Mathematics, Impossible - Research Article from Macmillan Science Library: Mathematics

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Local Versus Global

In the study of mathematics, distinctions are routinely made between the local properties of an object—what small pieces of the object look like—and the properties of the object as a whole. Impossible objects are all "wellbehaved" locally; it is only when we consider them globally that contradictions arise.

Consider two lithographs by Dutch artist M. C. Escher. (Although not shown in this entry, these artworks are easily viewed on various Internet web sites and on books of Escher's art.) The first is "Belvedere," created in 1958. At first glance, this seems to be a straightforward depiction of an open-air building with pillars and archways, with people scattered around at various points. But it does not take long to notice that this picture is filled with incompatibilities; many of the pillars do not start or end where they should, causing the building to...

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This section contains 1,682 words
(approx. 6 pages at 300 words per page)
Buy the Mathematics, Impossible Encyclopedia Article
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Macmillan Science Library: Mathematics
Mathematics, Impossible from Macmillan Science Library: Mathematics. Copyright © 2001-2006 by Macmillan Reference USA, an imprint of the Gale Group. All rights reserved.
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