Mechanical Theorem Proving in Geometries : Basic Principles

Wen-Tsün Wu

ISBN 10: 3211825061 / ISBN 13: 9783211825068

Published by Springer, 1994

About this Item

Druck auf Anfrage Neuware - Printed after ordering - 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.

Seller Inventory # 9783211825068

Bibliographic Details

• Title: Mechanical Theorem Proving in Geometries : Basic Principles
• Publisher: Springer
• Publication Date: 1994
• Language: English
• ISBN 10: 3211825061
• ISBN 13: 9783211825068
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 244W x 170H x 17D millimeters 244 millimeters width by 170 millimeters height by 17 millimeters depth
• Weight: 535 grams

About this title

Synopsis

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.

Synopsis

This book is a translation of Professor Wu's seminal Chinese book of 1984 on Automated Geometric Theorem Proving. The translation was done by his former student Dongming Wang jointly with Xiaofan Jin so that authenticity is guaranteed. Meanwhile, automated geometric theorem proving based on Wu's method of characteristic sets has become one of the fundamental, practically successful, methods in this area that has drastically enhanced the scope of what is computationally tractable in automated theorem proving. This book is a source book for students and researchers who want to study both the intuitive first ideas behind the method and the formal details together with many examples.