Frederick S. Woods

Frederick Shenstone Woods (1864–1950) was an American mathematician.

He was a part of the mathematics faculty of the Massachusetts Institute of Technology from 1895 to 1934, being head of the department of mathematics from 1930 to 1934 and chairman of the MIT faculty from 1931 to 1933.

In 1901 and 1903 he published two papers on non-Euclidean geometry. He also wrote several textbooks.

Non-Euclidean geometry

Further information: History of Lorentz transformations § Lorentz transformation via hyperbolic functions

Following Wilhelm Killing (1885) and others, Woods described motions in spaces of non-Euclidean geometry in the form:

$x_{1}^{\prime }=x_{1}\cos kl+x_{0}{\frac {\sin kl}{k}},\quad x_{2}^{\prime }=x_{2},\quad x_{2}^{\prime }=x_{3},\quad x_{0}^{\prime }=-x_{1}k\sin kl+x_{0}\cos kl$

which becomes a Lorentz boost by setting $k^{2}=-1$, as well as general motions in hyperbolic space

${\begin{matrix}{\begin{aligned}x_{1}^{\prime }&=x_{1}\cosh \alpha -x_{0}\sinh \alpha \\x_{2}^{\prime }&=x_{2}\cos \beta -x_{3}\sin \beta \\x_{3}^{\prime }&=x_{2}\sin \beta +x_{3}\cos \beta \\x_{0}^{\prime }&=-x_{1}\sinh \alpha +x_{0}\cosh \alpha \end{aligned}}\end{matrix}}$