Youtor
A moving light source in a Penrose unilluminable room
>> YOUR LINK HERE: ___ http://youtube.com/watch?v=LXej5rQq_Bc
This #short video gives yet another illustration of how Penrose's solution of the illumination problem works. It shows a light source moving on a circular path inside the room. The path of light rays sent in 14 different directions is shown, giving an idea of which regions are illuminated. Each ray has a different color, and its luminosity decreases after each reflection on a wall of the room. In total, 7 reflections are shown for each beam. • The illumination problem asks the following question: assume you have a room with mirrored walls. Is it always possible to place a light source in such a way that no dark corners remain in the room? Of course, the room has to be in one piece (connected, as we say in mathematics): it should not consist of several separate rooms. • The problem was formulated by Ernst Straus in the 1950s, and first solved by Roger Penrose in 1958. He constructed a room that cannot be illuminated completely, wherever you put the light source. The room is constructed with two half-ellipses connected by straight parts, in the middle of which one puts two mushroom-shaped protuberances. The rounded parts of the mushrooms are also half-ellipses, whose vertices are placed at the focal points of the large half-ellipses. • Render time: 30 seconds • Color scheme: HSLuv https://www.hsluv.org/ • Music: Snappy by Audionautix is licensed under a Creative Commons Attribution 4.0 licence. https://creativecommons.org/licenses/... • Artist: http://audionautix.com/ • Current version of the C code used to make these animations: https://github.com/nilsberglund-orlea... • https://www.idpoisson.fr/berglund/sof... • Some outreach articles on mathematics: • https://images.math.cnrs.fr/_Berglund... • (in French, some with a Spanish translation)
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