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Tag Archives: Poincaré disc
Various projections of hyperbolic kaleidoscopic images
Similarly to the earlier post “Different projections of spherical kaleidoscopic images” I am now showing the same kaleidoscopic image using different projections you can use in my kaleidoscope browser app http://geometricolor.ch/sphericalKaleidoscopeApp.html. It primarily generates images as Poincaré discs. A typical result … Continue reading
Straight lines in elliptic and hyperbolic space
A straight line is the shortest path between two points. Discussing curved space we would better call them geodesic lines to avoid confusion. I want to discuss these geodesic lines for surfaces of a sphere, elliptic space and hyperbolic space. … Continue reading
Posted in Kaleidoscopes, programming
Tagged elliptic geometry, geodesic line, hyperbolic geometry, Poincaré disc, straight line
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How to program fast kaleidoscopes
This post repeats parts of earlier posts but I am trying to expand the ideas and explain them better. First, I am showing you how to make rosettes with rotational symmetry and mirror symmetry. This is easier than making kaleidoscopic images, … Continue reading
Further hyperbolic kaleidoscopes
In the last post I have used reflections at two parallel lines and a circle to get a Poincaré plane that shows a periodic decoration of hyperbolic space. What happens if the straight lines are not parallel and intersect? Then … Continue reading
Posted in Kaleidoscopes
Tagged hyperbolic space, kaleidoscope, Poincaré disc, rose window, Rotational symmetry
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