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The golden ratio has decimal expansion phi=1.618033988749894848... (OEIS A001622). It can be computed to 10^(10) digits of precision in 24 CPU-minutes on modern hardware and ...

The conic sections are the nondegenerate curves generated by the intersections of a plane with one or two nappes of a cone. For a plane perpendicular to the axis of the cone, ...

The lines of a pencil joining the points of a line segment range to another point.

K=-e^2, where e is the eccentricity of a conic section.

A trigonal trapezohedron, also called a trigonal deltohedron, is a polyhedron formed by six congruent rhombi. Special cases include the cube, acute golden rhombohedron, and ...

The period for a quasiperiodic trajectory to pass through the same point in a surface of section. If the rotation number is irrational, the trajectory will densely fill out a ...

Each centered convex body of sufficiently high dimension has an "almost spherical" k-dimensional central section.

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, ...

The beautiful arrangement of leaves in some plants, called phyllotaxis, obeys a number of subtle mathematical relationships. For instance, the florets in the head of a ...

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 ...