Skip to main content
SpringerLink
Log in

Mechanical Theorem Proving in Geometries

Basic Principles

  • Book
  • © 1994

Overview

Authors:
  1. Wen-tsün Wu

    1. Institute of Systems Science, Academia Sinica, Beijing, People’s Republic of China

    View author publications

    You can also search for this author in PubMed   Google Scholar

Part of the book series: Texts & Monographs in Symbolic Computation (TEXTSMONOGR)

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (7 chapters)

  1. Front Matter

    Pages i-xiv
    Download chapter PDF

  2. Author’s note to the English-language edition

    • Wen-tsün Wu
    Pages 1-11

  3. Desarguesian geometry and the Desarguesian number system

    • Wen-tsün Wu
    Pages 13-62

  4. Orthogonal geometry, metric geometry and ordinary geometry

    • Wen-tsün Wu
    Pages 63-113

  5. Mechanization of theorem proving in geometry and Hilbert’s mechanization theorem

    • Wen-tsün Wu
    Pages 115-147

  6. The mechanization theorem of (ordinary) unordered geometry

    • Wen-tsün Wu
    Pages 149-211

  7. Mechanization theorems of (ordinary) ordered geometries

    • Wen-tsün Wu
    Pages 213-234

  8. Mechanization theorems of various geometries

    • Wen-tsün Wu
    Pages 235-280

  9. Back Matter

    Pages 281-290
    Download chapter PDF
Back to top

Keywords

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.

Authors and Affiliations

  • Institute of Systems Science, Academia Sinica, Beijing, People’s Republic of China

    Wen-tsün Wu

Bibliographic Information

Publish with us

Policies and ethics

Back to top

Search

Navigation