Mechanical Theorem Proving in Geometries

1. Front Matter

   Pages i-xiv

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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

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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.

• Area
• Multiplication
• algebraic varieties
• automated theorem proving
• commutative property
• geometry
• sets
• theorem proving
• combinatorics

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

  Wen-tsün Wu

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