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List of mathematical shapes
Discussion started by Adam Rangihana 8 years ago
List of mathematical shapes
From Wikipedia, the free encyclopedia
Following is a list of some mathematically well-defined shapes.
Contents
[hide]- 1Algebraic curves
- 2Transcendental curves
- 3Piecewise constructions
- 4Curves generated by other curves
- 5Space curves
- 6Surfaces in 3-space
- 7Minimal surfaces
- 8Non-orientable surfaces
- 9Quadrics
- 10Pseudospherical surfaces
- 11Algebraic surfaces
- 12Miscellaneous surfaces
- 13Fractals
- 14Regular Polytopes
- 14.1Polytope elements
- 14.2Tessellations
- 14.3Zero dimension
- 14.4One-dimensional regular polytope
- 14.5Two-dimensional regular polytopes
- 14.6Three-dimensional regular polytopes
- 14.7Four-dimensional regular polytopes
- 14.8Five-dimensional regular polytopes and higher
- 14.9Apeirotopes
- 14.10Abstract polytopes
- 15Non-regular polytopes
- 162D with 1D surface
- 175D with 4D surfaces
- 18Six dimensions
- 19Seven dimensions
- 20Eight dimension
- 21Nine dimensions
- 22Ten dimensions
- 23Dimensional families
- 24Geometry
- 25Geometry and other areas of mathematics
- 26Glyphs and symbols
- 27References
Algebraic curves[edit]
Rational curves[edit]
Degree 2[edit]
Degree 3[edit]
Degree 4[edit]
Degree 5[edit]
Degree 6[edit]
Families of variable degree[edit]
- Epicycloid
- Epispiral
- Epitrochoid
- Hypocycloid
- Lissajous curve
- Poinsot's spirals
- Rational normal curve
- Rose curve
Curves of genus one[edit]
Curves with genus greater than one[edit]
- Butterfly curve (algebraic)
- Elkies trinomial curves
- Hyperelliptic curve
- Klein quartic
- Classical modular curve
- Bolza surface
- Macbeath surface
Curve families with variable genus[edit]
Transcendental curves[edit]
- Bowditch curve
- Brachistochrone
- Butterfly curve (transcendental)
- Catenary
- Clélies
- Cochleoid
- Cycloid
- Horopter
- Interscendental curve: A curve defined using irrational exponents, such as y=x√2. See Salmon (1879, p. 206)
- Isochrone
- Lamé curve
- Pursuit curve
- Rhumb line
- Spirals
- Syntractrix
- Tractrix
- Trochoid
Piecewise constructions[edit]
Curves generated by other curves[edit]
- Caustic including Catacaustic and Diacaustic
- Cissoid
- Conchoid
- Evolute
- Glissette
- Inverse curve
- Involute
- Isoptic including Orthoptic
- Orthotomic
- Negative pedal curve
- Pedal curve
- Parallel curve
- Radial curve
- Roulette
- Strophoid
Space curves[edit]
- Conchospiral
- Helix
- Tendril perversion (a transition between back-to-back helices)
- Hemihelix, a quasi-helical shape characterized by multiple tendril perversions
- Seiffert's spiral [5]
- Slinky spiral [6]
- Twisted cubic
- Viviani's curve
Surfaces in 3-space[edit]
Main article: List of surfaces
Minimal surfaces[edit]
- Catalan's minimal surface
- Costa's minimal surface
- Catenoid
- Enneper surface
- Gyroid
- Helicoid
- Lidinoid
- Riemann's minimal surface
- Saddle tower
- Scherk surface
- Schwarz minimal surface
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