Geometry and the Imagination - Hardcover

D. Hilbert; S. Cohn-Vossen

Hardcover

ISBN 10: 0828400873 ISBN 13: 9780828400879

Publisher: Chelsea Publishing House, 1952

Synopsis

In 1899, Hilbert proposed the Hilbert's axioms, substituting the traditional axioms of Euclid. They avoid weaknesses identified in those of Euclid, whose works at the time were still used textbook-fashion. Hilbert's approach signaled the shift to the modern axiomatic method. Axioms are not taken as self-evident truths. Geometry may treat things, about which we have powerful intuitions, but it is not necessary to assign any explicit meaning to the undefined concepts. The elements, such as point, line, plane, and others, could be substituted, as Hilbert is reported to have said, by tables, chairs, glasses of beer and other such objects. It is their defined relationships that are discussed. Hilbert first enumerates the undefined concepts: point, line, plane, lying on (a relation between points and lines, points and planes, and lines and planes), betweenness, congruence of pairs of points (line segments), and congruence of angles. The axioms unify both the plane geometry and solid geometry of Euclid in a single system. Hilbert put forth a most influential list of 23 unsolved problems at the International Congress of Mathematicians in Paris in 1900. This is generally reckoned the most successful and deeply considered compilation of open problems ever to be produced by an individual mathematician.

Edition details

• Publisher: Chelsea Publishing House
• Publication date: 1952
• ISBN 10: 0828400873
• ISBN 13: 9780828400879
• Binding: Hardcover
• Language: English
• Edition number: 1
• Number of pages: 357