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The gear curve is a curve resembling a gear with n teeth given by the parametric equations x = rcost (1) y = rsint, (2) where r=a+1/btanh[bsin(nt)], (3) where tanhx is the ...

There are two curves commonly known as the Lamé curve: the ellipse evolute and the superellipse.

The n-roll mill curve is given by the equation x^n-(n; 2)x^(n-2)y^2+(n; 4)x^(n-4)y^4-...=a^n, where (n; k) is a binomial coefficient.

The curve with trilinear coordinates a^t:b^t:c^t for a given power t.

The Scarabaeus curve is a sextic curve given by the equation (x^2+y^2)(x^2+y^2+ax)^2-b^2(x^2-y^2)^2=0 and by the polar equation r=bcos(2theta)-acostheta where a,b!=0.

A Steinmetz curve is a curve of intersection of two perpendicularly placed cylinders of radii a and b comprising a Steinmetz solid. If the vertical cylinder has radius a and ...

Informally, an elliptic curve is a type of cubic curve whose solutions are confined to a region of space that is topologically equivalent to a torus. The Weierstrass elliptic ...

Given a regular surface M, an asymptotic curve is formally defined as a curve x(t) on M such that the normal curvature is 0 in the direction x^'(t) for all t in the domain of ...

Let a^p+b^p=c^p be a solution to Fermat's last theorem. Then the corresponding Frey curve is y^2=x(x-a^p)(x+b^p). (1) Ribet (1990a) showed that such curves cannot be modular, ...

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 ...