{"id":{"repo_id":"unm","oai_identifier":"oai:digitalrepository.unm.edu:math_etds-1010"},"canonical_url":"https://search.dev.ndltd.org/etd/unm/oai:digitalrepository.unm.edu:math_etds-1010","repository":{"repo_id":"unm","name":"University of New Mexico","base_url":"https://digitalrepository.unm.edu/do/oai/"},"display":{"title":"Pell's Equation and nearly equilateral triangles","abstract":"In this paper, we seek a family of triangles that have integer sides and integer area. We focus mainly on scalene triangles since it is impossible to have such triangles that are equilateral and isoceles triangles with these properties are fairly simple to construct. We restrict the scalene triangles we study to Nearly Equilateral Triangles which have consecutive integer sides. In the process of constructing this family, we find an application of Pell's Equation. 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We focus mainly on scalene triangles since it is impossible to have such triangles that are equilateral and isoceles triangles with these properties are fairly simple to construct. We restrict the scalene triangles we study to Nearly Equilateral Triangles which have consecutive integer sides. In the process of constructing this family, we find an application of Pell's Equation. We follow this with a few other interesting notes on Pell's Equation."]},{"key":"dc:title","label":"Title","values":["Pell's Equation and nearly equilateral triangles"]}]}],"canonical_facts":{"dc:contributor":["Stone, Alexander","Alexander Stone","Jens Lorenz","Kristin Umland"],"dc:creator":["Christensen, Laurel"],"dc:description.abstract":["In this paper, we seek a family of triangles that have integer sides and integer area. We focus mainly on scalene triangles since it is impossible to have such triangles that are equilateral and isoceles triangles with these properties are fairly simple to construct. We restrict the scalene triangles we study to Nearly Equilateral Triangles which have consecutive integer sides. In the process of constructing this family, we find an application of Pell's Equation. We follow this with a few other interesting notes on Pell's Equation."],"dc:identifier":["http://hdl.handle.net/1928/11086","https://digitalrepository.unm.edu/math_etds/11"],"dc:language":["English"],"dc:subject":["Triangle","Pell's equation."],"dc:title":["Pell's Equation and nearly equilateral triangles"],"thesis:degree_discipline":["Mathematics & Statistics"],"thesis:degree_level":["Masters","Thesis"],"thesis:degree_name":["Mathematics"]},"updated_at":"2026-07-24T05:27:37Z"}