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Every modular system has a modular system basis consisting of a finite number of polynomials. Stated another way, for every order n there exists a nonsingular curve with the ...

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 configuration formed by two curves starting at a point, called the vertex V, in a common direction. Horn angles are concrete illustrations of non-Archimedean geometries.

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 ...

y^(n/m)+c|x/a|^(n/m)-c=0, with n/m>2. If n/m<2, the curve is a hypoellipse.

y^(n/m)+c|x/a|^(n/m)-c=0, with n/m<2. If n/m>2, the curve is a hyperellipse.

The term "ice fractal" refers to a fractal (square, triangle, etc.) that is based on a simple generating motif. The above plots show the ice triangle, antitriangle, square, ...

Given a commutative unit ring R and an extension ring S, an element s of S is called integral over R if it is one of the roots of a monic polynomial with coefficients in R.

The point that inversion of a curve is performed with respect to.

The circle with respect to which an inverse curve is computed or relative to which inverse points are computed. In three dimensions, inverse points can be computed relative ...