Geometry is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. Geometry is one of the oldest mathematical sciences. Modern geometry also extends into non-Euclidean spaces, topology, and fractal dimensions, bridging pure mathematics with applications in physics, computer science, and data visualization.
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Types, methodologies, and terminologies of geometry.
- Absolute geometry
- Affine geometry
- Algebraic geometry
- Analytic geometry
- Birational geometry
- Complex 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
- Euclidean 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
- Ordered geometry
- Parabolic geometry
- Plane geometry
- Projective geometry
- Quantum geometry
- Riemannian geometry
- Ruppeiner geometry
- Solid geometry
- Spherical geometry
- Symplectic geometry
- Synthetic geometry
- Systolic geometry
- Taxicab geometry
- Toric geometry
- Transformation geometry
- Tropical geometry
General geometry concepts
General concepts
- Chirality
- Coordinate-free treatment
- Four-dimensional space
- Infinitesimal transformation
- Geometric progression
- Geometric shape
- Pi
- Angular velocity
- Linear velocity
- De Moivre's theorem
- Similar triangles
- Unit circle
- Point
- Line and Ray
- Plane
Measurements
Trigonometric functions
Vectors
Main article: Vector (geometric)
- Amplitude
- Dot product
- Norm (mathematics) (also known as magnitude)
- Position vector
- Scalar multiplication
- Vector addition
- Zero vector
Vector spaces and complex dimensions
- Complex plane
- Imaginary axis
- Linear interpolation
- One-to-one
- Orthogonal
- Polar coordinate system
- Pole
- Real axis
- Secant line
- Circular sector or "sector"
- Semiperimeter
Symmetry, shape and pattern
- 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
Euclidean geometry foundations
Main article: Euclidean geometry
Euclidean plane geometry
Main article: Plane geometry
- 2D computer graphics
- 2D geometric model
- Altitude
- Brahmagupta's formula
- Bretschneider's formula
- Compass and straightedge constructions
- Complex geometry
- Conic section
- Curve of constant width
- Frieze group
- Golden angle
- Holditch's theorem
- Interactive geometry software
- Involutes
- Parallel postulate
- Polygon
- Pons asinorum
- Quadrilateral
- Sangaku
- Straightedge
- Symmedian
- Tessellation
- Trapezoid (trapezium)
- Triangle
- Trigonometry
- Wallpaper group
3-dimensional Euclidean geometry
Main article: Solid geometry
- 3D projection
- 3D computer graphics
- 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
- 3-sphere, spheroid, ellipsoid
- Soddy's hexlet
- Sphericon
- Stereographic projection
- Stereometry
n-dimensional Euclidean geometry
- Ball
- Convex
- Coxeter group
- Euclidean distance
- Homothetic center
- Hyperplane
- Lattice
- Packing
- Parallelogram law
- Polytope
- Sphere
- Quadric
- Torus
- Root system
- Similarity
- Zonotope
Other geometries (not Euclidean)
Main article: Non-Euclidean Geometry
- 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
- Projective space
- Complex projective line
- Complex projective plane
- Fundamental theorem of projective geometry
- Projective transformation
- Cross-ratio
- Duality
- Homogeneous coordinates
- Pappus's hexagon theorem
- Incidence
- Pascal's theorem
- Affine geometry
- Finite geometry
- Differential geometry
- Non-Euclidean plane geometry
- Angle excess
- Hyperbolic geometry
- Elliptic geometry
- Minkowski space
- Thurston's conjecture
Numerical geometry
Geometric algorithms
- Convex hull construction
- Euclidean shortest path
- Point in polygon
- Point location
- Hidden line removal
History of geometry
- Timeline of geometry
- Babylonian geometry
- Egyptian geometry
- Ancient Greek geometry
- Indian mathematics
- Modern geometry
Generalizations
Geometric algorithms
- Convex hull construction
- Euclidean shortest path
- Point in polygon
- Point location
- Hidden line removal
Connections to other fields
- Mathematics and fiber arts
- Van Hiele model - Prevailing theory of how children learn to reason in geometry
- 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
Lists
- List of mathematical shapes
- List of geometers
- List of curves
- List of curves topics
- List of trigonometric identities
See also
Further reading
- Rich, Barnett (2009). Schaum's Outline of Geometry (4th ed.). New York: McGraw-Hill. ISBN 978-0-07-154412-2.