DC Field | Value | Language |
---|---|---|
dc.contributor.author | Dragović, Vladimir | en_US |
dc.contributor.author | Radnović, Milena | en_US |
dc.date.accessioned | 2024-11-25T13:17:35Z | - |
dc.date.available | 2024-11-25T13:17:35Z | - |
dc.date.issued | 2024 | - |
dc.identifier.issn | 2331-8422 | - |
dc.identifier.uri | http://researchrepository.mi.sanu.ac.rs/handle/123456789/5398 | - |
dc.description | 23 pages, 33 figures | en_US |
dc.description.abstract | Using Marden's Theorem from geometric theory of polynomials, we show that for every triangle there is a unique ellipse such that the triangle is a billiard trajectory within that ellipse. Since $3$-periodic trajectories of billiards within ellipses are examples of the Poncelet polygons, our considerations provide a new insight into the relationship between Marden's Theorem and the Poncelet Porism, two gems of exceptional classical beauty. We also show that every parallelogram is a billiard trajectory within a unique ellipse. We prove a similar result for the self-intersecting polygonal lines consisting of two pairs of congruent sides, named "Darboux butterflies". In each of three considered cases, we effectively calculate the foci of the boundary ellipses. | en_US |
dc.publisher | arXiv | en_US |
dc.rights | CC0 1.0 Universal | * |
dc.rights.uri | http://creativecommons.org/publicdomain/zero/1.0/ | * |
dc.subject | Mathematics - Dynamical Systems; Mathematics - Dynamical Systems; Mathematical Physics; Mathematics - Complex Variables; Mathematics - Metric Geometry; Mathematics - Mathematical Physics; Nonlinear Sciences - Exactly Solvable and Integrable Systems; 51N20, 30C15, 37J35, 70H06 | en_US |
dc.title | Is every triangle a trajectory of an elliptical billiard? | en_US |
dc.type | Other | en_US |
dc.identifier.scopus | 2-s2.0-85195179102 | - |
dc.identifier.url | http://arxiv.org/abs/2405.08922v2 | - |
dc.contributor.affiliation | Mechanics | en_US |
dc.contributor.affiliation | Mathematical Institute of the Serbian Academy of Sciences and Arts | en_US |
item.fulltext | With Fulltext | - |
item.openairetype | Other | - |
item.grantfulltext | open | - |
item.cerifentitytype | Publications | - |
item.openairecristype | http://purl.org/coar/resource_type/c_18cf | - |
crisitem.author.orcid | 0000-0002-0295-4743 | - |
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File | Description | Size | Format | |
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MRadnovic.pdf | 283.8 kB | Adobe PDF | View/Open |
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