| Geometry and the Imagination | |
| Title Orig: | Anschauliche Geometrie |
| Translator: | Paul Neményi |
| Publisher: | Chelsea Publishing (American Mathematical Society) |
| Pub Date: | 1952 |
| Pages: | 357 |
| Isbn: | 9780821819982 |
| Oclc: | 542459 |
Geometry and the Imagination is the English translation of the 1932 book German: Anschauliche Geometrie by David Hilbert and Stefan Cohn-Vossen.[1]
The book was based on a series of lectures Hilbert made in the winter of 1920–21. The book is an attempt to present some then-current mathematical thought to "contribute to a more just appreciation of mathematics by a wider range of people than just the specialists."[2] It differentiates between two tendencies in mathematics and any other scientific research: on the one hand, toward abstraction and logical relations, correlating the subject matter in a systematic and orderly manner, and on the other hand an intuitive approach, which moves toward a more immediate grasp of and a "live rapport" with the same material. Further he asserts that intuitive understanding actually plays a major role for the researcher as well as anyone who wishes to study and appreciate Geometry.[3]
Topics covered by the chapters in the book include the Leibniz formula for , configurations of points and lines with equally many points on each line and equally many lines through each point,curvature and non-Euclidean geometry, mechanical linkages, the classification of manifolds by their Euler characteristic, and the four color theorem.
The Mathematical Association of America said about the book, "this book is a masterpiece — a delightful classic that should never go out of print".[4] Physics Today called it "a readable exposition of modern geometry and its relation to other branches of mathematics".[5] The Scientific Monthly said about it "has been a classic for twenty years . . . Although it deals with elementary topics, it reaches the fringe of our knowledge in many directions".[6]