{"id":"https://openalex.org/W2899805102","doi":"https://doi.org/10.1080/00029890.2018.1503512","title":"Quadratic Forms, Chebyshev Polynomials, and Geometric Inequalities","display_name":"Quadratic Forms, Chebyshev Polynomials, and Geometric Inequalities","publication_year":2018,"publication_date":"2018-10-21","ids":{"openalex":"https://openalex.org/W2899805102","doi":"https://doi.org/10.1080/00029890.2018.1503512","mag":"2899805102"},"language":"en","primary_location":{"id":"doi:10.1080/00029890.2018.1503512","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.2018.1503512","pdf_url":null,"source":{"id":"https://openalex.org/S156280010","display_name":"American Mathematical Monthly","issn_l":"0002-9890","issn":["0002-9890","1930-0972"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The American Mathematical Monthly","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5007380590","display_name":"Titu Andreescu","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Titu Andreescu","raw_affiliation_strings":["School of Natural Sciences and Mathematics, The University of Texas at Dallas, 800 W. Campbell Road, Richardson, TX 75080"],"affiliations":[{"raw_affiliation_string":"School of Natural Sciences and Mathematics, The University of Texas at Dallas, 800 W. Campbell Road, Richardson, TX 75080","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5048158212","display_name":"\u041e\u043b\u0435\u0433 \u041c\u0443\u0448\u043a\u0430\u0440\u043e\u0432","orcid":"https://orcid.org/0000-0002-0169-2809"},"institutions":[{"id":"https://openalex.org/I4210105926","display_name":"Institute of Mathematics and Informatics","ror":"https://ror.org/01b5dy719","country_code":"BG","type":"facility","lineage":["https://openalex.org/I24768866","https://openalex.org/I4210105926"]},{"id":"https://openalex.org/I24768866","display_name":"Bulgarian Academy of Sciences","ror":"https://ror.org/01x8hew03","country_code":"BG","type":"funder","lineage":["https://openalex.org/I24768866"]}],"countries":["BG"],"is_corresponding":false,"raw_author_name":"Oleg Mushkarov","raw_affiliation_strings":["Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str. Bl. 8, 1113 Sofia, Bulgaria"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str. Bl. 8, 1113 Sofia, Bulgaria","institution_ids":["https://openalex.org/I24768866","https://openalex.org/I4210105926"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5007380590"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.2208089,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"125","issue":"9","first_page":"811","last_page":"819"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.9976000189781189,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.9976000189781189,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13267","display_name":"Advanced Theoretical and Applied Studies in Material Sciences and Geometry","score":0.984000027179718,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9822999835014343,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8086410760879517},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.6700466275215149},{"id":"https://openalex.org/keywords/inequality","display_name":"Inequality","score":0.6311270594596863},{"id":"https://openalex.org/keywords/chebyshev-polynomials","display_name":"Chebyshev polynomials","score":0.5097567439079285},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.48098719120025635},{"id":"https://openalex.org/keywords/chebyshevs-inequality","display_name":"Chebyshev's inequality","score":0.46759456396102905},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.44894787669181824},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4462955594062805},{"id":"https://openalex.org/keywords/log-sum-inequality","display_name":"Log sum inequality","score":0.3874390721321106},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.33590736985206604},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3201724886894226},{"id":"https://openalex.org/keywords/rearrangement-inequality","display_name":"Rearrangement inequality","score":0.22926494479179382},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.21138185262680054},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.16087982058525085}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8086410760879517},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.6700466275215149},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.6311270594596863},{"id":"https://openalex.org/C129785596","wikidata":"https://www.wikidata.org/wiki/Q619511","display_name":"Chebyshev polynomials","level":2,"score":0.5097567439079285},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.48098719120025635},{"id":"https://openalex.org/C71564387","wikidata":"https://www.wikidata.org/wiki/Q249514","display_name":"Chebyshev's inequality","level":5,"score":0.46759456396102905},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.44894787669181824},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4462955594062805},{"id":"https://openalex.org/C46979015","wikidata":"https://www.wikidata.org/wiki/Q6666859","display_name":"Log sum inequality","level":3,"score":0.3874390721321106},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33590736985206604},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3201724886894226},{"id":"https://openalex.org/C126087398","wikidata":"https://www.wikidata.org/wiki/Q1149189","display_name":"Rearrangement inequality","level":4,"score":0.22926494479179382},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.21138185262680054},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.16087982058525085}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00029890.2018.1503512","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.2018.1503512","pdf_url":null,"source":{"id":"https://openalex.org/S156280010","display_name":"American Mathematical Monthly","issn_l":"0002-9890","issn":["0002-9890","1930-0972"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The American Mathematical Monthly","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":2,"referenced_works":["https://openalex.org/W4206454995","https://openalex.org/W4231489933"],"related_works":["https://openalex.org/W2554340414","https://openalex.org/W2218882867","https://openalex.org/W2367379155","https://openalex.org/W1646360038","https://openalex.org/W1162220133","https://openalex.org/W2363706313","https://openalex.org/W4213342932","https://openalex.org/W2050309655","https://openalex.org/W2366121247","https://openalex.org/W3209040720"],"abstract_inverted_index":{"We":[0],"discuss":[1],"a":[2],"geometric":[3,51,58],"inequality":[4,26,52],"for":[5,60],"2n-gons":[6],"proved":[7,33],"in":[8],"[Mushkarov,":[9],"O.,":[10],"Nikolov":[11],"N.":[12],"(2006).":[13],"Semiregular":[14],"polygons.":[15],"Amer.":[16],"Math.":[17],"Monthly.":[18],"113(4):":[19],"339\u2013344]":[20],"and":[21],"show":[22],"how":[23],"the":[24,36,50],"algebraic":[25],"it":[27],"is":[28],"based":[29],"on":[30],"can":[31],"be":[32],"by":[34],"using":[35],"standard":[37],"theory":[38],"of":[39,49,66],"quadratic":[40],"forms.":[41],"In":[42],"addition,":[43],"we":[44],"prove":[45],"an":[46,63],"\u201codd\u201d":[47],"version":[48],"which":[53],"leads":[54],"to":[55],"some":[56],"interesting":[57],"problems":[59],"polygons":[61],"with":[62],"odd":[64],"number":[65],"sides.":[67]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}