E104-03 - Forschungsbereich Differentialgeometrie und geometrische Strukturen
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Journal:
FME Transactions
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ISSN:
1451-2092
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Date (published):
2019
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Number of Pages:
5
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Publisher:
University of Belgrade
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Peer reviewed:
Yes
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Keywords:
Mechanical Engineering; Mechanics of Materials
en
Abstract:
Ivory's Theorem states that in each curvilinear quadrangle of a confocal net of conics the two diagonals have the same lengths. This theorem is valid not only in the Euclidean plane, but also in planar hyperbolic, spherical and pseudo-Euclidean (or Minkowski) geometry, and similar statements hold in all dimensions. Recent publications on this theorem and its generalizations on surfaces are the reason to focus again on this topic and to show a few algebraic consequences.
