Sextic curves

Sextic curves are algebraic curves of degree six. In the context of algebraic geometry, a curve can be defined as the set of points in a projective plane (or affine plane) that satisfy a polynomial equation in two variables. For a sextic curve, the defining polynomial is of degree six.

An "astroid" refers to a particular type of mathematical curve, specifically a hypocycloid with four cusps. It is defined as the path traced by a point on the circumference of a smaller circle that rolls within a larger circle, where the radius of the smaller circle is one-fourth that of the larger one.

As of my last update in October 2023, "Atriphtaloid" does not appear to represent a widely recognized term or concept in science, medicine, or other common fields of knowledge. It is possible that it could refer to a specific concept or term not widely known or documented, or it might be a typographical error or a misspelling of another term.

The Butterfly curve is a famous algebraic curve in mathematics, notable for its unique shape that resembles a butterfly when plotted.

Cayley's sextic refers to a particular algebraic curve that is defined by a specific equation in projective geometry. It is a smooth, non-singular curve of degree six in the projective plane. This curve is named after the mathematician Arthur Cayley.

A Coble curve is a type of algebraic curve that arises in the study of algebraic geometry, specifically in the context of the geometry of rational curves. More precisely, Coble curves are introduced as specific types of plane curves characterized by their defining algebraic equations. The most common way to introduce Coble curves is in terms of a particular polynomial equation, typically of degree 6.

A nephroid is a type of mathematical curve that resembles the shape of a kidney, which is where it gets its name (from the Greek word "nephros," meaning kidney). It is defined as the envelope of a family of circles or can be described parametrically in Cartesian coordinates.

"Quadrifolium" can refer to different contexts depending on its usage. In botany, it often denotes a plant or plant structure that features four leaves. The term derives from Latin, where "quadri-" means four and "folium" means leaf. In a broader context, "Quadrifolium" may also refer to artistic and architectural motifs, particularly those with a four-leaf design, commonly seen in decorative styles or patterns.

Watt's curve, also known as the "Watt curve" or "Watt's line," is a graphical representation that illustrates the relationship between the pressure and the flow rate in a hydraulic system, typically in the context of pumps or turbines. The concept is named after the engineer James Watt, who made significant contributions to the development of steam engines and hydraulic machinery.

Wiman's sextic refers to a specific algebraic curve known as the Wiman sextic, denoted often as \(W\). It is defined by a certain equation in projective space and is notable in the field of algebraic geometry for its interesting properties.

The Wirtinger sextic refers to a particular type of polynomial that arises in the context of algebraic geometry and is related to the study of algebraic curves. Specifically, the term "Wirtinger sextic" often refers to a degree-six (or sextic) polynomial associated with the geometric properties of certain curves, particularly in relation to their moduli.