The Ptolemy–Alhazen Problem and Spherical Mirror Reflection

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dc.contributor.authorMasayo Fujimura
dc.contributor.authorParisa Hariri
dc.contributor.authorMarcelina Mocanu
dc.contributor.authorMatti Vuorinen
dc.contributor.organizationfi=matematiikka|en=Mathematics|
dc.contributor.organization-code1.2.246.10.2458963.20.41687507875
dc.converis.publication-id37108274
dc.converis.urlhttps://research.utu.fi/converis/portal/Publication/37108274
dc.date.accessioned2025-08-27T22:34:47Z
dc.date.available2025-08-27T22:34:47Z
dc.description.abstractAn 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.
dc.format.pagerange135
dc.format.pagerange155
dc.identifier.eissn2195-3724
dc.identifier.jour-issn1617-9447
dc.identifier.olddbid202410
dc.identifier.oldhandle10024/185437
dc.identifier.urihttps://www.utupub.fi/handle/11111/46973
dc.identifier.urlhttps://doi.org/10.1007/s40315-018-0257-z
dc.identifier.urnURN:NBN:fi-fe2021042720429
dc.language.isoen
dc.okm.affiliatedauthorVuorinen, Matti
dc.okm.discipline111 Mathematicsen_GB
dc.okm.discipline111 Matematiikkafi_FI
dc.okm.internationalcopublicationinternational co-publication
dc.okm.internationalityInternational publication
dc.okm.typeA1 ScientificArticle
dc.publisherSpringer
dc.publisher.countryGermanyen_GB
dc.publisher.countrySaksafi_FI
dc.publisher.country-codeDE
dc.relation.doi10.1007/s40315-018-0257-z
dc.relation.ispartofjournalComputational Methods and Function Theory
dc.relation.issue1
dc.relation.volume19
dc.source.identifierhttps://www.utupub.fi/handle/10024/185437
dc.titleThe Ptolemy–Alhazen Problem and Spherical Mirror Reflection
dc.year.issued2019

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