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Polynomial generated polygons
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dc.contributor.advisor | O'Connor, John J. (John Joseph) | |
dc.contributor.author | Soares, Benedict J. | |
dc.coverage.spatial | 185 p. | en_US |
dc.date.accessioned | 2018-06-18T12:49:54Z | |
dc.date.available | 2018-06-18T12:49:54Z | |
dc.date.issued | 1999 | |
dc.identifier.uri | https://hdl.handle.net/10023/14198 | |
dc.description.abstract | A turtle geometric construction on the plane, called a polynomial generated polygon (PGP) and represented by 𝒫[sub]f,[sub]pᵐ, is generated from the sequence obtained from evaluating f(𝓍) ∈ ℤ [𝓍] over ℤ modulo pᵐ where p is a prime and m ∈ ℕ. Computational methods are developed to pre-calculate the symmetries exhibited by [sub]f,[sub]pᵐ for a given f and pᵐ. These include procedures to find whether [sub]f,[sub]pᵐ is bounded or unbounded, the degree of rotational symmetry present, whether lines of reflectional symmetry can be observed, and in the case of 𝒫[sub]f,[sub]pᵐ unbounded, whether the PGP has a glide reflection. Methods are also sought to find a suitable f and pᵐ to produce a desired 'feasible' shape in a PGP construction, and how the same shape might be generated modulo pᵐ⁺ᵏ if it cannot be produced modulo pᵐ. | en_US |
dc.language.iso | en | en_US |
dc.publisher | University of St Andrews | en |
dc.subject.lcc | QA481.S7 | |
dc.subject.lcsh | Axioms | en |
dc.title | Polynomial generated polygons | en_US |
dc.type | Thesis | en_US |
dc.contributor.sponsor | Caledonian Research Foundation | en_US |
dc.type.qualificationlevel | Doctoral | en_US |
dc.type.qualificationname | PhD Doctor of Philosophy | en_US |
dc.publisher.institution | The University of St Andrews | en_US |
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