RecordNumber
2133
Author
De Comit´e, Francesco
Title of Article
Yvon-Villarceau Circle Equivalents on Dupin Cyclides
Title Of Journal
Bridges
Publication Year
2015
Page
253-258
Notes
Proceedings of Bridges 2015: Mathematics, Music, Art, Architecture, Culture , براي مشاهده و دانلود مقاله به لينك مدارك مرتبط مراجعه نماييد
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.
URL
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