# 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,[1] being head of the department of mathematics from 1930 to 1934[2] and chairman of the MIT faculty from 1931 to 1933.[3]

In 1901 and 1903 he published two papers on non-Euclidean geometry.[4][5] He also wrote several textbooks.[6]

Following Wilhelm Killing (1885) and others (see History of Lorentz transformations#Woods), Woods described motions in spaces of non-Euclidean geometry in the form:[7]

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

which becomes a Lorentz boost by setting ${\displaystyle k^{2}=-1}$, as well as general motions in hyperbolic space[8]

{\displaystyle {\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}}}

## Notes

1. "Faculty - MIT Mathematics". math.mit.edu.
2. "Facts - MIT Mathematics". math.mit.edu.
3. "MIT History - MIT Faculty". libraries.mit.edu.
4. Woods, F. S. (1901). "Space of constant curvature". The Annals of Mathematics. 3 (1/4): 71–112. JSTOR 1967636.
5. Woods, F. S. (1905) [1903]. "Forms of non-Euclidean space". The Boston Colloquium: Lectures on Mathematics for the year 1903: 31–74.
6. A course in mathematics (1907), Analytic geometry and calculus (1917), Elementary calculus (1922), Higher geometry (1922)
7. Woods (1903/05), p. 55
8. Woods (1903/05), p. 72