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Let gamma(t) be a smooth curve in a manifold M from x to y with gamma(0)=x and gamma(1)=y. Then gamma^'(t) in T_(gamma(t)), where T_x is the tangent space of M at x. The ...

The links curve is the quartic curve given by the Cartesian equation (x^2+y^2-3x)^2=4x^2(2-x). (1) The area enclosed by the outer envelope is A_(envelope)=1/6(9pi+8) (2) and ...

The locus of points whose first polars with regard to the curves of a linear net have a common point. It is also the locus of points of concurrence of line polars of points ...

The stirrup curve is the quartic curve given by the equation (x^2-1)^2=y^2(y-1)(y-2)(y+5).

A plane curve given by the parametric equations x = cost (1) y = sintsin^m(1/2t). (2) The plots above show curves for values of m from 0 to 7. The teardrop curve has area ...

A curve which can be turned continuously inside an equilateral triangle. There are an infinite number of delta curves, but the simplest are the circle and lens-shaped ...

The knot curve is a quartic curve with implicit Cartesian equation (x^2-1)^2=y^2(3+2y). (1) The x- and y-intercepts are (0,-1), (0,1/2), and (+/-1,0). It has horizontal ...

A nonuniform rational B-spline curve defined by C(t)=(sum_(i=0)^(n)N_(i,p)(t)w_iP_i)/(sum_(i=0)^(n)N_(i,p)(t)w_i), where p is the order, N_(i,p) are the B-spline basis ...

An adjoint curve which bears a special relation to the base curve.

The swastika curve is Cundy and Rollett's (1989, p. 71) name for the quartic plane curve with Cartesian equation y^4-x^4=xy and polar equation ...