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A spherical image of a curve. The most common indicatrix is Dupin's indicatrix.

The principal normal indicatrix of a closed space curve with nonvanishing curvature bisects the area of the unit sphere if it is embedded.

A curve whose name means "shell form." Let C be a curve and O a fixed point. Let P and P^' be points on a line from O to C meeting it at Q, where P^'Q=QP=k, with k a given ...

An elliptic fixed point of a differential equation is a fixed point for which the stability matrix has purely imaginary eigenvalues lambda_+/-=+/-iomega (for omega>0). An ...

A hyperbolic fixed point of a differential equation is a fixed point for which the stability matrix has eigenvalues lambda_1<0<lambda_2, also called a saddle point. A ...

A curve also known as Gutschoven's curve which was first studied by G. van Gutschoven around 1662 (MacTutor Archive). It was also studied by Newton and, some years later, by ...

A conical surface modeled after the shape of a seashell. One parameterization (left figure) is given by x = 2[1-e^(u/(6pi))]cosucos^2(1/2v) (1) y = ...

Given a system of two ordinary differential equations x^. = f(x,y) (1) y^. = g(x,y), (2) let x_0 and y_0 denote fixed points with x^.=y^.=0, so f(x_0,y_0) = 0 (3) g(x_0,y_0) ...

A number which can be specified implicitly or explicitly by exponential, logarithmic, and algebraic operations.

The curve defined by the Cartesian equation f(x)=ln|(sinx)/x|=ln|sinc(x)|. The Kilroy curve arises in the study of spread spectra plotted on a logarithmic (decibel) scale, ...