Ebook: Mechanical Theorem Proving in Geometries: Basic Principles

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.

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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.

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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.
Content:
Front Matter....Pages i-xiv
Author’s note to the English-language edition....Pages 1-11
Desarguesian geometry and the Desarguesian number system....Pages 13-62
Orthogonal geometry, metric geometry and ordinary geometry....Pages 63-113
Mechanization of theorem proving in geometry and Hilbert’s mechanization theorem....Pages 115-147
The mechanization theorem of (ordinary) unordered geometry....Pages 149-211
Mechanization theorems of (ordinary) ordered geometries....Pages 213-234
Mechanization theorems of various geometries....Pages 235-280
Back Matter....Pages 281-290

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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.
Content:
Front Matter....Pages i-xiv
Author’s note to the English-language edition....Pages 1-11
Desarguesian geometry and the Desarguesian number system....Pages 13-62
Orthogonal geometry, metric geometry and ordinary geometry....Pages 63-113
Mechanization of theorem proving in geometry and Hilbert’s mechanization theorem....Pages 115-147
The mechanization theorem of (ordinary) unordered geometry....Pages 149-211
Mechanization theorems of (ordinary) ordered geometries....Pages 213-234
Mechanization theorems of various geometries....Pages 235-280
Back Matter....Pages 281-290
....