Gubachelier: /* Bibtex */

2016-12-27T11:20:16Z

‎Bibtex

Gubachelier: Die Seite wurde neu angelegt: „ == Reference == Chamberlain Fong: The Conformal Hyperbolic Square and Its Ilk. In: Bridges 2016, Pages 179–186. == DOI == == Abstract == We pres…“

2016-12-26T22:18:36Z

Die Seite wurde neu angelegt: „ == Reference == Chamberlain Fong: The Conformal Hyperbolic Square and Its Ilk. In: Bridges 2016, Pages 179–186. == DOI == == Abstract == We pres…“

Neue Seite

== Reference ==
Chamberlain Fong: [[The Conformal Hyperbolic Square and Its Ilk]]. In: [[Bridges 2016]], Pages 179–186.

== DOI ==

== Abstract ==
We present explicit equations for three different mappings between the disk and the square. We then use these
smooth and invertible mappings to convert the Poincaré disk into a square. In doing so, we come up with three
square models of the hyperbolic plane. Although these hyperbolic square models probably have limited use in
mathematics, we argue that they have artistic merit. In particular, we discuss their use for aesthetic visualization of
infinite patterns within the confines of a square region.

== Extended Abstract ==

== Bibtex ==
@inproceedings{bridges2016:179,
author = {Chamberlain Fong},
title = {The Conformal Hyperbolic Square and Its Ilk},
pages = {179--186},
booktitle = {Proceedings of Bridges 2016: Mathematics, Music, Art, Architecture, Education, Culture},
year = {2016},
editor = {Eve Torrence, Bruce Torrence, Carlo S\'equin, Douglas McKenna, Krist\'of Fenyvesi and Reza Sarhangi},
isbn = {978-1-938664-19-9},
issn = {1099-6702},
publisher = {Tessellations Publishing},
address = {Phoenix, Arizona},
url = {http://de.evo-art.org/index.php?title=The_Conformal_Hyperbolic_Square_and_Its_Ilk},
note = {Available online at \url{http://archive.bridgesmathart.org/2016/bridges2016-179.html}}
}

== Used References ==
[1] V. Bulatov, Conformal Models of the Hyperbolic Geometry. MAA-AMS Joint Math. Meeting. 2010

[2] D. Dunham, Hamiltonian Paths and Hyperbolic Patterns, Contemporary Mathematics, Vol. 479, 2009

[3] M. Fernandez-Guasti, Analytic Geometry of Some Rectilinear Figures, International Journal of
Mathematical Education in Science and Technology. 23, pp. 895-901. 1992.

[4] C. Fong, Analytical Methods for Squaring the Disc. (poster) Seoul International Congress of
Mathematicians, 2014. http://arxiv.org/abs/1509.06344

[5] J. Langer, The Conformal Vega Disk. Bridges 2011, Coimbra Portugal, pp.483-484

[6] H. Müller, The Conformal Mapping of a Circle Onto a Regular Polygon, with an Application to
Image Distortion. http://herbert-mueller.info

[7] P. Nowell, Mapping a Square to a Circle (blog)
http://mathproofs.blogspot.com/2005/07/mapping-square-to-circle.html

[8] P. Ouyang, F. Ding, X. Wang, Beautiful Math, Part 4: Polygonal Aesthetic Patterns Based on the
Schwarz-Christoffel Mapping. IEEE Computer Graphics & Applications, pp. 22-25, July-Aug. 2015

[9] D. Schattschneider, Escher’s Metaphors. Scientific American, pp.66-71, November 1994

[10] D. Swart, Warping Pictures Nicely. Bridges 2011, Coimbra Portugal, pp.303-310

== Links ==
=== Full Text ===
http://archive.bridgesmathart.org/2016/bridges2016-179.pdf

[[intern file]]

=== Sonstige Links ===
http://archive.bridgesmathart.org/2016/bridges2016-179.html

@@ Zeile 27: / Zeile 27: @@
    publisher   = {Tessellations Publishing},
    address     = {Phoenix, Arizona},
-   url         = {http://de.evo-art.org/index.php?title=The_Conformal_Hyperbolic_Square_and_Its_Ilk},
+   url         = {http://de.evo-art.org/index.php?title=The_Conformal_Hyperbolic_Square_and_Its_Ilk },
    note        = {Available online at \url{http://archive.bridgesmathart.org/2016/bridges2016-179.html}}
+  }
 == Used References ==

The Conformal Hyperbolic Square and Its Ilk - Versionsgeschichte

Gubachelier: /* Bibtex */

Gubachelier: Die Seite wurde neu angelegt: „ == Reference == Chamberlain Fong: The Conformal Hyperbolic Square and Its Ilk. In: Bridges 2016, Pages 179–186. == DOI == == Abstract == We pres…“