Frederick Shenstone Woods (1864–1950) was an

American American(s) may refer to: * American, something of, from, or related to the United States of America, commonly known as the "United States" or "America" ** Americans, citizens and nationals of the United States of America ** American ancestry, pe ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

. He was a part of the mathematics faculty of the

Massachusetts Institute of Technology The Massachusetts Institute of Technology (MIT) is a private land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern technology and science, and is one of the ...

from 1895 to 1934, being head of the

department of mathematics Department may refer to: * Departmentalization, division of a larger organization into parts with specific responsibility Government and military *Department (administrative division), a geographical and administrative division within a country, ...

from 1930 to 1934 and chairman of the MIT faculty from 1931 to 1933. His

textbook A textbook is a book containing a comprehensive compilation of content in a branch of study with the intention of explaining it. Textbooks are produced to meet the needs of educators, usually at educational institutions. Schoolbooks are textboo ...

analytic geometry In classical mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts with synthetic geometry. Analytic geometry is used in physics and engineerin ...

in 1897 was reviewed by Maxime Bocher. In 1901 he wrote on

Riemannian geometry Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, smooth manifolds with a ''Riemannian metric'', i.e. with an inner product on the tangent space at each point that varies smoothly from point to poin ...

and

curvature of Riemannian manifolds In mathematics, specifically differential geometry, the infinitesimal geometry of Riemannian manifolds with dimension greater than 2 is too complicated to be described by a single number at a given point. Riemann introduced an abstract and rigorou ...

. In 1903 he spoke on

non-Euclidean geometry In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry. As Euclidean geometry lies at the intersection of metric geometry and affine geometry, non-Euclidean geo ...

Works

* 1901: * 1905: * 1907: (with Frederick H. Bailey)
A course in mathematics
' via

Internet Archive The Internet Archive is an American digital library with the stated mission of "universal access to all knowledge". It provides free public access to collections of digitized materials, including websites, software applications/games, music, ...

* 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
'

Non-Euclidean geometry

Following

Wilhelm Killing Wilhelm Karl Joseph Killing (10 May 1847 – 11 February 1923) was a German mathematician who made important contributions to the theories of Lie algebras, Lie groups, and non-Euclidean geometry. Life Killing studied at the University of Mü ...

(1885) and others, Woods described motions in spaces of

in the form: :

x_^=x_\cos kl+x_\frac,\quad x_^=x_,\quad x_^=x_,\quad x_^=-x_k\sin kl+x_\cos kl

which becomes a

Lorentz boost In physics, the Lorentz transformations are a six-parameter family of linear transformations from a coordinate frame in spacetime to another frame that moves at a constant velocity relative to the former. The respective inverse transformation i ...

by setting

k^=-1

, as well as general motions in hyperbolic spaceWoods (1903/05), p. 72

Notes

External links

* {{DEFAULTSORT:Woods, Frederick S. 1864 births 1950 deaths Mathematicians from Massachusetts Massachusetts Institute of Technology School of Science faculty American textbook writers