Frederick S. Woods Explained

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. 10.2307/1967636 . 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:^[5]

	\prime
x
	1

=x₁\coskl+x₀

	\sinkl
	k

	\prime
x
	2

=x₂,

	\prime
x
	2

=x₃,

	\prime
x
	0

=-x₁k\sinkl+x₀\coskl

which becomes a Lorentz boost by setting

k²=-1

, as well as general motions in hyperbolic space^[6]

Notes and References

Web site: Faculty - MIT Mathematics. math.mit.edu.
Web site: Facts - MIT Mathematics. math.mit.edu.
Web site: MIT History - MIT Faculty. libraries.mit.edu.
Maxime Bocher (1897) Review of Plane and Solid Analytic geometry via Project Euclid
Woods (1903/05), p. 55
Woods (1903/05), p. 72