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If a triangle is inscribed in a conic section, any line conjugate to one side meets the other two sides in conjugate points.

A simple path is a path which is a simple curve. More precisely, a continuous mapping gamma:[a,b]->C^0 is a simple path if it has no self-intersections. Here, C^0 denotes the ...

A smooth curve is a curve which is a smooth function, where the word "curve" is interpreted in the analytic geometry context. In particular, a smooth curve is a continuous ...

A plot of a function expressed in spherical coordinates, with radius r as a function of angles theta and phi. Polar plots can be drawn using SphericalPlot3D[r, {phi, phimin, ...

The evolute of the tractrix given by parametric equations x = t-tanht (1) y = secht (2) is the catenary x_e = t (3) y_e = cosht. (4)

To inscribe an equilateral triangle in an ellipse, place the top polygon vertex at (0,b), then solve to find the (x,y) coordinate of the other two vertices. ...

Jacobi theta functions can be used to uniformize all elliptic curves. Jacobi elliptic functions may also be used to uniformize some hyperelliptic curves, although only two ...

If each of two curves meets the line at infinity in distinct, nonsingular points, and if all their intersections are finite, then if to each common point there is attached a ...

If two curves of the same curve genus >1 are in rational correspondence, then that correspondence is birational.

An natural equation which expresses a curve in terms of its arc length s and tangential angle phi.