Reversion Porisms in Conics
Lorenz Halbeisen, Norbert Hungerb\"uhler, Marco Schiltknecht
TL;DR
This paper provides a projective proof of the butterfly porism for cyclic quadrilaterals and extends the concept to polygons with any number of vertices on a conic, exploring related projective properties.
Contribution
It introduces a general reversion porism for polygons on conics and analyzes their projective properties, expanding classical porisms to broader polygonal cases.
Findings
Proof of butterfly porism using projective methods
Generalization of porisms to polygons with arbitrary vertices on conics
Investigation of projective properties related to these porisms
Abstract
We give a projective proof of the butterfly porism for cyclic quadrilaterals and present a general reversion porism for polygons with an arbitrary number of vertices on a conic. We also investigate projective properties of the porisms.
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Taxonomy
TopicsStructural Analysis and Optimization · Mathematics and Applications · Point processes and geometric inequalities