Access this book
Tax calculation will be finalised at checkout
Other ways to access
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.
Similar content being viewed by others
Table of contents (7 chapters)
-
Front Matter
-
Back Matter
Authors and Affiliations
Accessibility Information
PDF accessibility summary
This PDF is not accessible. It is based on scanned pages and does not support features such as screen reader compatibility or described non-text content (images, graphs etc). However, it likely supports searchable and selectable text based on OCR (Optical Character Recognition). Users with accessibility needs may not be able to use this content effectively. Please contact us at accessibilitysupport@springernature.com if you require assistance or an alternative format.
Bibliographic Information
Book Title: Mechanical Theorem Proving in Geometries
Book Subtitle: Basic Principles
Authors: Wen-tsün Wu
Series Title: Texts & Monographs in Symbolic Computation
DOI: https://doi.org/10.1007/978-3-7091-6639-0
Publisher: Springer Vienna
-
eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag Wien 1994
Softcover ISBN: 978-3-211-82506-8Published: 14 April 1994
eBook ISBN: 978-3-7091-6639-0Published: 06 December 2012
Series ISSN: 0943-853X
Series E-ISSN: 2197-8409
Edition Number: 1
Number of Pages: XIV, 288
Additional Information: Original Chinese edition published by Science Press, Beijing 1984
Topics: Theory of Computation, Mathematical Logic and Foundations, Algebraic Geometry, Combinatorics, Symbolic and Algebraic Manipulation, Mathematical Logic and Formal Languages