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Dimension engl

In: π und Co

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  • Timothy Gowers

Abstract

A notable feature of advanced mathematics is that much of it is concerned with geometry in more than three dimensions. This fact is baffling to non-mathematieians: lines and curves are one-dimensional, surfaces are two-dimensional, and solid objects are three-dimensional, but how could something be four-dimensional? Once an object has height, width, and depth, it completely fills up a portion of space, and there just doesn’t seem to be seope for any further dimensions. It is sometimes suggested that the fourth dimension is time, which is a good answer in eertain contexts, such as Special relativity, but does not help us to make sense of, say, twenty-six-dimensional or even infinite-dimensional geometry, both of which are of mathematical importance.

Suggested Citation

  • Timothy Gowers, 2008. "Dimension engl," Springer Books, in: Ehrhard Behrends & Peter Gritzmann & Günter M. Ziegler (ed.), π und Co, pages 128-143, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-77889-9_17
    DOI: 10.1007/978-3-540-77889-9_17
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