# Category: Plane curves

Kampyle of Eudoxus
The Kampyle of Eudoxus (Greek: καμπύλη [γραμμή], meaning simply "curved [line], curve") is a curve with a Cartesian equation of from which the solution x = y = 0 is excluded.
Oval
An oval (from Latin ovum 'egg') is a closed curve in a plane which resembles the outline of an egg. The term is not very specific, but in some areas (projective geometry, technical drawing, etc.) it i
Butterfly curve (transcendental)
The butterfly curve is a transcendental plane curve discovered by Temple H. Fay of University of Southern Mississippi in 1989.
Bicuspid curve
No description available.
Syntractrix
A syntractrix is a curve of the form It is the locus of a point on the tangent of a tractrix at a constant distance from the point of tangency, as the point of tangency is moved along the curve.
Ellipse
In mathematics, an ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant. It generalizes a circle
Fish curve
A fish curve is an ellipse negative pedal curve that is shaped like a fish. In a fish curve, the pedal point is at the focus for the special case of the squared eccentricity . The parametric equations
Cruciform curve
No description available.
Osgood curve
In mathematical analysis, an Osgood curve is a non-self-intersecting curve that has positive area. Despite its area, it is not possible for such a curve to cover a convex set, distinguishing them from
Quartic plane curve
In algebraic geometry, a quartic plane curve is a plane algebraic curve of the fourth degree. It can be defined by a bivariate quartic equation: with at least one of A, B, C, D, E not equal to zero. T
Spiric section
In geometry, a spiric section, sometimes called a spiric of Perseus, is a quartic plane curve defined by equations of the form Equivalently, spiric sections can be defined as bicircular quartic curves
Lemniscate
In algebraic geometry, a lemniscate is any of several figure-eight or ∞-shaped curves. The word comes from the Latin "lēmniscātus" meaning "decorated with ribbons", from the Greek λημνίσκος meaning "r
Cyclocycloid
An cyclocycloid is a roulette traced by a point attached to a circle of radius r rolling around, a fixed circle of radius R, where the point is at a distance d from the center of the exterior circle.
Superellipse
A superellipse, also known as a Lamé curve after Gabriel Lamé, is a closed curve resembling the ellipse, retaining the geometric features of semi-major axis and semi-minor axis, and symmetry about the
Euler spiral
An Euler spiral is a curve whose curvature changes linearly with its curve length (the curvature of a circular curve is equal to the reciprocal of the radius). Euler spirals are also commonly referred
Polynomial lemniscate
In mathematics, a polynomial lemniscate or polynomial level curve is a plane algebraic curve of degree 2n, constructed from a polynomial p with complex coefficients of degree n. For any such polynomia
Bifolium
A bifolium is a quartic plane curve with equation in Cartesian coordinates:
Semicubical parabola
In mathematics, a cuspidal cubic or semicubical parabola is an algebraic plane curve that has an implicit equation of the form (with a ≠ 0) in some Cartesian coordinate system. Solving for y leads to
Cassini oval
In geometry, a Cassini oval is a quartic plane curve defined as the locus of points in the plane such that the product of the distances to two fixed points (foci) is constant. This may be contrasted w
Lituus (mathematics)
In mathematics, a lituus is a spiral with polar equation where k is any non-zero constant.Thus, the angle θ is inversely proportional to the square of the radius r. This spiral, which has two branches
Squircle
A squircle is a shape intermediate between a square and a circle. There are at least two definitions of "squircle" in use, the most common of which is based on the superellipse. The word "squircle" is
Serpentine curve
A serpentine curve is a curve whose equation is of the form Equivalently, it has a parametric representation , or functional representation The curve has an inflection point at the origin. It has loca
Logarithmic spiral
A logarithmic spiral, equiangular spiral, or growth spiral is a self-similar spiral curve that often appears in nature. The first to describe a logarithmic spiral was Albrecht Dürer (1525) who called
Troposkein
In physics and geometry, the troposkein is the curve an idealized rope assumes when anchored at its ends and spun around its long axis at a constant angular velocity. This shape is similar to the shap
Tschirnhausen cubic
In algebraic geometry, the Tschirnhausen cubic, or Tschirnhaus' cubic is a plane curve defined, in its left-opening form, by the polar equation where sec is the secant function.
Epispiral
The epispiral is a plane curve with polar equation . There are n sections if n is odd and 2n if n is even. It is the polar or circle inversion of the rose curve. In astronomy the epispiral is related
Folium of Descartes
In geometry, the folium of Descartes (from Latin folium 'leaf'; named for René Decartes) is an algebraic curve defined by the implicit equation
Lemniscate of Bernoulli
In geometry, the lemniscate of Bernoulli is a plane curve defined from two given points F1 and F2, known as foci, at distance 2c from each other as the locus of points P so that PF1·PF2 = c2. The curv
Plane spiral
No description available.
