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- W4291146670 abstract "AbstractWe study the two-parameter manifold of parabolas circumscribed to triangles in a Poncelet porism between two circles (Chapple’s porism). It turns out that the focal points of the parabolas in a certain one-parameter subfamily trace a straight line. The vertices of these parabolas move on rational cubic curves whose acnodes trace an ellipse centered at the poristic stationary triangle center which is the midpoint of the common incenter and the common circumcenter. The axes of the circumparabolas envelop a Steiner hypocycloid over the course of a porism. Varying the pivot point of the circumparabola, the one-parameter family of Steiner cycloids envelops two ellipses, one with the fixed common incenter and circumcenter as foci, the other one carrying the cusps of all cycloids.KeywordsCircumparabolaTrianglePorismPoint orbitEnvelopeFocusAxisVertexQuinticSeptic" @default.
- W4291146670 created "2022-08-13" @default.
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- W4291146670 date "2022-08-13" @default.
- W4291146670 modified "2023-09-30" @default.
- W4291146670 title "Circumparabolas in Chapple’s Porism" @default.
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- W4291146670 doi "https://doi.org/10.1007/978-3-031-13588-0_4" @default.
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