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A spheroidal section is the curve formed by the intersection of a plane with a spheroid. A spheroidal section is either a circle (for planes parallel to an equator, i.e., ...

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 ...

Given three curves phi_1, phi_2, phi_3 with the common group of ordinary points G (which may be empty), let their remaining groups of intersections g_(23), g_(31), and g_(12) ...

A parallel of a surface of revolution is the intersection of the surface with a plane orthogonal to the axis of revolution.

Given a matrix A, let |A| denote its determinant. Then |A||A_(rs,pq)|=|A_(r,p)||A_(s,q)|-|A_(r,q)||A_(s,p)|, (1) where A_(u,w) is the submatrix of A formed by the ...

The planes passing through the vertices of a tetrahedron ABCD and tangent to the circumsphere at these points form another tetrahedron called the tangential tetrahedron. The ...

The triquetra is a geometric figure consisting of three mutually intersecting vesica piscis lens shapes, as illustrated above. The central region common to all three lenses ...

The tritangent of a cubic surface is a plane which intersects the surface in three mutually intersecting lines. Each intersection of two lines is then a tangent point of the ...

For any point P on the boundary of an ordinary ball, find a neighborhood of P in which the intersection with the ball's boundary cuts the neighborhood into two parts, each ...

The points of tangency t_1 and t_2 for the four lines tangent to two circles with centers x_1 and x_2 and radii r_1 and r_2 are given by solving the simultaneous equations ...