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...

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...

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...

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...

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

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

{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 =...

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...

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...

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)...

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...

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...

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...

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

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

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...

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...

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...

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...

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...

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

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...

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...

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...

heart-shaped, or it may be oval. A limaçon is a bicircular rational plane algebraic curve of degree 4. The earliest formal research on limaçons is generally...