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The hippopede, also known as the horse fetter, is a curve given by the polar equation r^2=4b(a-bsin^2theta). Hippopedes are plotted above for values of a/b=0.2 to 2.0.

The mathematical study of a nonlinear equation f(phi)=y, where f maps from a Hilbert space X to a Hilbert space Y and y in Y which abstracts the construction of optical ...

A solution of a linear homogeneous ordinary differential equation with polynomial coefficients.

A function which satisfies f(tx,ty)=t^nf(x,y) for a fixed n. Means, the Weierstrass elliptic function, and triangle center functions are homogeneous functions. A ...

The necessary and sufficient condition that an algebraic curve has an algebraic involute is that the arc length is a two-valued algebraic function of the coordinates of the ...

A sextic surface given by the implicit equation 4(x^2+y^2+z^2-13)^3+27(3x^2+y^2-4z^2-12)^2=0.

The evolute of a hyperbola with parametric equations x = acosht (1) y = bsinht (2) is x_e = ((a^2+b^2))/acosh^3t (3) y_e = -((a^2+b^2))/bsinh^3t, (4) which is similar to a ...

A hyperelliptic curve is an algebraic curve given by an equation of the form y^2=f(x), where f(x) is a polynomial of degree n>4 with n distinct roots. If f(x) is a cubic or ...

The evolute of a hypotrochoid is a complicated equation. Examples are illustrated above.

A partial differential equation whose solution does not depend continuously on its parameters (including but not limited to boundary conditions) is said to be ill-posed.