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The spherical curve taken by a ship which travels from the south pole to the north pole of a sphere while keeping a fixed (but not right) angle with respect to the meridians. ...

A square pyramid is a pyramid with a square base. It is a pentahedron. The lateral edge length e and slant height s of a right square pyramid of side length a and height h ...

Consider the solid enclosed by the three hyperboloids specified by the inequalities x^2+y^2-z^2 <= 1 (1) y^2+z^2-x^2 <= 1 (2) z^2+x^2-y^2 <= 1. (3) This work dubs this solid ...

Just as the ratio of the arc length of a semicircle to its radius is always pi, the ratio P of the arc length of the parabolic segment formed by the latus rectum of any ...

The curve a hanging flexible wire or chain assumes when supported at its ends and acted upon by a uniform gravitational force. The word catenary is derived from the Latin ...

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 ...

A general prism is a polyhedron possessing two congruent polygonal faces and with all remaining faces parallelograms (Kern and Bland 1948, p. 28; left figure). A right prism ...

A projective plane, sometimes called a twisted sphere (Henle 1994, p. 110), is a surface without boundary derived from a usual plane by addition of a line at infinity. Just ...

A superellipse is a curve with Cartesian equation |x/a|^r+|y/b|^r=1, (1) first discussed in 1818 by Lamé. A superellipse may be described parametrically by x = acos^(2/r)t ...

Pre-Calculus