{"id":"https://openalex.org/W4412093259","doi":"https://doi.org/10.3390/fractalfract9070444","title":"A Multidisciplinary Approach to Triangular Shapes: Philosophy, Art, Mathematical Properties, and Application Purposes for High-Frequency Signal Processing Using Sierpi\u0144ski Geometry","display_name":"A Multidisciplinary Approach to Triangular Shapes: Philosophy, Art, Mathematical Properties, and Application Purposes for High-Frequency Signal Processing Using Sierpi\u0144ski Geometry","publication_year":2025,"publication_date":"2025-07-04","ids":{"openalex":"https://openalex.org/W4412093259","doi":"https://doi.org/10.3390/fractalfract9070444"},"language":"en","primary_location":{"id":"doi:10.3390/fractalfract9070444","doi":"https://doi.org/10.3390/fractalfract9070444","is_oa":true,"landing_page_url":"https://doi.org/10.3390/fractalfract9070444","pdf_url":"https://www.mdpi.com/2504-3110/9/7/444/pdf?version=1751627221","source":{"id":"https://openalex.org/S4210227020","display_name":"Fractal and Fractional","issn_l":"2504-3110","issn":["2504-3110"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","norway-1","poland-20","russia-white-list-1"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fractal and Fractional","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2504-3110/9/7/444/pdf?version=1751627221","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5051401626","display_name":"Romolo Marcelli","orcid":"https://orcid.org/0000-0002-4815-9470","observed_orcids":["https://orcid.org/0000-0002-4815-9470"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Romolo Marcelli","raw_affiliation_strings":["CNR-IMM Roma ;","CNR-IMM Roma, Via del Fosso del Cavaliere 100, 00133 Roma, Italy"],"raw_orcid":"https://orcid.org/0000-0002-4815-9470","affiliations":[{"raw_affiliation_string":"CNR-IMM Roma ;","institution_ids":[]},{"raw_affiliation_string":"CNR-IMM Roma, Via del Fosso del Cavaliere 100, 00133 Roma, Italy","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5051401626"],"corresponding_institution_ids":[],"apc_list":{"value":2700,"currency":"CHF","value_usd":3258},"apc_paid":{"value":2700,"currency":"CHF","value_usd":3258},"fwci":5.3722,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.9580539,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":97},"biblio":{"volume":"9","issue":"7","first_page":"444","last_page":"444"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.6118000149726868,"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":0.6118000149726868,"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/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.08659999817609787,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T14002","display_name":"Art, Technology, and Culture","score":0.06430000066757202,"subfield":{"id":"https://openalex.org/subfields/1213","display_name":"Visual Arts and Performing Arts"},"field":{"id":"https://openalex.org/fields/12","display_name":"Arts and Humanities"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/sierpinski-triangle","display_name":"Sierpinski gasket","score":0.8619999885559082},{"id":"https://openalex.org/keywords/equilateral-triangle","display_name":"equilateral triangle","score":0.6980000138282776},{"id":"https://openalex.org/keywords/fractal-geometry","display_name":"fractal geometry","score":0.7590000033378601},{"id":"https://openalex.org/keywords/high-frequency-signal-processing","display_name":"high-frequency signal processing","score":0.7300000190734863},{"id":"https://openalex.org/keywords/microwave-antennas","display_name":"microwave antennas","score":0.6389999985694885},{"id":"https://openalex.org/keywords/millimeter-wave-antenna","display_name":"millimeter-wave antennas","score":0.8889999985694885},{"id":"https://openalex.org/keywords/medieval-art","display_name":"medieval art","score":0.765999972820282},{"id":"https://openalex.org/keywords/plato-s-theory-of-forms","display_name":"Plato's theory of