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 (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 (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
• 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
• 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

Undergraduate Texts in Mathematics

Graduate Texts in Mathematics

Graduate Studies in Mathematics

Mathematics Encyclopedia

World

Index

Hellenica World - Scientific Library

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