Texts & Monographs in Symbolic Computation

Mechanical Theorem Proving in Geometries

Basic Principles

Authors: Wu, Wen-tsün

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About this book

There seems to be no doubt that geometry originates from such practical activ­ ities as weather observation and terrain survey. But there are different manners, methods, and ways to raise the various experiences to the level of theory so that they finally constitute a science. F. Engels said, "The objective of mathematics is the study of space forms and quantitative relations of the real world. " Dur­ ing the time of the ancient Greeks, there were two different methods dealing with geometry: one, represented by the Euclid's "Elements," purely pursued the logical relations among geometric entities, excluding completely the quantita­ tive relations, as to establish the axiom system of geometry. This method has become a model of deduction methods in mathematics. The other, represented by the relevant work of Archimedes, focused on the study of quantitative re­ lations of geometric objects as well as their measures such as the ratio of the circumference of a circle to its diameter and the area of a spherical surface and of a parabolic sector. Though these approaches vary in style, have their own features, and reflect different viewpoints in the development of geometry, both have made great contributions to the development of mathematics. The development of geometry in China was all along concerned with quanti­ tative relations.

Table of contents (7 chapters)

  • Author’s note to the English-language edition

    Wu, Dr. Wen-tsün

    Pages 1-11

  • Desarguesian geometry and the Desarguesian number system

    Wu, Dr. Wen-tsün

    Pages 13-62

  • Orthogonal geometry, metric geometry and ordinary geometry

    Wu, Dr. Wen-tsün

    Pages 63-113

  • Mechanization of theorem proving in geometry and Hilbert’s mechanization theorem

    Wu, Dr. Wen-tsün

    Pages 115-147

  • The mechanization theorem of (ordinary) unordered geometry

    Wu, Dr. Wen-tsün

    Pages 149-211

Buy this book

eBook $74.99
price for USA in USD (gross)
  • ISBN 978-3-7091-6639-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $99.00
price for USA in USD
  • ISBN 978-3-211-82506-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Mechanical Theorem Proving in Geometries
Book Subtitle
Basic Principles
Authors
Translated by
Jin, X., Wang, D.
Series Title
Texts & Monographs in Symbolic Computation
Copyright
1994
Publisher
Springer-Verlag Wien
Copyright Holder
Springer-Verlag Wien
eBook ISBN
978-3-7091-6639-0
DOI
10.1007/978-3-7091-6639-0
Softcover ISBN
978-3-211-82506-8
Series ISSN
0943-853X
Edition Number
1
Number of Pages
XIV, 288
Additional Information
Original Chinese edition published by Science Press, Beijing 1984
Topics