- Source: 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.
His textbook on analytic geometry in 1897 was reviewed by Maxime Bôcher.
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
Following Wilhelm Killing (1885) and others, Woods described motions in spaces of non-Euclidean geometry in the form:
x
1
′
=
x
1
cos
k
l
+
x
0
sin
k
l
k
,
x
2
′
=
x
2
,
x
2
′
=
x
3
,
x
0
′
=
−
x
1
k
sin
k
l
+
x
0
cos
k
l
{\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
k
2
=
−
1
{\displaystyle k^{2}=-1}
, as well as general motions in hyperbolic space
Notes
External links
Frederick S. Woods at the Mathematics Genealogy Project
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