# List of geometry topics

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List of geometry topics

*Geometric shape covers standard terms for plane shapes
*List of mathematical shapes covers all dimensions
*List of differential geometry topics
*List of geometers

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
*Euclidean geometry
*Finite geometry
*Geometry of numbers

*Hyperbolic geometry
*Information geometry
*Integral geometry
*Inversive geometry
*Non-Euclidean geometry
*Numerical geometry
*Parabolic geometry
*Plane geometry
*Projective geometry
*Riemannian geometry
*Spherical geometry
*Symplectic geometry
*Synthetic geometry
*Systolic geometry
*Transformation geometry

Euclidean geometry, foundations

*Hilbert's axioms
*Point
*Locus
*Line
*Parallel
*Angle
**Concurrent lines
**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
*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
*Euler's line
*Equilateral triangle
*Frieze group
*Golden angle
*Heron's formula
**Heronian triangle
*Holditch's theorem
*Interactive geometry software
*Pappus's theorem
*Parallel postulate
*Pedal triangle
*Polygon
**Star polygon
**Pick's theorem
**Shape dissection
**Bolyai-Gerwien theorem
**Poncelet-Steiner theorem
**Polygon triangulation
*Pons asinorum
*Pythagorean triangle
*Sangaku
*Straightedge
*Symmedian
*Tessellation
**Prototile
**Aperiodic tiling
***Wang tile
***Penrose tiling
*Trapezoid, trapezium
**Isosceles trapezoid
*Triangle
**Pythagorean theorem
**Triangle inequality
**Pedoe's 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
*Cross section
*Crystal
*Cuisenaire rods
*Desargues' theorem
*Right circular cone
*Hyperboloid
*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 hull
*Coxeter group
*Euclidean distance
*Homothetic center
*Hyperplane
*Lattice
**Ehrhart polynomial
**Leech lattice
**Minkowski's theorem
*Packing and covering
**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
**Hypersphere, sphere
**Spheroid
**Ellipsoid
**Hyperboloid
**Paraboloid
**Cone
*Torus
*Root system
*Similarity
*Zonotope

Non-Euclidean geometry

*Projective geometry
**Desargues' theorem
**Girard Desargues
**Desarguesian plane
**Line at infinity
**Point at infinity
**Plane at infinity
**Hyperplane at infinity
**Projective line
**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

* Curve interpolation
* Parametric curve
** Bezier curve
** Spline
***Hermite spline
****Beta spline
*****B-spline
***Higher-order spline
***NURBS

* Parametric surface
** Parametric patch

Geometric algorithms

* Convex hull construction
* Point in polygon
* Point location
* Hidden line removal

Mathematical morphology

Generalizations

*Noncommutative geometry
*Topology

Various

*Coordinate-free treatment
*Chirality
**Handedness
**Left and right
**Mirror image
*Erlangen program
*Four dimensions
*Group action, invariant
*Infinitesimal transformation
*List of terms based on the word cube
*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

Applications

*Astronomy
*Computer graphics
*Image analysis
*Robot control
*The Strähle construction is used in the design of some musical instruments.

ee also

*Mathematics

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