Limaçon trisectrix
In geometry, a limaçon trisectrix is the name for the quartic plane curve that is a trisectrix that is specified as a limaçon. The shape of the limaçon trisectrix can be specified by other curves part
Swastika curve
The swastika curve is the name given by Martyn Cundy and A. P. Rollett in their book Mathematical Models to a type of quartic plane curve.
Three-leaved clover
No description available.
Conchoid of de Sluze
In algebraic geometry, the conchoids of de Sluze are a family of plane curves studied in 1662 by Walloon mathematician René François Walter, baron de Sluze. The curves are defined by the polar equatio
Rose curve
No description available.
Radiodrome
In geometry, a radiodrome is the pursuit curve followed by a point that is pursuing another linearly-moving point. The term is derived from the Greek words ῥᾴδιος, rhā́idios, 'easier' and δρόμος, dróm
Brachistochrone curve
In physics and mathematics, a brachistochrone curve (from Ancient Greek βράχιστος χρόνος (brákhistos khrónos) 'shortest time'), or curve of fastest descent, is the one lying on the plane between a poi
Earth section paths
Earth section paths are plane curves defined by the intersection of an earth ellipsoid and a plane (ellipsoid plane sections). Common examples include the great ellipse (containing the center of the e
Lissajous curve
A Lissajous curve /ˈlɪsəʒuː/, also known as Lissajous figure or Bowditch curve /ˈbaʊdɪtʃ/, is the graph of a system of parametric equations which describe complex harmonic motion. This family of curve
Zindler curve
A Zindler curve is a simple closed plane curve with the defining property that: (L) All chords, which cut the curve length into halves, have the same length. The most simple examples are circles. The
Trisectrix of Maclaurin
In algebraic geometry, the trisectrix of Maclaurin is a cubic plane curve notable for its trisectrix property, meaning it can be used to trisect an angle. It can be defined as locus of the point of in
Tractrix
In geometry, a tractrix (from Latin trahere 'to pull, drag'; plural: tractrices) is the curve along which an object moves, under the influence of friction, when pulled on a horizontal plane by a line
Nodary
In physics and geometry, the nodary is the curve that is traced by the focus of a hyperbola as it rolls without slipping along the axis, a roulette curve. The differential equation of the curve is:. I
Weighted catenary
A weighted catenary is a catenary curve, but of a special form. A "regular" catenary has the equation for a given value of a. A weighted catenary has the equation and now two constants enter: a and b.
Kappa curve
In geometry, the kappa curve or Gutschoven's curve is a two-dimensional algebraic curve resembling the Greek letter ϰ (kappa). The kappa curve was first studied by around 1662. In the history of mathe
Cochleoid
In geometry, a cochleoid is a snail-shaped curve similar to a strophoid which can be represented by the polar equation the Cartesian equation or the parametric equations The cochleoid is the inverse c
Conchoid (mathematics)
In geometry, a conchoid is a curve derived from a fixed point O, another curve, and a length d. It was invented by the ancient Greek mathematician Nicomedes.
Bullet-nose curve
In mathematics, a bullet-nose curve is a unicursal quartic curve with three inflection points, given by the equation The bullet curve has three double points in the real projective plane, at x = 0 and
Sinusoidal spiral
In algebraic geometry, the sinusoidal spirals are a family of curves defined by the equation in polar coordinates where a is a nonzero constant and n is a rational number other than 0. With a rotation
Tautochrone curve
A tautochrone or isochrone curve (from Greek prefixes tauto- meaning same or iso- equal, and chrono time) is the curve for which the time taken by an object sliding without friction in uniform gravity
Hedgehog (geometry)
In differential geometry, a hedgehog or plane hedgehog is a type of plane curve, the envelope of a family of lines determined by a support function. More intuitively, sufficiently well-behaved hedgeho
Rose (mathematics)
In mathematics, a rose or rhodonea curve is a sinusoid specified by either the cosine or sine functions with no phase angle that is plotted in polar coordinates. Rose curves or "rhodonea" were named b
Plane curve
In mathematics, a plane curve is a curve in a plane that may be either a Euclidean plane, an affine plane or a projective plane. The most frequently studied cases are smooth plane curves (including pi
Bicorn
In geometry, the bicorn, also known as a cocked hat curve due to its resemblance to a bicorne, is a rational quartic curve defined by the equation It has two cusps and is symmetric about the y-axis.
Devil's curve
In geometry, a Devil's curve, also known as the Devil on Two Sticks, is a curve defined in the Cartesian plane by an equation of the form The polar equation of this curve is of the form . Devil's curv