The geometry of M. C. Escher's circle-Limit-Woodcuts

1999 ◽  
Vol 31 (5) ◽  
pp. 144-148
Author(s):  
Peter Herfort
Keyword(s):  
Circle Limit

A Circle Limit in Stone

2003 ◽  
pp. 166-174
Author(s):  
Helaman Ferguson ◽  
Claire Ferguson
Keyword(s):  
Circle Limit

The Non-Euclidean Symmetry of Escher's Picture 'Circle Limit III'

Leonardo ◽  
1979 ◽  
Vol 12 (1) ◽  
pp. 19 ◽  
Author(s):  
H. S. M. Coxeter
Keyword(s):  
Euclidean Symmetry ◽  
Circle Limit

scholarly journals Limit Circle/Limit Point Criteria for Second-Order Superlinear Differential Equations with a Damping Term

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Lihong Xing ◽  
Wei Song ◽  
Zhengqiang Zhang ◽  
Qiyi Xu
Keyword(s):  
Differential Equations ◽  
Limit Point ◽  
Second Order ◽  
Damping Term ◽  
Limit Circle ◽  
New Criteria ◽  
Point Type ◽  
Circle Limit

The purpose of the present paper is to establish some new criteria for the classifications of superlinear differential equations as being of the nonlinear limit circle type or of the nonlinear limit point type. The criteria presented here generalize some known results in literature.

scholarly journals Isometries, Tessellations and Escher, Oh My!

2005 ◽  
Vol 3 (4) ◽  
Author(s):  
Melissa Potter ◽  
Jason Ribando
Keyword(s):  
Hyperbolic Plane ◽  
Poincaré Disk ◽  
Circle Limit

Motivated to better understand the wonderful artistry and hyperbolic tessellations of M.C. Escher’s Circle Limit prints, we study the isometries of the hyperbolic plane and create tessellations of the Poincaré disk using the Euclidean tools of compass and straightedge.

scholarly journals Hard spheres on the gyroid surface

2012 ◽  
Vol 2 (5) ◽  
pp. 575-581 ◽  
Author(s):  
Tomonari Dotera ◽  
Masakiyo Kimoto ◽  
Junichi Matsuzawa
Keyword(s):  
Monte Carlo ◽  
Minimal Surface ◽  
Gaussian Curvature ◽  
Hard Spheres ◽  
Order Parameters ◽  
Unit Cell ◽  
Acceptance Ratio ◽  
Self Organized ◽  
Negative Gaussian Curvature ◽  
Circle Limit

We find that 48/64 hard spheres per unit cell on the gyroid minimal surface are entropically self-organized. Striking evidence is obtained in terms of the acceptance ratio of Monte Carlo moves and order parameters. The regular tessellations of the spheres can be viewed as hyperbolic tilings on the Poincaré disc with a negative Gaussian curvature, one of which is, equivalently, the arrangement of angels and devils in Escher's Circle Limit IV .

scholarly journals Limit Circle/Limit Point Criteria for Second-Order Sublinear Differential Equations with Damping Term

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Jing Shao ◽  
Wei Song
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Limit Point ◽  
Second Order ◽  
Damping Term ◽  
Limit Circle ◽  
New Criteria ◽  
Point Type ◽  
Circle Limit

The purpose of the present paper is to establish some new criteria for the classification of the sublinear differential equation as of the nonlinear limit circle type or of the nonlinear limit point type. The criteria presented here generalize some known results in the literature.

Sign in / Sign up

Export Citation Format

Share Document