Geometric Constructions with Ellipses

The geometric problems of trisecting a general angle and doubling the cube cannot be solved by the use of a straightedge and compass alone. These beautiful results were a triumph of modern algebra, first published by Pierre Laurent Wantzel. Here, Gibbins and Smolinsky details their geometric constru...

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Bibliographic Details
Published in:The Mathematical intelligencer 2009, Vol.31 (1), p.57-62
Main Authors: Gibbins, Aliska, Smolinsky, Lawrence
Format: Article
Language:English
Subjects:
Applied mathematics
Construction
Geometry
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematical problems
Mathematics
Mathematics and Statistics
Numerical and Computational Physics
Simulation
Theorems
Theoretical
Wantzel, Pierre Laurent
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Summary:The geometric problems of trisecting a general angle and doubling the cube cannot be solved by the use of a straightedge and compass alone. These beautiful results were a triumph of modern algebra, first published by Pierre Laurent Wantzel. Here, Gibbins and Smolinsky details their geometric constructions with ellipses. Moreover, they mention three approaches for constructing ellipses that were known to the Ancients and can be used to extend straightedge-and-compass constructions to constructions with ellipses.
ISSN:0343-6993
1866-7414
DOI:10.1007/s00283-008-9000-3