{"id":"https://openalex.org/W2056845641","doi":"https://doi.org/10.1145/1186107.1186138","title":"Animation of mathematical concepts using polynomiography","display_name":"Animation of mathematical concepts using polynomiography","publication_year":2004,"publication_date":"2004-01-01","ids":{"openalex":"https://openalex.org/W2056845641","doi":"https://doi.org/10.1145/1186107.1186138","mag":"2056845641"},"language":"en","primary_location":{"id":"doi:10.1145/1186107.1186138","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1186107.1186138","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM SIGGRAPH 2004 Educators program on   - SIGGRAPH '04","raw_type":"proceedings-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/A5018333582","display_name":"Bahman Kalantari","orcid":"https://orcid.org/0000-0001-6217-9227"},"institutions":[{"id":"https://openalex.org/I102322142","display_name":"Rutgers, The State University of New Jersey","ror":"https://ror.org/05vt9qd57","country_code":"US","type":"education","lineage":["https://openalex.org/I102322142"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Bahman Kalantari","raw_affiliation_strings":["Rutgers University, New Brunswick, NJ","Rutgers UNiv., New Brunswick, NJ"],"affiliations":[{"raw_affiliation_string":"Rutgers University, New Brunswick, NJ","institution_ids":["https://openalex.org/I102322142"]},{"raw_affiliation_string":"Rutgers UNiv., New Brunswick, NJ","institution_ids":["https://openalex.org/I102322142"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001735536","display_name":"Iraj Kalantari","orcid":null},"institutions":[{"id":"https://openalex.org/I117942362","display_name":"Western Illinois University","ror":"https://ror.org/02sshz518","country_code":"US","type":"education","lineage":["https://openalex.org/I117942362"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Iraj Kalantari","raw_affiliation_strings":["Western Illinois University, Macomb, IL","\u2020Western Illinois University, Macomb, IL"],"affiliations":[{"raw_affiliation_string":"Western Illinois University, Macomb, IL","institution_ids":["https://openalex.org/I117942362"]},{"raw_affiliation_string":"\u2020Western Illinois University, Macomb, IL","institution_ids":["https://openalex.org/I117942362"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5002299473","display_name":"F. V. Andreev","orcid":"https://orcid.org/0000-0001-8644-5497"},"institutions":[{"id":"https://openalex.org/I117942362","display_name":"Western Illinois University","ror":"https://ror.org/02sshz518","country_code":"US","type":"education","lineage":["https://openalex.org/I117942362"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Fedor Andreev","raw_affiliation_strings":["Western Illinois University, Macomb, IL","\u2020Western Illinois University, Macomb, IL"],"affiliations":[{"raw_affiliation_string":"Western Illinois University, Macomb, IL","institution_ids":["https://openalex.org/I117942362"]},{"raw_affiliation_string":"\u2020Western Illinois University, Macomb, IL","institution_ids":["https://openalex.org/I117942362"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5018333582"],"corresponding_institution_ids":["https://openalex.org/I102322142"],"apc_list":null,"apc_paid":null,"fwci":1.5037,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.808933,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"27","last_page":"27"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.98580002784729,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.98580002784729,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.98089998960495,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T12504","display_name":"Mathematics and Applications","score":0.9782999753952026,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/animation","display_name":"Animation","score":0.78962242603302},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.7210399508476257},{"id":"https://openalex.org/keywords/visualization","display_name":"Visualization","score":0.7115438580513},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5710573196411133},{"id":"https://openalex.org/keywords/computer-graphics","display_name":"Computer graphics (images)","score":0.5641055107116699},{"id":"https://openalex.org/keywords/interpretation","display_name":"Interpretation (philosophy)","score":0.5345062017440796},{"id":"https://openalex.org/keywords/computer-animation","display_name":"Computer animation","score":0.504644513130188},{"id":"https://openalex.org/keywords/rotation","display_name":"Rotation (mathematics)","score":0.4781026244163513},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.45298275351524353},{"id":"https://openalex.org/keywords/the-internet","display_name":"The Internet","score":0.4353978931903839},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3026806712150574},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.20086213946342468},{"id":"https://openalex.org/keywords/world-wide-web","display_name":"World