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

Numerical geometry

Ordered geometry

Parabolic geometry

Plane geometry

Projective geometry

Quantum geometry

Reticular 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 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

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

Curve interpolation

Parametric curve

Bézier curve

Spline

Hermite spline

Beta spline

B-spline

Higher-order spline

NURBS

Parametric surface

Parametric patch

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