Comparing Volumes

  • A. Gardiner


In Chapter III.3 we discovered that comparing shapes in 2-dimensions was noticeably more complicated than comparing plain line segments. The proverbial optimist might of course declare that we should have expected 1-dimension to be rather special, and that, now we know (more or less) how to make the jump from 1- to 2-dimensions, we shall probably find that 3-, 4- and higher dimensions are really no more difficult than 2-dimensions. The pessimist, on the other hand, might point out that, since 2-dimensions gave rise to so many unexpected difficulties, we must surely expect 3-, 4- and higher dimensions to become steadily more complicated.


Outer Approximation Small Polygon Unexpected Difficulty General Pyramid Rectangular Base 
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Copyright information

© Springer-Verlag New York Inc. 1982

Authors and Affiliations

  • A. Gardiner
    • 1
  1. 1.Department of MathematicsUniversity of BirminghamBirminghamEngland

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