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A Cartesian curve is a curve specified in Cartesian coordinates. The term "Cartesian curve" is sometimes also used to refer to the Cartesian ovals.

The metric of Felix Klein's model for hyperbolic geometry, g_(11) = (a^2(1-x_2^2))/((1-x_1^2-x_2^2)^2) (1) g_(12) = (a^2x_1x_2)/((1-x_1^2-x_2^2)^2) (2) g_(22) = ...

An ellipse intersects a circle in 0, 1, 2, 3, or 4 points. The points of intersection of a circle of center (x_0,y_0) and radius r with an ellipse of semi-major and ...

The orthotomic of the unit circle represented by x = cost (1) y = sint (2) with a source at (x,y) is x_o = xcos(2t)-ysin(2t)+2sint (3) y_o = -xsin(2t)-ycos(2t)+2cost. (4)

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

The plane spanned by two coordinate axes in the three-dimensional Euclidean space. The coordinate plane spanned by the x- and the y-axis is called xy-plane.

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).

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

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.