Forms","score":0.578000009059906},{"id":"https://openalex.org/keywords/triangle-subdivision","display_name":"triangle subdivision","score":0.5450000166893005}],"concepts":[{"id":"https://openalex.org/C22467394","wikidata":"https://www.wikidata.org/wiki/Q849359","display_name":"Multidisciplinary approach","level":2,"score":0.5712053775787354},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.5284547805786133},{"id":"https://openalex.org/C2779843651","wikidata":"https://www.wikidata.org/wiki/Q7390335","display_name":"SIGNAL (programming language)","level":2,"score":0.49161702394485474},{"id":"https://openalex.org/C104267543","wikidata":"https://www.wikidata.org/wiki/Q208163","display_name":"Signal processing","level":3,"score":0.45217540860176086},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.44180119037628174},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.39365336298942566},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2848687171936035},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.26528429985046387},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.12271413207054138},{"id":"https://openalex.org/C36289849","wikidata":"https://www.wikidata.org/wiki/Q34749","display_name":"Social science","level":1,"score":0.0},{"id":"https://openalex.org/C554190296","wikidata":"https://www.wikidata.org/wiki/Q47528","display_name":"Radar","level":2,"score":0.0},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/fractalfract9070444","doi":"https://doi.org/10.3390/fractalfract9070444","is_oa":true,"landing_page_url":"https://doi.org/10.3390/fractalfract9070444","pdf_url":"https://www.mdpi.com/2504-3110/9/7/444/pdf?version=1751627221","source":{"id":"https://openalex.org/S4210227020","display_name":"Fractal and Fractional","issn_l":"2504-3110","issn":["2504-3110"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","norway-1","poland-20","russia-white-list-1"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fractal and Fractional","raw_type":"journal-article"},{"id":"doi:10.20944/preprints202504.1528.v1","doi":"https://doi.org/10.20944/preprints202504.1528.v1","is_oa":true,"landing_page_url":"https://doi.org/10.20944/preprints202504.1528.v1","pdf_url":"https://www.preprints.org/frontend/manuscript/dca3181b38bb9160c5183194ac56dd6f/download_pub","source":{"id":"https://openalex.org/S6309402219","display_name":"Preprints.org","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"posted-content"},{"id":"pmh:oai:doaj.org/article:dd70845e8cfb4f40aca28ed5bf342833","doi":null,"is_oa":true,"landing_page_url":"https://doaj.org/article/dd70845e8cfb4f40aca28ed5bf342833","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Fractal and Fractional, Vol 9, Iss 7, p 444 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/fractalfract9070444","doi":"https://doi.org/10.3390/fractalfract9070444","is_oa":true,"landing_page_url":"https://doi.org/10.3390/fractalfract9070444","pdf_url":"https://www.mdpi.com/2504-3110/9/7/444/pdf?version=1751627221","source":{"id":"https://openalex.org/S4210227020","display_name":"Fractal and Fractional","issn_l":"2504-3110","issn":["2504-3110"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","norway-1","poland-20","russia-white-list-1"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fractal and Fractional","raw_type":"journal-article"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4412093259.pdf","grobid_xml":"https://content.openalex.org/works/W4412093259.grobid-xml"},"referenced_works_count":55,"referenced_works":["https://openalex.org/W87104624","https://openalex.org/W562911111","https://openalex.org/W569319969","https://openalex.org/W1587176568","https://openalex.org/W1975911501","https://openalex.org/W1999026496","https://openalex.org/W2013386580","https://openalex.org/W2027285022","https://openalex.org/W2032121576","https://openalex.org/W2038295163","https://openalex.org/W2046659235","https://openalex.org/W2075492324","https://openalex.org/W2076490903","https://openalex.org/W2078206416","https://openalex.org/W2091041127","https://