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arXiv · 1706.06924

The Ptolemy-Alhazen problem and spherical mirror reflection

Masayo Fujimura·Parisa Hariri·Marcelina Mocanu·Matti Vuorinen
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Abstract

An ancient optics problem of Ptolemy, studied later by Alhazen, is discussed. This problem deals with reflection of light in spherical mirrors. Mathematically this reduces to the solution of a quartic equation, which we solve and analyze using a symbolic computation software. Similar problems have been recently studied in connection with ray-tracing, catadioptric optics, scattering of electromagnetic waves, and mathematical billiards, but we were led to this problem in our study of the so-called triangular ratio metric.

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Masayo Fujimura, Parisa Hariri, Marcelina Mocanu, Matti Vuorinen. 2017-06-21. The Ptolemy-Alhazen problem and spherical mirror reflection. https://arxiv.org/abs/1706.06924

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