Outline of geometry
(Redirected from Geometries)
| Geometry |
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| Geometers |
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.
Types, methodologies, and terminologies of geometry.
[edit]- 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
[edit]General concepts
[edit]Measurements
[edit]Trigonometric functions
[edit]Vectors
[edit]- Amplitude
- Dot product
- Norm (mathematics) (also known as magnitude)
- Position vector
- Scalar multiplication
- Vector addition
- Zero vector
Vector spaces and complex dimensions
[edit]Symmetry, shape and pattern
[edit]Euclidean geometry foundations
[edit]Euclidean plane geometry
[edit]- 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
[edit]- 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
[edit]Other geometries (not Euclidean)
[edit]- 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
[edit]Geometric algorithms
[edit]History of geometry
[edit]- Timeline of geometry
- Babylonian geometry
- Egyptian geometry
- Ancient Greek geometry
- Indian mathematics
- Modern geometry
Generalizations
[edit]Connections to other fields
[edit]- 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
[edit]See also
[edit]Further reading
[edit]- Rich, Barnett (2009). Schaum's Outline of Geometry (4th ed.). New York: McGraw-Hill. ISBN 978-0-07-154412-2.