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2015-10-30T21:36:40Z

‎Bibtex

Gubachelier: Die Seite wurde neu angelegt: „== Reference == Francesco De Comité: Yvon-Villarceau Circle Equivalents on Dupin Cyclides. In: Bridges 2015. Pages 253–258 == DOI == == Abstract…“

2015-10-24T20:40:10Z

Die Seite wurde neu angelegt: „== Reference == Francesco De Comité: Yvon-Villarceau Circle Equivalents on Dupin Cyclides. In: Bridges 2015. Pages 253–258 == DOI == == Abstract…“

Neue Seite

== Reference ==
Francesco De Comité: [[Yvon-Villarceau Circle Equivalents on Dupin Cyclides]]. In: [[Bridges 2015]]. Pages 253–258

== DOI ==

== 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.

== Extended Abstract ==

== Bibtex ==
@inproceedings{bridges2015:253,
author = {Francesco De Comit\'e},
title = {Yvon-Villarceau Circle Equivalents on Dupin Cyclides},
pages = {253--258},
booktitle = {Proceedings of Bridges 2015: Mathematics, Music, Art, Architecture, Culture},
year = {2015},
editor = {Kelly Delp, Craig S. Kaplan, Douglas McKenna and Reza Sarhangi},
isbn = {978-1-938664-15-1},
issn = {1099-6702},
publisher = {Tessellations Publishing},
address = {Phoenix, Arizona},
note = {Available online at \url{http://archive.bridgesmathart.org/2015/bridges2015-253.html}}
}

== Used References ==
[1] Torus/Villarceau Circles Slide-Together Pattern. https://www.flickr.com/photos/yoshinobu_
miyamoto/5555289192 (accessed 24/01/2015).

[2] V. Chandru, D. Dutta, and C.M. Hoffmann. On the Geometry of Dupin Cyclides. The Visual Computer,
5(5):277–290, 1989.

[3] Francesco De Comit´e. Circle Packing Explorations. In George W. Hart and Reza Sarhangi, editors,
Proceedings of Bridges 2013: Mathematics, Music, Art, Architecture, Culture, pages 399–402, Phoenix,
Arizona, 2013. Tessellations Publishing.
Available online at http://archive.bridgesmathart.org/2013/bridges2013-399.pdf
(accessed 22/01/2015).

[4] Francesco De Comit´e. Cardioidal Variations. In George Hart Gary Greenfield and Reza Sarhangi,
editors, Proceedings of Bridges 2014: Mathematics, Music, Art, Architecture, Culture, pages 349–352,
Phoenix, Arizona, 2014. Tessellations Publishing.
Available online at http://archive.bridgesmathart.org/2014/bridges2014-349.html.

[5] Mar´ıa Garc´ıa Monera and Juan Monterde. Building a Torus with Villarceau Sections. Journal for
Geometry and Graphics, 15(1):93–99, 2011.

[6] Lionel Garnier, Hichem Barki, Sebti Foufou, and Loic Puech. Computation of Yvon-Villarceau Circles
on Dupin Cyclides and Construction of Circular Edge Right Triangles on Tori and Dupin Cyclides.
Computers & Mathematics with Applications, 68(12):1689–1709, 2014.

[7] George W. Hart. Slide-Together Geometric Paper Constructions. http://www.georgehart.com/
slide-togethers/slide-togethers.html
(accessed 07/04/2015).

[8] Gabriela Ligenza. Gabriela Ligenza’s website. http:www.gabrielaligenza.com
(accessed 27/01/2015).

[9] Michael Schrott and Boris Odehnal. Ortho-Circles of Dupin Cyclides. Journal for Geometry and Graphics,
10(1):73,98, 2006.

== Links ==
=== Full Text ===
http://archive.bridgesmathart.org/2015/bridges2015-253.pdf

[[intern file]]

=== Sonstige Links ===
http://archive.bridgesmathart.org/2015/bridges2015-253.html

@@ Zeile 21: / Zeile 21: @@
    publisher   = {Tessellations Publishing},
    address     = {Phoenix, Arizona},
-   note        = {Available online at \url{http://archive.bridgesmathart.org/2015/bridges2015-253.html}}
+   note        = {Available online at \url{http://archive.bridgesmathart.org/2015/bridges2015-253.html }},
+  }

Yvon-Villarceau Circle Equivalents on Dupin Cyclides - Versionsgeschichte

Gubachelier: /* Bibtex */

Gubachelier: Die Seite wurde neu angelegt: „== Reference == Francesco De Comité: Yvon-Villarceau Circle Equivalents on Dupin Cyclides. In: Bridges 2015. Pages 253–258 == DOI == == Abstract…“