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Given a point P, the point P^' which is the antipodal point of P is said to be the antipode of P. The term antipode is also used in plane geometry. Given a central conic (or ...

The directrix of a conic section is the line which, together with the point known as the focus, serves to define a conic section as the locus of points whose distance from ...

The de Longchamps ellipse of a triangle DeltaABC is the conic circumscribed on the incentral triangle and the Cevian triangle of the isogonal mittenpunkt X_(57). (Since a ...

Let A_1, B_2, C_1, A_2, and B_1 be five points determining a conic. Then the conic is the locus of the point C_2=A_1(L·C_1A_2)·B_1(L·C_1B_2), where L is a line through the ...

A point related to the construction and properties of conic sections. Hyperbolas and noncircular ellipses have two distinct foci and two associated conic section directrices, ...

Pick any point P on a conic section, and draw a series of right angles having this point as their vertices. Then the line segments connecting the rays of the right angles ...

The latus rectum of a conic section is the chord through a focus parallel to the conic section directrix (Coxeter 1969). "Latus rectum" is a compound of the Latin latus, ...

An algebraic surface of order 3. Schläfli and Cayley classified the singular cubic surfaces. On the general cubic, there exists a curious geometrical structure called double ...

A double bubble is pair of bubbles which intersect and are separated by a membrane bounded by the intersection. The usual double bubble is illustrated in the left figure ...

Confocal conics are conic sections sharing a common focus. Any two confocal central conics are orthogonal (Ogilvy 1990, p. 77).