algebraic geometry, a quartic plane curve is a plane algebraic curve of the fourth degree. It can be defined by a bivariate quartic equation: A x 4 + B...

In mathematics, a plane curve is a curve in a plane that may be a Euclidean plane, an affine plane or a projective plane. The most frequently studied cases...

algebraic plane curve is the zero set of a polynomial in two variables. A projective algebraic plane curve is the zero set in a projective plane of a homogeneous...

infinity", not holes, hence the open quartic is still complete. The Klein quartic can be viewed as a projective algebraic curve over the complex numbers C, defined...

Trident curve Trisectrix of Maclaurin Tschirnhausen cubic Witch of Agnesi Quartic plane curves include Ampersand curve Bean curve Bicorn Bow curve Bullet-nose...

the theory of algebraic plane curves, a general quartic plane curve has 28 bitangent lines, lines that are tangent to the curve in two places. These lines...

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...

wool from which the ribbons were made. Curves that have been called a lemniscate include three quartic plane curves: the hippopede or lemniscate of Booth...

is a list of some mathematically well-defined shapes. Cubic plane curve Quartic plane curve Fractal Conic sections Unit circle Unit hyperbola Folium of...

The trifolium curve (also three-leafed clover curve, 3-petaled rose curve, and paquerette de mélibée) is a type of quartic plane curve. The name comes...

In mathematics, a Lüroth quartic is a nonsingular quartic plane curve containing the 10 vertices of a complete pentalateral. They were introduced by Jacob...

geometry, a spiric section, sometimes called a spiric of Perseus, is a quartic plane curve defined by equations of the form ( x 2 + y 2 ) 2 = d x 2 + e y 2...

Bitangents of a quartic Cartesian coordinate system Caustic Cesàro equation Chord (geometry) Cissoid Circumference Closed timelike curve concavity Conchoid...

{AC\cdot BC}{AB}}\\[4pt]\end{aligned}}} The cruciform curve or cross curve is a quartic plane curve given by the equation x 2 y 2 − b 2 x 2 − a 2 y 2 =...

a modular curve Y(Γ) is a Riemann surface, or the corresponding algebraic curve, constructed as a quotient of the complex upper half-plane H by the action...

degree four, called a quartic polynomial. A quartic equation, or equation of the fourth degree, is an equation that equates a quartic polynomial to zero...

projective plane, branched over a quartic plane curve. This map is generically 2 to 1, so this surface is sometimes called a del Pezzo double plane. The 56...

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 particularly...

A bifolium is a quartic plane curve with equation in Cartesian coordinates: ( x 2 + y 2 ) 2 = a x 2 y . {\displaystyle (x^{2}+y^{2})^{2}=ax^{2}y.} Given...

geometry, an intersection is a point, line, or curve common to two or more objects (such as lines, curves, planes, and surfaces). The simplest case in Euclidean...

Thus for g = 3 the canonical curves (non-hyperelliptic case) are quartic plane curves. All non-singular plane quartics arise in this way. There is explicit...

ternary quartic form is a degree 4 homogeneous polynomial in three variables. Hilbert (1888) showed that a positive semi-definite ternary quartic form over...

In mathematics, a bullet-nose curve is a unicursal quartic curve with three inflection points, given by the equation a 2 y 2 − b 2 x 2 = x 2 y 2 {\displaystyle...

S) − m d(Q, S) = ± a are closely related; together they form a quartic plane curve called the ovals of Descartes. In the equation d(P, S) + m d(Q, S)...

Four points P0, P1, P2 and P3 in the plane or in higher-dimensional space define a cubic Bézier curve. The curve starts at P0 going toward P1 and arrives...

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 y 2 ( a 2 − x 2...

Bicuspid curve Cassini oval Cubic curve Elliptic curve Watt's curve Butterfly curve (algebraic) Elkies trinomial curves Hyperelliptic curve Klein quartic Classical...

on a quartic is 16, and in this case they are all simple nodes (to show that p {\displaystyle p} is simple project from another node). A quartic which...

A conic section, conic or a quadratic curve is a curve obtained from a cone's surface intersecting a plane. The three types of conic section are the hyperbola...

case of a quartic plane curve, and the external and internal tangent lines are the bitangents to this quartic curve. A generic quartic curve has 28 bitangents...