Yvon-Villarceau Circle Equivalents on Dupin Cyclides

Abstract : A torus contains four families of circles: parallels, meridians and two sets of Yvon-Villarceau circles. Craftworks and artworks based on Yvon-Villarceau circles can be very attractive. Dupin cyclides are images of tori under sphere inversion, so they contain the images of the torus circles families. I applied operations that are known to create effective artworks on tori to Dupin cyclides, and proved them to be feasible. The regularity and the hidden complexity of the objects I obtained make them very attractive. Reviving the 19th century's tradition of mathematical models making, I printed several models, which can help in understanding their geometry. The tools I developed can be generalized to explore transformations of other mathematical objects under sphere inversion. This exploration is just at its beginning, but has already produced interesting new objects.
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https://hal.archives-ouvertes.fr/hal-01258718
Contributor : Francesco de Comite <>
Submitted on : Tuesday, January 19, 2016 - 2:54:33 PM
Last modification on : Thursday, June 27, 2019 - 2:48:06 PM
Long-term archiving on : Wednesday, April 20, 2016 - 12:16:48 PM

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Francesco de Comite. Yvon-Villarceau Circle Equivalents on Dupin Cyclides. Bridges 2015: Mathematics, Music, Art, Architecture, Culture , Jul 2015, Baltimore, United States. ⟨hal-01258718⟩

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