Geometry
Projecting a sphere to a plane
Outline History (Timeline)
Branches Euclidean Non-Euclidean Elliptic Spherical Hyperbolic Non-Archimedean geometry Projective Affine Synthetic Analytic Algebraic Arithmetic Diophantine Differential Riemannian Symplectic Discrete differential Complex Finite Discrete/Combinatorial Digital Convex Computational Fractal Incidence Noncommutative geometry Noncommutative algebraic geometry
Concepts Features Dimension Straightedge and compass constructions Angle Curve Diagonal Orthogonality (Perpendicular) Parallel Vertex Congruence Similarity Symmetry
Zero-dimensional Point
One-dimensional Line segment ray Length
Two-dimensional Plane Area Polygon Triangle Altitude Hypotenuse Pythagorean theorem Parallelogram Square Rectangle Rhombus Rhomboid Quadrilateral Trapezoid Kite Circle Diameter Circumference Area
Three-dimensional Volume Cube cuboid Cylinder Dodecahedron Icosahedron Octahedron Pyramid Platonic Solid Sphere Tetrahedron
Four- / other-dimensional Tesseract Hypersphere
Geometers
by name Aida Aryabhata Ahmes Alhazen Apollonius Archimedes Atiyah Baudhayana Bolyai Brahmagupta Cartan Coxeter Descartes Euclid Euler Gauss Gromov Hilbert Huygens Jyeṣṭhadeva Kātyāyana Khayyám Klein Lobachevsky Manava Minkowski Minggatu Pascal Pythagoras Parameshvara Poincaré Riemann Sakabe Sijzi al-Tusi Veblen Virasena Yang Hui al-Yasamin Zhang List of geometers
by period BCE Ahmes Baudhayana Manava Pythagoras Euclid Archimedes Apollonius 1–1400s Zhang Kātyāyana Aryabhata Brahmagupta Virasena Alhazen Sijzi Khayyám al-Yasamin al-Tusi Yang Hui Parameshvara 1400s–1700s Jyeṣṭhadeva Descartes Pascal Huygens Minggatu Euler Sakabe Aida 1700s–1900s Gauss Lobachevsky Bolyai Riemann Klein Poincaré Hilbert Minkowski Cartan Veblen Coxeter Present day Atiyah Gromov
v t e

This is a list of geometry topics.

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
• Noncommutative algebraic geometry
• Noncommutative 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

• 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

Mathematical morphology

• Minkowski addition

Generalizations

• Noncommutative geometry
• Topology

Various

• Coordinate-free treatment
• Chirality
  • Handedness
  • Relative direction
  • Mirror image
• Erlangen program
• Four-dimensional space
• Geometric shape
• Geometric 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