hyperbolic-geometry

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Experiments in Processing: curious eels in hyperbolic sea.

I love hyperbolic geometry, heptagons, and Escher.

The eels move on the sides of a triheptagonal tiling of the hyperbolic plane in the Poincaré disk model. You better appreciate this because getting the coordinates is a real pain in the *** (done with a python script, <a href=“https://github.com/rantonels/poincare“>source</a>).

BONUS: nauseating Moebius translation.

youtube

Ok. MIND : BLOWN. Margaret Wertheim is officially my newest crush. In this TED talk she explains how hyperbolic geometrical shapes that look very much like coral can be expressed through crochet.

The idea of translating hyperbolic planes into crochet was first thought by Daina Taimina (you can watch her TED talk about it here) and for the first time, an actual hyperbolic shape could be translated into a real, physical shape.

Margaret Wertheim is one of the creators of The Institute for Figuring and has also written many interesting books on the cultural history of physics. Her first book was called Pythagoras’ Trousers: God, Physics, and the Gender Wars. The google books summary of it is:

Here is a fresh, astute social and cultural history of physics, from ancient Greece to our own time. From its inception, Margaret Wertheim shows, physics has been an overwhelmingly male-dominated activity; she argues that gender inequity in physics is a result of the religious origins of the enterprise.

Now I’m pumped for reading AND doing some hyperbolic crochet! (iomikron, are you up for some crafts?)

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Escher’s Circle Limit I - IV and Hyperbolic Geometry

All four of M.C. Escher’s Circle Limit woodcuts are great works of art and superb examples of hyperbolic geometry.  Hyperbolic geometry is a form of geometry where the parallel postulate of Euclidean geometry does not hold.  This is reflected in the world represented in each of the woodcuts. In each one, the figures are not getting smaller as the reach the edge of the circle as they would in Euclidean geometry. From the figures’ perspective, they are all the same size, regardless of where they are in the circle.  Their entire world lies completely within the flat plain of the circle, the edge of which to them remains infinitely far away.