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mathwonk
#7
Mar2-11, 08:55 PM
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here i a quote from david hilbert's " anschaulich geometrie" translated as geometry and the imagination, but more accurately as perhaps "descriptive geometry" or "visual geometry".

"In mathematics as in any scientific research, we find two tendencies present. On the one hand the tendency toward abstraction seeks to crystallize the logical relations inherent in the maze of material that is being studied, and to correlate the material in a systematic and orderly manner. On the other hand the tendency toward intuitive understanding fosters a more immediate grasp of the objects one studies, a live rapport with them so to speak, which stresses the concrete meaning of their relations.

.......It is till true today as it ever was that intuitive understanding plays a major role in geometry. And such concrete intuition is of great value not only for the research worker, but also for anyone who wishes to study and appreciate the results of research in geometry.

In this book it is our purpose to give a presentation of geometry as it stands today, in its visual intuitive aspects....."