The Ptolemy–Alhazen Problem and Spherical Mirror Reflection
: Masayo Fujimura, Parisa Hariri, Marcelina Mocanu, Matti Vuorinen
Publisher: Springer
: 2019
: Computational Methods and Function Theory
: COMPUTATIONAL METHODS AND FUNCTION THEORY
: COMPUT METH FUNCT TH
: 19
: 1
: 135
: 155
: 21
: 1617-9447
: 2195-3724
DOI: https://doi.org/10.1007/s40315-018-0257-z
: https://doi.org/10.1007/s40315-018-0257-z
: https://research.utu.fi/converis/portal/detail/Publication/37108274
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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