Outline of geometry
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.
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Types, methodologies, and terminologies of geometry.
- Absolute geometry
- Affine geometry
- Algebraic geometry
- Analytic geometry
- 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
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
- Ray
- Plane
Trigonometric functions
Vectors
- 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
- Hilbert's axioms
- Locus
- Line
- Line segment
- Parallel
- Angle
- Congruence
- Reflection
- Rotation
- Coordinate rotations and reflections
- Translation
- Glide reflection
- Similarity
- Shear mapping
Euclidean plane geometry
- 2D computer graphics
- 2D geometric model
- Altitude
- Brahmagupta's formula
- Bretschneider's formula
- Compass and straightedge constructions
- 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
- Hyperbola
- Parabola
- Matrix representation of conic sections
- Dandelin spheres
- Curve of constant width
- Frieze group
- Golden angle
- Holditch's theorem
- Interactive geometry software
- Involutes
- Goat grazing problem
- Parallel postulate
- Polygon
- Pons asinorum
- Quadrilateral
- Sangaku
- Straightedge
- Symmedian
- Tessellation
- Trapezoid (trapezium)
- Triangle
- Acute and obtuse triangles
- Equilateral triangle
- Euler's line
- Heron's formula
- Integer 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
- 3-sphere, spheroid, ellipsoid
- Soddy's hexlet
- Sphericon
- Stereographic projection
- Stereometry
n-dimensional Euclidean geometry
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
- 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.
External links
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