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.
Cycloid
Constructing the tangent of the cycloid dates to August 1638 when Mersenne received unique methods from Roberval, Pierre de Fermat and René Descartes. Mersenne passed these results along to Galileo, who gave them to his students Torricelli and Viviana, who were able to produce a quadrature. This result and others were published by Torricelli in 1644, which is also the first printed work on the cycloid. This led to Roberval charging Torricelli with plagiarism, with the controversy cut short by Torricelli's early death in 1647.