Quad (figure skating)
A quad, or quadruple, is a figure skating jump with at least three but less than four revolutions. Most quadruple jumps have 3 1/2 revolutions; the quadruple Axel has 4 1/2 revolutions, although no figure skater to date has completed this jump in competition. The quadruple toe loop and quadruple Salchow are the two most commonly skated in the discipline. Quadruple jumps have become increasingly common among World and Olympic level men's single skaters, to the point that not having one in a program has come to be seen as a severe handicap. The first person to land a ratified quadruple jump in competition was Canadian Kurt Browning in 1988. In 2002, Miki Ando became the first woman to do so, and she remains one of only two women to have landed a ratified quadruple jump in competition.
Split-quaternion
In abstract algebra, the split-quaternions or coquaternions are elements of a 4-dimensional associative algebra introduced by James Cockle in 1849 under the latter name. Like the quaternions introduced by Hamilton in 1843, they form a four dimensional real vector space equipped with a multiplicative operation. Unlike the quaternion algebra, the split-quaternions contain nontrivial zero divisors, nilpotent elements, and idempotents. (For example, is an idempotent zero-divisor, and is nilpotent.) As a mathematical structure, they form an algebra over the real numbers, which is isomorphic to the algebra of 2 × 2 real matrices. For other names for split-quaternions see the Synonyms section below.