Date post: | 13-Apr-2017 |
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Science |
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Hyperbolic Prisms, Poicaré Disc, and Foams
Alberto Tufaile, Adriana P. B. TufaileSoft Matter Laboratory
EACH-University of São PauloBrazil
C’est souvent à partir d’une petite experience que la nature d’um phénomène se precise. Pierre-Gilles de Gennes
Hyperbolic Prism
• The hyperbolic prism is a transparent optical element with spherical surfaces.
Poincaré Disc• The points of the
geometry are in a n-dimensional disc, and the straight lines consist of all segments of circles contained within a disc that are orthogonal to the boundary of the disc.
Foams• We are talking about liquid foam or aqueous
foam. For example, pour a bottle of beer. A foam or froth is formed. The prism was inspired in such type of foam.
Geometrical Optics• Foams – Hyperbolic prisms – Kaleidoscopes;• Kaleidoscopes – Reflections – Möbius transformations• Möbius transformations – Hyperbolic geometry –
Poincaré disc model;• Poincaré disc – Fractal – Chaotic scattering of light;
Möbius and Stereographic Projections
-Inversion in a Sphere;-Preservation of circles;-Presevation of angles...
Iterations
Hyperbolic Kaleidoscope
Simulation Experiment
Some Results
Prism
Kaleidoscope
Exploringthe hyperbolic
prism
Thank You