Wide Web","score":0.13168779015541077},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.10613840818405151},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07277992367744446}],"concepts":[{"id":"https://openalex.org/C502989409","wikidata":"https://www.wikidata.org/wiki/Q11425","display_name":"Animation","level":2,"score":0.78962242603302},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7210399508476257},{"id":"https://openalex.org/C36464697","wikidata":"https://www.wikidata.org/wiki/Q451553","display_name":"Visualization","level":2,"score":0.7115438580513},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5710573196411133},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.5641055107116699},{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.5345062017440796},{"id":"https://openalex.org/C69369342","wikidata":"https://www.wikidata.org/wiki/Q1401416","display_name":"Computer animation","level":3,"score":0.504644513130188},{"id":"https://openalex.org/C74050887","wikidata":"https://www.wikidata.org/wiki/Q848368","display_name":"Rotation (mathematics)","level":2,"score":0.4781026244163513},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.45298275351524353},{"id":"https://openalex.org/C110875604","wikidata":"https://www.wikidata.org/wiki/Q75","display_name":"The Internet","level":2,"score":0.4353978931903839},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3026806712150574},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.20086213946342468},{"id":"https://openalex.org/C136764020","wikidata":"https://www.wikidata.org/wiki/Q466","display_name":"World Wide Web","level":1,"score":0.13168779015541077},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.10613840818405151},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07277992367744446}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/1186107.1186138","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1186107.1186138","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM SIGGRAPH 2004 Educators program on   - SIGGRAPH '04","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.8600000143051147,"id":"https://metadata.un.org/sdg/4","display_name":"Quality Education"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W33980575","https://openalex.org/W43573985","https://openalex.org/W117718904","https://openalex.org/W585195230","https://openalex.org/W1482997031","https://openalex.org/W1608551107","https://openalex.org/W1967312706","https://openalex.org/W1970664499","https://openalex.org/W1983087877","https://openalex.org/W1989196613","https://openalex.org/W2011777324","https://openalex.org/W2033859228","https://openalex.org/W2038968784","https://openalex.org/W2048632019","https://openalex.org/W2064055621","https://openalex.org/W2078206416","https://openalex.org/W2090960299","https://openalex.org/W2103463156","https://openalex.org/W2104237288","https://openalex.org/W2313644845","https://openalex.org/W2529003330"],"related_works":["https://openalex.org/W2121378366","https://openalex.org/W3112102641","https://openalex.org/W2013184069","https://openalex.org/W2535923857","https://openalex.org/W2989004599","https://openalex.org/W1976926596","https://openalex.org/W126583968","https://openalex.org/W2532377291","https://openalex.org/W2359575859","https://openalex.org/W2999276620"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3,35,109],"demonstrate":[4],"how":[5,38],"a":[6,28,104],"medium":[7],"called":[8],"polynomiography,":[9],"which":[10],"consists":[11],"of":[12,16,50,56,65,72,74,94,98,106],"techniques":[13],"for":[14,31,91,123],"visualization":[15,71],"polynomial":[17,66,76],"equations,":[18],"can":[19,40,120],"be":[20,41,101,121,128],"used":[21,42],"to":[22,43,114,134],"animate":[23],"mathematical":[24],"concepts,":[25],"thereby":[26],"offering":[27],"valuable":[29],"tool":[30],"education.":[32],"More":[33],"specifically,":[34],"will":[36,100,127],"show":[37],"it":[39],"visualize":[44],"the":[45,53,83,92,111,115],"following":[46],"topics:":[47],"Voronoi":[48],"regions":[49],"points":[51],"in":[52],"plane;":[54],"multiplication":[55],"complex":[57],"numbers":[58],"and":[59,108,126,130],"their":[60],"interpretation":[61],"as":[62,68,87,89],"rotation;":[63],"sensitivity":[64],"roots":[67],"coefficients":[69],"change;":[70],"classes":[73],"special":[75],"equations":[77],"arising":[78],"from":[79,82,132],"two":[80],"problems":[81],"American":[84],"Mathematical":[85],"Monthly;":[86],"well":[88],"animation":[90],"sake":[93],"visual":[95],"art.":[96],"Each":[97],"these":[99],"exhibited":[102],"through":[103],"series":[105],"images":[107],"give":[110],"Internet":[112],"links":[113],"corresponding":[116],"animations.":[117],"These":[118],"sites":[119],"accessed":[122],"educational":[124],"purposes":[125],"upgraded":[129],"expanded":[131],"time":[133],"time.":[135]},"counts_by_year":[{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}