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The pedal curve of the parabola with parametric equations x = at^2 (1) y = 2at (2) with pedal point (x_0,y_0) is x_p = ((x_0-a)t^2+y_0t)/(t^2+1) (3) y_p = ...

The inverse curve of the circle with parametric equations x = acost (1) y = asint (2) with respect to an inversion circle with center (x,y) and radius R is given by x_i = ...

The dimension of a special series can never exceed half its order.

The inverse curve of the lituus is an Archimedean spiral with m=2, which is Fermat's spiral.

The Maltese cross curve is the cubic algebraic curve with Cartesian equation xy(x^2-y^2)=x^2+y^2 (1) and polar equation r=2/(sqrt(sin(4theta))) (2) (Cundy and Rollett 1989, ...

Given a general quadratic curve Ax^2+Bxy+Cy^2+Dx+Ey+F=0, (1) the quantity X is known as the discriminant, where X=B^2-4AC, (2) and is invariant under rotation. Using the ...

Curves which, when rotated in a square, make contact with all four sides. Such curves are sometimes also known as rollers. The "width" of a closed convex curve is defined as ...

If the cusp of the cardioid is taken as the inversion center, the cardioid inverts to a parabola.

For an ellipse with parametric equations x = acost (1) y = bsint, (2) the negative pedal curve with respect to the origin has parametric equations x_n = ...

The use of coordinates (such as Cartesian coordinates) in the study of geometry. Cartesian geometry is named after René Descartes (Bell 1986, p. 48), although Descartes may ...