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.

Scattering in the Poincaré Disk and in the Poincaré Upper Half-Plane

2021 ◽  
Author(s):  
Anderson Luiz de Jesus ◽  
Alan C Maioli ◽  
Alexandre G M Schmidt
Keyword(s):  
Plane Wave ◽  
Half Plane ◽  
Hyperbolic Plane ◽  
Dirac Delta ◽  
Upper Half Plane ◽  
Delta Functions ◽  
Concentric Circles ◽  
Poincaré Disk

Abstract We investigate the scattering of a plane wave in the hyperbolic plane. We formulate the problem in terms of the Lippmann-Schwinger equation and solve it exactly for barriers modeled as Dirac delta functions running along: (i) N−horizontal lines in the Poincaré upper half-plane; (ii) N− concentric circles centered at the origin; and, (iii) a hypercircle in the Poincaré disk.

In a Class With Klein: Generating A Model of the Hyperbolic Plane

PRIMUS ◽  
2012 ◽  
Vol 22 (2) ◽  
pp. 85-96
Author(s):  
Samuel Otten ◽  
Christopher Zin
Keyword(s):  
Hyperbolic Plane

On the inversion of the geodesic Radon transform on the hyperbolic plane

1997 ◽  
Vol 13 (4) ◽  
pp. 1053-1062 ◽  
Author(s):  
Sergei Lissianoi ◽  
Igor Ponomarev
Keyword(s):  
Radon Transform ◽  
Hyperbolic Plane
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