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]

His textbook on analytic geometry in 1897 was reviewed by Maxime Bôcher.^[4]

In 1901 he wrote on Riemannian geometry and curvature of Riemannian manifolds. In 1903 he spoke on non-Euclidean geometry.

Works

• 1901: Woods, F. S. (1901). "Space of constant curvature". The Annals of Mathematics. 3 (1/4): 71–112. doi:10.2307/1967636. JSTOR 1967636.
• 1905: Woods, F. S. (1905) [1903]. "Forms of non-Euclidean space". The Boston Colloquium: Lectures on Mathematics for the Year 1903: 31–74.
• 1907: (with Frederick H. Bailey) A course in mathematics via Internet Archive
• 1917: (with Frederick H. Bailey) Analytic geometry and calculus via Internet Archive
• 1922: (with Frederick H. Bailey) Elementary calculus via Internet Archive
• 1922: Higher geometry
• 1926: Advanced Calculus: A Course Arranged With Special Reference To The Needs Of Students Of Applied Mathematics, Ginn and Company, 1926

Non-Euclidean geometry

Further information: History of Lorentz transformations

Following Wilhelm Killing (1885) and others, Woods described motions in spaces of non-Euclidean geometry in the form:^[5]

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

which becomes a Lorentz boost by setting ${\displaystyle k^{2}=-1}$, as well as general motions in hyperbolic space^[6]