following is a list of some mathematically well-defined shapes. ==algebraic curves== *cubic plane curve *quartic plane curve ===rational curves=== ====degree 2==== *conic sections *unit circle *unit hyperbola ====degree 3====  *folium of descartes *cissoid of diocles *conchoid of de sluze *right strophoid *semicubical parabola *serpentine curve *trident curve *trisectrix of maclaurin *tschirnhausen cubic *witch of agnesi  ====degree 4====  *ampersand curve *bean curve *bicorn *bow curve *bullet-nose curve *cruciform curve *deltoid curve *devil's curve *hippopede *kampyle of eudoxus *kappa curve *lemniscate of booth *lemniscate of gerono *lemniscate of bernoulli *limaÃ§on **cardioid **limaÃ§on trisectrix *trifolium curve  ====degree 5==== *quintic of l'hospital  ====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 (algebraic) *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 (transcendental) *catenary *clÃ©lies *cochleoid *cycloid *horopter *interscendental curve: a curve defined using irrational exponents, such as y=xâ2. see  *isochrone **isochrone of huygens (tautochrone) **isochrone of leibniz **isochrone of varignon *lamÃ© 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 *syntractrix *tractrix *trochoid ==piecewise constructions== *bÃ©zier curve *splines **b-spline **nonuniform rational b-spline *ogee *loess curve *lowess *[[
Mathematics-related_lists