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The strophoid of a circle with pole at the center and fixed point on the circumference is a Freeth's nephroid.

A geometric figure which touches only the vertices (or other extremities) of another figure.

The depth of a box is the horizontal distance from front to back (usually not necessarily defined to be smaller than the width, the horizontal distance from side to side).

The desmic configuration is three-dimensional configuration of points consisting of three tetrads of points, each two of the tetrads of which are perspective from the four ...

Given a quadrilateral ABCD, the three diagonal points P, Q, and R defined as the pairwise intersections of the lines determined by the sides AB intersection CD, AC ...

Two cones placed apex to apex. The double cone is given by algebraic equation (z^2)/(c^2)=(x^2+y^2)/(a^2).

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 ...

An ellipsoidal section is the curve formed by the intersection of a plane with an ellipsoid. An ellipsoidal section is always an ellipse.

Line segment ranges and pencils which have equal cross ratios are said to be equicross.

For signed distances on a line segment, AB^_·CD^_+AC^_·DB^_+AD^_·BC^_=0, since (b-a)(d-c)+(c-a)(b-d)+(d-a)(c-b)=0.