[{"publication_status":"published","publication_identifier":{"issn":["0002-9890"],"eissn":["1930-0972"]},"external_id":{"arxiv":["1706.05919"]},"title":"Rational right triangles of a given area","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"apa":"Chan, S. (2018). Rational right triangles of a given area. <i>The American Mathematical Monthly</i>. Taylor &#38; Francis. <a href=\"https://doi.org/10.1080/00029890.2018.1495491\">https://doi.org/10.1080/00029890.2018.1495491</a>","ieee":"S. Chan, “Rational right triangles of a given area,” <i>The American Mathematical Monthly</i>, vol. 125, no. 8. Taylor &#38; Francis, pp. 689–703, 2018.","mla":"Chan, Stephanie. “Rational Right Triangles of a given Area.” <i>The American Mathematical Monthly</i>, vol. 125, no. 8, Taylor &#38; Francis, 2018, pp. 689–703, doi:<a href=\"https://doi.org/10.1080/00029890.2018.1495491\">10.1080/00029890.2018.1495491</a>.","ama":"Chan S. Rational right triangles of a given area. <i>The American Mathematical Monthly</i>. 2018;125(8):689-703. doi:<a href=\"https://doi.org/10.1080/00029890.2018.1495491\">10.1080/00029890.2018.1495491</a>","short":"S. Chan, The American Mathematical Monthly 125 (2018) 689–703.","ista":"Chan S. 2018. Rational right triangles of a given area. The American Mathematical Monthly. 125(8), 689–703.","chicago":"Chan, Stephanie. “Rational Right Triangles of a given Area.” <i>The American Mathematical Monthly</i>. Taylor &#38; Francis, 2018. <a href=\"https://doi.org/10.1080/00029890.2018.1495491\">https://doi.org/10.1080/00029890.2018.1495491</a>."},"extern":"1","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.1706.05919","open_access":"1"}],"doi":"10.1080/00029890.2018.1495491","oa_version":"Preprint","fulldoi":"https://doi.org/10.1080/00029890.2018.1495491","language":[{"iso":"eng"}],"_id":"19494","day":"28","article_processing_charge":"No","type":"journal_article","issue":"8","arxiv":1,"page":"689-703","article_type":"original","OA_place":"repository","month":"09","date_published":"2018-09-28T00:00:00Z","date_created":"2025-04-05T10:51:16Z","date_updated":"2025-07-10T11:51:49Z","publication":"The American Mathematical Monthly","year":"2018","volume":125,"intvolume":"       125","status":"public","quality_controlled":"1","OA_type":"green","scopus_import":"1","abstract":[{"lang":"eng","text":"Starting from any given rational-sided, right triangle, for example, the (3,4,5)-triangle with area 6, we use Euclidean geometry to show that there are infinitely many other rational-sided, right triangles of the same area. We show further that the set of all such triangles of a given area is finitely generated under our geometric construction. Such areas are known as “congruent numbers” and have a rich history in which all the results in this article have been proved and far more. Yet, as far as we can tell, this seems to be the first exploration using this kind of geometric technique."}],"author":[{"full_name":"Chan, Yik Tung","id":"c4c0afc8-9262-11ed-9231-d8b0bc743af1","first_name":"Yik Tung","orcid":"0000-0001-8467-4106","last_name":"Chan"}],"oa":1,"publisher":"Taylor & Francis"},{"date_created":"2018-12-11T12:06:49Z","acknowledgement":"Research supported by Amoco Fnd. Fac. Dev. Comput. Sci. 1-6-44862","date_updated":"2022-02-11T12:59:01Z","month":"01","date_published":"1989-01-01T00:00:00Z","author":[{"orcid":"0000-0002-9823-6833","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner"},{"last_name":"Skiena","first_name":"Steven","full_name":"Skiena, Steven"}],"publisher":"Mathematical Association of America","publication":"American Mathematical Monthly","volume":96,"year":"1989","status":"public","quality_controlled":"1","intvolume":"        96","main_file_link":[{"url":"http://www.jstor.org/stable/2325182 "}],"extern":"1","citation":{"apa":"Edelsbrunner, H., &#38; Skiena, S. (1989). On the number of furthest neighbor pairs in a point set. <i>American Mathematical Monthly</i>. Mathematical Association of America. <a href=\"https://doi.org/10.1080/00029890.1989.11972250\">https://doi.org/10.1080/00029890.1989.11972250</a>","short":"H. Edelsbrunner, S. Skiena, American Mathematical Monthly 96 (1989) 614–618.","ama":"Edelsbrunner H, Skiena S. On the number of furthest neighbor pairs in a point set. <i>American Mathematical Monthly</i>. 1989;96(7):614-618. doi:<a href=\"https://doi.org/10.1080/00029890.1989.11972250\">10.1080/00029890.1989.11972250</a>","ieee":"H. Edelsbrunner and S. Skiena, “On the number of furthest neighbor pairs in a point set,” <i>American Mathematical Monthly</i>, vol. 96, no. 7. Mathematical Association of America, pp. 614–618, 1989.","mla":"Edelsbrunner, Herbert, and Steven Skiena. “On the Number of Furthest Neighbor Pairs in a Point Set.” <i>American Mathematical Monthly</i>, vol. 96, no. 7, Mathematical Association of America, 1989, pp. 614–18, doi:<a href=\"https://doi.org/10.1080/00029890.1989.11972250\">10.1080/00029890.1989.11972250</a>.","chicago":"Edelsbrunner, Herbert, and Steven Skiena. “On the Number of Furthest Neighbor Pairs in a Point Set.” <i>American Mathematical Monthly</i>. Mathematical Association of America, 1989. <a href=\"https://doi.org/10.1080/00029890.1989.11972250\">https://doi.org/10.1080/00029890.1989.11972250</a>.","ista":"Edelsbrunner H, Skiena S. 1989. On the number of furthest neighbor pairs in a point set. American Mathematical Monthly. 96(7), 614–618."},"title":"On the number of furthest neighbor pairs in a point set","publication_identifier":{"eissn":["1930-0972"],"issn":["0002-9890"]},"publication_status":"published","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","publist_id":"2042","type":"journal_article","page":"614 - 618","article_type":"original","issue":"7","fulldoi":"https://doi.org/10.1080/00029890.1989.11972250","oa_version":"None","language":[{"iso":"eng"}],"day":"01","_id":"4079","doi":"10.1080/00029890.1989.11972250","article_processing_charge":"No"}]