Poncelet's Theorem in the four nonisomorphic finite projective planes of order 9
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Date
2014-06-30Type
- Working Paper
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yes
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Abstract
We study Poncelet's Theorem in the four nonisomorphic planes of order 9. We first prove that Poncelet's Closure Theorem holds for the coordinate plane over the Galois field with 9 elements. On the contrary, we will see that the other three nonisomorphic planes of order 9, which are constructed over the miniquaternion near-field of order 9, will fail to be Poncelet planes. This gives a complete discussion of Poncelet's Theorem in finite projective planes of order 9. In addition, we offer a proof of Poncelet's Theorem for triangles in all finite projective coordinate planes which is based upon Pascal's Theorem. Show more
Publication status
publishedExternal links
Journal / series
arXivPages / Article No.
Publisher
Cornell UniversityOrganisational unit
03874 - Hungerbühler, Norbert / Hungerbühler, Norbert
Related publications and datasets
Is original form of: http://hdl.handle.net/20.500.11850/279507
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Is original form of: http://hdl.handle.net/20.500.11850/318422
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ETH Bibliography
yes
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