Development of the Minkowski Geometry of Numbers Volume 1 (Phoenix Edition) - Hardcover

Hancock, Harris

Hardcover

ISBN 10: 0486446468 ISBN 13: 9780486446462

Publisher: Dover Publications, 2005

Synopsis

A pioneering genius of pure and applied mathematics, Hermann Minkowski (1864 1909) founded the geometry of numbers and wrote extensively about his researches into the field. Until the distinguished American mathematician Harris Hancock interpreted Minkowski's writings, they were accessible only to a few specialists. Hancock elaborated on the master's writings, placing them in clear, readable form. This classic two-volume edition returns Hancock's brilliant exposition to the mathematics community after a long hiatus.
Development of the Minkowski Geometry of Numbers concerns itself primarily with geometric problems involving integers and with algebraic problems approachable through geometrical insights. In addition to demonstrating that geometric proofs and theorems in number theory are often simpler and more elegant than arithmetic proofs, the author illuminates many other algebraic and geometric topics. Starting with preliminary background and historical remarks, Volume 1 examines surfaces that are nowhere concave; the volume of bodies; linear forms; the arithmetical theory of a pair of lines; algebraic numbers; and the theory of continuous fractions. Some of Minkowski’s shorter papers are discussed as well. Topics featured in the subsequent volume include approximations of algebraic numbers and of real quantity through rational numbers, the arithmetic of the ellipsoid, and extreme standard bodies.

Edition details

• Publisher: Dover Publications
• Publication date: 2005
• ISBN 10: 0486446468
• ISBN 13: 9780486446462
• Binding: Hardcover
• Language: English
• Number of pages: 480