Figure skating jumps
Jumps are referred to by how many times the skater turns in the air. One revolution (one and a half for the Axel) is a "single" jump. Two revolutions (two and a half for the Axel) is a "double" jump. Three revolutions (three and a half for the Axel) is a "triple" jump. Four revolutions (four and a half for the Axel, although this has never been done in competition) is a "quadruple" or "quad" jump. The first triple jump landed in competition was a loop jump. It was landed by Dick Button in 1952. The first quadruple jump landed in competition was a toe loop jump. It was landed by Kurt Browning in 1988. Currently, men in world-class competition usually attempt a full set of triples and sometimes one or two quadruple jumps in their free skating programs. Triple Axels are rare for ladies, and quadruple jump attempts even more so.
Versor
This versor was used by Homersham Cox (1882/83) in relation to quaternion multiplication. The primary exponent of hyperbolic versors was Alexander Macfarlane as he worked to shape quaternion theory to serve physical science. He saw the modelling power of hyperbolic versors operating on the split-complex number plane, and in 1891 he introduced hyperbolic quaternions to extend the concept to 4-space. Problems in that algebra led to use of biquaternions after 1900. In a widely circulated review of 1899, Macfarlane said:
Today the concept of a one-parameter group subsumes the concepts of versor and hyperbolic versor as the terminology of Sophus Lie has replaced that of Hamilton and Macfarlane.
In particular, for each ' such that or , the mapping formula_14 takes the real line to a group of hyperbolic or ordinary versors. In the ordinary case, when ' and − are antipodes on a sphere, the one-parameter groups have the same points but are oppositely directed. In physics, this aspect of rotational symmetry is termed a doublet.