Tag Archives: elliptic geometry

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

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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

Posted in Anamorphosis, Kaleidoscopes, programming, Tilings | Tagged , , , , | Leave a comment

Elliptic kaleidoscopes

In “further hyperbolic kaleidoscopes” I used two straight lines and a circle to make a triangle that defines a kaleidoscope. For k,n and m-fold rotational symmetries at its corners, the sum of its three angles is π(1/k+1/n+1/m). If this sum is … Continue reading

Posted in Anamorphosis, Kaleidoscopes | Tagged , , , , | 3 Comments