openalex.org/W2101106287","https://openalex.org/W2127673957","https://openalex.org/W2134578464","https://openalex.org/W2136654530","https://openalex.org/W2148822495","https://openalex.org/W2163614532","https://openalex.org/W2186924066","https://openalex.org/W2288638723","https://openalex.org/W2648205875","https://openalex.org/W2766147490","https://openalex.org/W2794724177","https://openalex.org/W2802635898","https://openalex.org/W2820172344","https://openalex.org/W2906424812","https://openalex.org/W3006574619","https://openalex.org/W3040532961","https://openalex.org/W3094870184","https://openalex.org/W3095953295","https://openalex.org/W3120980454","https://openalex.org/W4211133488","https://openalex.org/W4238652859","https://openalex.org/W4239891004","https://openalex.org/W4294237812","https://openalex.org/W4304943069","https://openalex.org/W4313352664","https://openalex.org/W4320477365","https://openalex.org/W4387140791","https://openalex.org/W4387789400","https://openalex.org/W4393353088","https://openalex.org/W4399423442","https://openalex.org/W4399451510","https://openalex.org/W4399701768","https://openalex.org/W4399701776","https://openalex.org/W4403937226","https://openalex.org/W4409290212","https://openalex.org/W4412093259","https://openalex.org/W6650207513","https://openalex.org/W6659784926","https://openalex.org/W6679845454","https://openalex.org/W6808932894"],"related_works":["https://openalex.org/W4286508873","https://openalex.org/W2185045523","https://openalex.org/W2175024588","https://openalex.org/W2007640890","https://openalex.org/W156969523","https://openalex.org/W184430638","https://openalex.org/W1982406023","https://openalex.org/W3031598356","https://openalex.org/W2729605695","https://openalex.org/W2052913792"],"abstract_inverted_index":{"Triangular":[0],"shapes":[1,100,143],"have":[2,94],"been":[3],"studied":[4],"from":[5],"different":[6,102],"perspectives":[7],"over":[8],"a":[9,50],"wide":[10],"temporal":[11],"frame":[12],"since":[13],"ancient":[14,54],"times.":[15],"Initially,":[16],"fundamental":[17],"theorems":[18],"were":[19],"formulated":[20],"to":[21,61],"demonstrate":[22],"their":[23,62],"geometrical":[24,41],"properties.":[25],"Philosophy":[26],"and":[27,56,98,114,125,164],"art":[28],"leveraged":[29],"the":[30,70,80,86,122,132,146,162],"peculiar":[31],"aspects":[32],"of":[33,73,140],"triangles":[34,47],"as":[35,83,152],"building":[36],"blocks":[37],"for":[38,101,158],"more":[39],"complex":[40],"shapes.":[42],"This":[43],"paper":[44],"will":[45,67,105,117,149],"review":[46],"by":[48,85,130],"adopting":[49],"multidisciplinary":[51],"approach,":[52],"recalling":[53],"science":[55],"Plato\u2019s":[57],"arguments":[58],"in":[59,76,155,161],"relation":[60],"connection":[63],"with":[64],"philosophy.":[65],"It":[66],"then":[68],"consider":[69],"artistic":[71],"utilization":[72],"triangles,":[74],"particularly":[75],"compositions":[77],"created":[78],"during":[79],"medieval":[81],"era,":[82],"exemplified":[84],"Cosmati":[87],"Italian":[88],"family\u2019s":[89],"masterpieces.":[90],"Various":[91],"scientific":[92],"environments":[93],"explored":[95],"triangular":[96,141],"2D":[97],"3D":[99],"purposes,":[103],"which":[104],"be":[106,118,150],"briefly":[107],"reviewed":[108],"here.":[109],"After":[110],"that,":[111],"Sierpi\u0144ski":[112,147],"geometry":[113,148],"its":[115,126],"properties":[116],"introduced,":[119],"focusing":[120],"on":[121],"equilateral":[123],"shape":[124],"internal":[127],"complexity":[128],"generated":[129],"subdividing":[131],"entire":[133],"triangle":[134],"into":[135],"smaller":[136],"sub-triangles.":[137],"Finally,":[138],"examples":[139],"planar":[142],"that":[144],"fulfill":[145],"presented":[151],"an":[153],"application":[154],"signal":[156],"processing":[157],"high-frequency":[159],"signals":[160],"microwave":[163],"millimeter-wave":[165],"range.":[166]},"counts_by_year":[{"year":2025,"cited_by_count":3}],"updated_date":"2026-10-14T16:39:01.820549","created_date":"2025-10-10T00:00:00"}