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About: Geometry and the Imagination     Goto   Sponge   NotDistinct   Permalink

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Geometry and the Imagination is the English translation of the 1932 book Anschauliche Geometrie by David Hilbert and Stefan Cohn-Vossen. 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." 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 understan