List of geometry topics

• Geometric shape covers standard terms for plane shapes

  Types, methodologies, and terminologies of geometry.

• Absolute geometry
• Affine geometry
• Algebraic geometry
• Analytic geometry
• Archimedes' use of infinitesimals
• Birational geometry
• Complex geometry
• Combinatorial 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
• 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
• Numerical geometry
• Ordered geometry
• Parabolic geometry
• Plane geometry
• Projective geometry
• Quantum geometry
• Riemannian geometry
• Ruppeiner geometry
• Spherical geometry
• Symplectic geometry
• Synthetic geometry
• Systolic geometry
• Taxicab geometry
• Toric geometry
• Transformation geometry
• Tropical geometry

  [Euclidean geometry], foundations

• Hilbert's axioms
• Point
• Locus
• Line
• 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 ([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
• 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
• * Orthodiagonal quadrilateral
• ** Rhombus
• *Rectangle
• **Square
• * Tangential quadrilateral
• *Trapezoid
• **Isosceles trapezoid
• Sangaku
• Straightedge
• Symmedian
• Tessellation
• * Prototile
• * Aperiodic tiling
• ** Wang tile
• ** Penrose tiling
• Trapezoid
• * 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 ([solid 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
• :Category:Convex geometry|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
• * Desargues' theorem
• * Girard Desargues
• * Desarguesian plane
• * Line at infinity
• * Point at infinity
• * Plane at infinity
• * Hyperplane at infinity
• * Projective line
• * Projective plane
• ** Oval
• ** 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

  [Mathematical morphology]

• Minkowski addition

  Generalizations

• Noncommutative geometry
• Topology

  Various

• Coordinate-free treatment
• Chirality
• * Handedness
• * Relative direction
• * Mirror image
• Erlangen program
• Four-dimensional space
• Group action, invariant
• Hadwiger's theorem
• Infinitesimal transformation
• Pi
• Polar sine
• 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
• Mathematics and fiber arts
• Van Hiele model - Prevailing theory of how children learn to reason in geometry

  Applications

• 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