List of mathematical shapes

Following is a list of shapes studied in mathematics. == Algebraic curves == Cubic plane curve Quartic plane curve Fractal === Rational curves === ==== Degree 2 ==== Conic sections Unit circle Unit hyperbola ==== Degree 3 ==== ==== Degree 4 ==== ==== Degree 5 ==== Quintic of l'Hospital CURVE WITH CONSTANT REACTION, L'HOSPITAL QUINTIC ==== Degree 6 ==== Astroid Atriphtaloid Nephroid Quadrifolium ==== Families of variable degree ==== Epicycloid Epispiral Epitrochoid Hypocycloid Lissajous curve Poinsot's spirals Rational normal curve Rose curve === Curves of genus one === Bicuspid curve Cassini oval Cassinoide Cubic curve Elliptic curve Watt's curve === Curves with genus greater than one === Butterfly curve Elkies trinomial curves Hyperelliptic curve Klein quartic Classical modular curve Bolza surface Macbeath surface === Curve families with variable genus === Polynomial lemniscate Fermat curve Sinusoidal spiral Superellipse Hurwitz surface == Transcendental curves == Bowditch curve Brachistochrone Butterfly curve Catenary Clélies Cochleoid Cycloid Horopter Isochrone Isochrone of Huygens (Tautochrone) Isochrone of Leibniz Isochrone of Varignon Lamé curve Pursuit curve Rhumb line Spirals Archimedean spiral Cornu spiral Cotes' spiral Fermat's spiral Galileo's spiral Hyperbolic spiral Lituus Logarithmic spiral Nielsen's spiral Golden spiral Syntractrix Tractrix Trochoid == Piecewise constructions == Bézier curve Splines B-spline Nonuniform rational B-spline Ogee Loess curve Lowess Polygonal curve Maurer rose Reuleaux triangle Bézier triangle == Curves generated by other curves == == Space curves == Conchospiral Helix Tendril perversion (a transition between back-to-back helices) Hemihelix, a quasi-helical shape characterized by multiple tendril perversions Seiffert's spiral Slinky spiral Twisted cubic Viviani's curve == Surfaces in 3-space == Plane Quadric surfaces Cone Cylinder Ellipsoid Spheroid Sphere Hyperboloid Paraboloid Bicylinder Tricylinder Möbius strip Torus == Minimal surfaces == 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 Triply periodic minimal surface == Non-orientable surfaces == Klein bottle Real projective plane Cross-cap Roman surface Boy's surface == Quadrics == Sphere Spheroid Oblate spheroid Cone Ellipsoid Hyperboloid of one sheet Hyperboloid of two sheets Hyperbolic paraboloid (a ruled surface) Paraboloid Sphericon Oloid == Pseudospherical surfaces == Dini's surface Pseudosphere == Algebraic surfaces == See the list of algebraic surfaces.

Source: Wikipedia — List of mathematical shapes (CC BY-SA 4.0)

List of mathematical shapes

Following is a list of shapes studied in mathematics. == Algebraic curves == Cubic plane curve Quartic plane curve Fractal === Rational curves === ==== Degree 2 ==== Conic sections Unit circle Unit hyperbola ==== Degree 3 ==== ==== Degree 4 ==== ==== Degree 5 ==== Quintic of l'Hospital CURVE WITH CONSTANT REACTION, L'HOSPITAL QUINTIC ==== Degree 6 ==== Astroid Atriphtaloid Nephroid Quadrifolium ==== Families of variable degree ==== Epicycloid Epispiral Epitrochoid Hypocycloid Lissajous curve Poinsot's spirals Rational normal curve Rose curve === Curves of genus one === Bicuspid curve Cassini oval Cassinoide Cubic curve Elliptic curve Watt's curve === Curves with genus greater than one === Butterfly curve Elkies trinomial curves Hyperelliptic curve Klein quartic Classical modular curve Bolza surface Macbeath surface === Curve families with variable genus === Polynomial lemniscate Fermat curve Sinusoidal spiral Superellipse Hurwitz surface == Transcendental curves == Bowditch curve Brachistochrone Butterfly curve Catenary Clélies Cochleoid Cycloid Horopter Isochrone Isochrone of Huygens (Tautochrone) Isochrone of Leibniz Isochrone of Varignon Lamé curve Pursuit curve Rhumb line Spirals Archimedean spiral Cornu spiral Cotes' spiral Fermat's spiral Galileo's spiral Hyperbolic spiral Lituus Logarithmic spiral Nielsen's spiral Golden spiral Syntractrix Tractrix Trochoid == Piecewise constructions == Bézier curve Splines B-spline Nonuniform rational B-spline Ogee Loess curve Lowess Polygonal curve Maurer rose Reuleaux triangle Bézier triangle == Curves generated by other curves == == Space curves == Conchospiral Helix Tendril perversion (a transition between back-to-back helices) Hemihelix, a quasi-helical shape characterized by multiple tendril perversions Seiffert's spiral Slinky spiral Twisted cubic Viviani's curve == Surfaces in 3-space == Plane Quadric surfaces Cone Cylinder Ellipsoid Spheroid Sphere Hyperboloid Paraboloid Bicylinder Tricylinder Möbius strip Torus == Minimal surfaces == 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 Triply periodic minimal surface == Non-orientable surfaces == Klein bottle Real projective plane Cross-cap Roman surface Boy's surface == Quadrics == Sphere Spheroid Oblate spheroid Cone Ellipsoid Hyperboloid of one sheet Hyperboloid of two sheets Hyperbolic paraboloid (a ruled surface) Paraboloid Sphericon Oloid == Pseudospherical surfaces == Dini's surface Pseudosphere == Algebraic surfaces == See the list of algebraic surfaces.

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Source: Wikipedia "List of mathematical shapes" · CC BY-SA 4.0

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