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

External links