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The intersection of an ellipse centered at the origin and semiaxes of lengths a and b oriented along the Cartesian axes with a line passing through the origin and point ...

Consider two cylinders as illustrated above (Hubbell 1965) where the cylinders have radii r_1 and r_2 with r_1<=r_2, the larger cylinder is oriented along the z-axis, and ...

The pedal of a curve C with respect to a point O is the locus of the foot of the perpendicular from O to the tangent to the curve. More precisely, given a curve C, the pedal ...

As defined by Gray (1997, p. 201), Viviani's curve, sometimes also called Viviani's window, is the space curve giving the intersection of the cylinder of radius a and center ...

A cubic curve is an algebraic curve of curve order 3. An algebraic curve over a field K is an equation f(X,Y)=0, where f(X,Y) is a polynomial in X and Y with coefficients in ...

Consider the plane figure obtained by drawing each diagonal in a regular polygon with n vertices. If each point of intersection is associated with a node and diagonals are ...

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 ...

The sum of the values of an integral of the "first" or "second" sort int_(x_0,y_0)^(x_1,y_1)(Pdx)/Q+...+int_(x_0,y_0)^(x_N,y_N)(Pdx)/Q=F(z) and ...

The general bivariate quadratic curve can be written ax^2+2bxy+cy^2+2dx+2fy+g=0. (1) Define the following quantities: Delta = |a b d; b c f; d f g| (2) J = |a b; b c| (3) I = ...

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 ...