Frederick S. Woods

Frederick Shenstone Woods (1864–1950) was an Americanmathematician.

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

Non-Euclidean geometry

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

x1′=x1cos⁡kl+x0sin⁡klk,x2′=x2,x2′=x3,x0′=−x1ksin⁡kl+x0cos⁡kl{\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 k2=−1{\displaystyle k^{2}=-1}, as well as general motions in hyperbolic space[6]

Notes

  1. ^"Faculty - MIT Mathematics". math.mit.edu.
  2. ^"Facts - MIT Mathematics". math.mit.edu.
  3. ^"MIT History - MIT Faculty". libraries.mit.edu.
  4. ^Maxime Bocher (1897) Review of Plane and Solid Analytic geometry via Project Euclid
  5. ^Woods (1903/05), p. 55
  6. ^Woods (1903/05), p. 72
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