometry Tropical geometry
General geometry concepts
General concepts Chirality Handedness Relative direction Mirror image Coordinate-free treatment Four-dimensional space Infinitesimal transformation Geometric progression Geometric shape Pi Angular velocity Linear velocity De Moivre's theorem Similar triangles Unit circle Point Line and Ray Plane
Measurements Bearing Angle Degree Minute Radian Circumference Diameter
Trigonometric functions Trigonometric function Asymptotes Circular functions Periodic functions Law of cosines Law of sines Polar sine
Vectors
Amplitude Dot product Norm (mathematics) (also known as magnitude) Position vector Scalar multiplication Vector addition Zero vector
Vector spaces and complex dimensions Complex plane Imaginary axis Linear interpolation One-to-one Orthogonal Polar coordinate system Pole Real axis Secant line Circular sector or "sector" Semiperimeter
Symmetry, shape and pattern Symmetry Shape Pattern Crystal system Frieze group Isometry Lattice Point group Point groups in two dimensions Point groups in three dimensions Space group Symmetry group Translational symmetry Wallpaper group
Euclidean geometry foundations
Hilbert's axioms Locus Line Line segment Parallel Angle Concurrent lines Adjacent angles Central angle Complementary angles Inscribed angle Internal angle Supplementary angles Angle trisection Congruence Reflection Rotation Coordinate rotations and reflections Translation Glide reflection Similarity Similarity transformation Homothety Shear mapping
Euclidean plane geometry
2D computer graphics 2D geometric model Altitude Brahmagupta's formula Bretschneider's formula Compass and straightedge constructions Squaring the circle Complex geometry Conic section Focus Circle List of circle topics Thales' theorem Circumcircle Concyclic Incircle and excircles of a triangle Orthocentric system Monge's theorem Power center Nine-point circle Circle points segments proof Mrs. Miniver's problem Isoperimetric theorem Annulus Ptolemaios' theorem Steiner chain Eccentricity Ellipse Semi-major axis Hyperbola Parabola Matrix representation of conic sections Dandelin spheres Curve of constant width Reuleaux triangle Frieze group Golden angle Holditch's theorem Interactive geometry software Involutes Goat grazing problem Parallel postulate Polygon Star polygon Pick's theorem Shape dissection Bolyai–Gerwien theorem Poncelet–Steiner theorem Polygon triangulation Pons asinorum Quadrilateral Bicentric quadrilateral Cyclic quadrilateral Equidiagonal quadrilateral Kite (geometry) Orthodiagonal quadrilateral Rhombus Rectangle Square Tangential quadrilateral Trapezoid Isosceles trapezoid Sangaku Straightedge Symmedian Tessellation Prototile Aperiodic tiling Wang tile Penrose tiling Trapezoid (trapezium) Isosceles trapezoid Triangle Acute and obtuse triangles Equilateral triangle Euler's line Heron's formula Integer triangle Heronian triangle Isosceles triangle List of triangle inequalities List of triangle topics Pedal triangle Pedoe's inequality Pythagorean theorem Pythagorean triangle Right triangle Triangle inequality Trigonometry List of trigonometry topics Wallpaper group
3-dimensional Euclidean geometry
3D projection 3D computer graphics Binary space partitioning Ray tracing Graham scan Borromean rings Cavalieri's principle Cross section Crystal Cuisenaire rods Desargues' theorem Right circular cone Hyperboloid Napkin ring problem Pappus's centroid theorem Paraboloid Polyhedron Defect Dihedral angle Prism Prismatoid Honeycomb Pyramid Parallelepiped Tetrahedron Heronian tetrahedron Platonic solid Archimedean solid Kepler-Poinsot polyhedra Johnson solid Uniform polyhedron Polyhedral compound Hilbert's third problem Deltahedron Surface normal 3-sphere, spheroid, ellipsoid Parabolic microphone Parabolic reflector Soddy's hexlet Sphericon Stereographic projection Stereometry
n-dimensional Euclidean geometry Ball Convex Convex hull Coxeter group Euclidean distance Homothetic center Hyperplane Lattice Ehrhart polynomial Leech lattice Minkowski's theorem Packing Sphere packing Kepler conjecture Kissing number problem Honeycomb Andreini tessellation Uniform tessellation Voronoi tessellation Delaunay triangulation Quasicrystal Parallelogram law Polytope Schläfli symbol Regular polytope Regular Polytopes Sphere Quadric Hypersphere, sphere Spheroid Ellipsoid Hyperboloid Paraboloid Cone Torus Root system Similarity Zonotope
Other geometries (not Euclidean)
Projective geometry Arc (projective geometry) Desargues' theorem Girard Desargues Desarguesian plane Line at infinity Point at infinity Plane at infinity Hyperplane at infinity Projective line Projective plane Oval (projective plane) Roman surface Projective space Complex projective line Complex projective plane Fundamental theorem of projective geometry Projective transformation Möbius transformation Cross-ratio Duality Homogeneous coordinates Pappus's hexagon theorem Incidence Pascal's theorem Affine geometry Affine space Affine transformation Finite geometry Differential geometry Contact geometry Riemannian geometry Symplectic geometry Non-Euclidean plane geometry Angle excess Hyperbolic geometry Pseudosphere Tractricoid Elliptic geometry Spherical geometry Minkowski space Thurston's conjecture
Numerical geometry Parametric curve Bézier curve Spline Hermite spline B-spline NURBS Parametric surface
Geometric algorithms Convex hull construction Euclidean shortest path Point in polygon Point location Hidden line removal
History of geometry History of geometry
Timeline of geometry Babylonian geometry Egyptian geometry Ancient Greek geometry Euclidean geometry Pythagorean theorem Euclid's Elements Measurement of a Circle Indian mathematics Bakhshali manuscript Modern geometry History of analytic geometry History of the Cartesian coordinate system History of non-Euclidean geometry History of topology History of algebraic geometry Erlangen program
Generalizations Noncommutative geometry Topology
Connections to other fields Mathematics and fiber arts Van Hiele model - Prevailing theory of how children learn to reason in geometry Astronomy Computer graphics Image analysis Robot control The Strähle construction is used in the design of some musical instruments. Burmester's theory for the design of mechanical linkages
Lists List of mathematical shapes List of geometers List of curves List of curves topics List of trigonometric identities
See also List of basic mathematics topics List of mathematics articles Table of mathematical symbols
Further reading Rich, Barnett (2009). Schaum's Outline of Geometry (4th ed.). New York: McGraw-Hill. ISBN 978-0-07-154412-2.
External links