{"id":"https://openalex.org/W4408053042","doi":"https://doi.org/10.3390/axioms14030182","title":"An Overview of \u03c0 and Euler Numbers, Including Their History, Relevance, and Current and Future Applications","display_name":"An Overview of \u03c0 and Euler Numbers, Including Their History, Relevance, and Current and Future Applications","publication_year":2025,"publication_date":"2025-02-28","ids":{"openalex":"https://openalex.org/W4408053042","doi":"https://doi.org/10.3390/axioms14030182"},"language":"en","primary_location":{"id":"doi:10.3390/axioms14030182","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14030182","pdf_url":"https://www.mdpi.com/2075-1680/14/3/182/pdf?version=1740756755","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"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":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/14/3/182/pdf?version=1740756755","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5055427739","display_name":"Juli\u00e1n Roa Gonz\u00e1lez","orcid":"https://orcid.org/0000-0002-4017-3067"},"institutions":[{"id":"https://openalex.org/I4210108168","display_name":"Universidad a Distancia de Madrid","ror":"https://ror.org/01r9skd65","country_code":"ES","type":"education","lineage":["https://openalex.org/I4210108168"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Juli\u00e1n Roa Gonz\u00e1lez","raw_affiliation_strings":["Department of Mathematics and Education, Universidad a Distancia de Madrid, 28400 Madrid, Spain"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Education, Universidad a Distancia de Madrid, 28400 Madrid, Spain","institution_ids":["https://openalex.org/I4210108168"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5116462298","display_name":"Yanko Ord\u00f3\u00f1ez","orcid":null},"institutions":[{"id":"https://openalex.org/I4210108168","display_name":"Universidad a Distancia de Madrid","ror":"https://ror.org/01r9skd65","country_code":"ES","type":"education","lineage":["https://openalex.org/I4210108168"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Yanko Ord\u00f3\u00f1ez","raw_affiliation_strings":["Department of Mathematics and Education, Universidad a Distancia de Madrid, 28400 Madrid, Spain"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Education, Universidad a Distancia de Madrid, 28400 Madrid, Spain","institution_ids":["https://openalex.org/I4210108168"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5116462299","display_name":"Silvia L\u00f3pez Araque","orcid":null},"institutions":[{"id":"https://openalex.org/I4210108168","display_name":"Universidad a Distancia de Madrid","ror":"https://ror.org/01r9skd65","country_code":"ES","type":"education","lineage":["https://openalex.org/I4210108168"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Silvia L\u00f3pez Araque","raw_affiliation_strings":["Department of Mathematics and Education, Universidad a Distancia de Madrid, 28400 Madrid, Spain"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Education, Universidad a Distancia de Madrid, 28400 Madrid, Spain","institution_ids":["https://openalex.org/I4210108168"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5049719217","display_name":"Jos\u00e9 Luis D\u00edaz Palencia","orcid":"https://orcid.org/0000-0002-4677-0970"},"institutions":[{"id":"https://openalex.org/I4210108168","display_name":"Universidad a Distancia de Madrid","ror":"https://ror.org/01r9skd65","country_code":"ES","type":"education","lineage":["https://openalex.org/I4210108168"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Jos\u00e9 Luis D\u00edaz Palencia","raw_affiliation_strings":["Department of Mathematics and Education, Universidad a Distancia de Madrid, 28400 Madrid, Spain"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Education, Universidad a Distancia de Madrid, 28400 Madrid, Spain","institution_ids":["https://openalex.org/I4210108168"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5049719217","https://openalex.org/A5055427739"],"corresponding_institution_ids":["https://openalex.org/I4210108168"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.07590865,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":"3","first_page":"182","last_page":"182"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11428","display_name":"Advanced Mathematical Identities","score":0.9945999979972839,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T11428","display_name":"Advanced Mathematical Identities","score":0.9945999979972839,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T11191","display_name":"Mathematical functions and polynomials","score":0.9254000186920166,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11564","display_name":"Mathematical Inequalities and Applications","score":0.9103999733924866,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/relevance","display_name":"Relevance (law)","score":0.6624079942703247},{"id":"https://openalex.org/keywords/current","display_name":"Current (fluid)","score":0.6563926935195923},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3657323122024536},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.21061739325523376},{"id":"https://openalex.org/keywords/political-science","display_name":"Political science","score":0.1515716314315796},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.06170135736465454}],"concepts":[{"id":"https://openalex.org/C158154518","wikidata":"https://www.wikidata.org/wiki/Q7310970","display_name":"Relevance (law)","level":2,"score":0.6624079942703247},{"id":"https://openalex.org/C148043351","wikidata":"https://www.wikidata.org/wiki/Q4456944","display_name":"Current (fluid)","level":2,"score":0.6563926935195923},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3657323122024536},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.21061739325523376},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.1515716314315796},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.06170135736465454},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms14030182","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14030182","pdf_url":"https://www.mdpi.com/2075-1680/14/3/182/pdf?version=1740756755","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"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":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:84610ec0708f42d19b4f52c7fd3eec60","is_oa":true,"landing_page_url":"https://doaj.org/article/84610ec0708f42d19b4f52c7fd3eec60","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 14, Iss 3, p 182 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms14030182","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14030182","pdf_url":"https://www.mdpi.com/2075-1680/14/3/182/pdf?version=1740756755","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"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":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4408053042.pdf"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W177399353","https://openalex.org/W1484326688","https://openalex.org/W1847162973","https://openalex.org/W1997093580","https://openalex.org/W2007185418","https://openalex.org/W2009463420","https://openalex.org/W2061171222","https://openalex.org/W2158816536","https://openalex.org/W2333976070","https://openalex.org/W2494624149","https://openalex.org/W2914659449","https://openalex.org/W4239679971","https://openalex.org/W4248269519","https://openalex.org/W4251103229","https://openalex.org/W6608815102","https://openalex.org/W6630755352","https://openalex.org/W6651275012","https://openalex.org/W7037106178"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W2390279801","https://openalex.org/W4391913857","https://openalex.org/W2358668433","https://openalex.org/W4396701345","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W4396696052"],"abstract_inverted_index":{"The":[0,105],"mathematical":[1,26,87,103,126],"constant":[2],"\u03c0":[3,46,108],"and":[4,25,40,47,61,74,89,92,109,116],"Euler":[5,48,110],"numbers":[6,49,80,111],"En":[7],"have":[8,50],"long":[9],"been":[10],"of":[11,16,34,82,107],"relevance":[12,84],"in":[13,19,53,85,101,124],"various":[14],"branches":[15],"mathematics,":[17],"particularly":[18],"number":[20],"theory,":[21],"combinatorics,":[22],"numerical":[23,62],"analysis,":[24],"physics.":[27],"This":[28],"review":[29],"article":[30],"introduces":[31],"an":[32],"exploration":[33],"their":[35,71,90,98,122],"historical":[36],"evolution,":[37],"theoretical":[38],"foundations,":[39],"recent":[41],"advancements.":[42],"We":[43,64],"examine":[44],"how":[45],"facilitated":[51],"advances":[52],"different":[54],"scientific":[55],"areas":[56],"like":[57,118],"quantum":[58],"field":[59],"theory":[60],"algorithms.":[63],"introduce":[65],"some":[66],"emerging":[67],"perspectives":[68],"that":[69],"highlight":[70],"interdisciplinary":[72],"applications":[73],"potential":[75,123],"future":[76,102],"trajectories.":[77],"Certainly,":[78],"both":[79],"are":[81],"great":[83],"current":[86],"research,":[88],"adaptability":[91],"ubiquity":[93],"will":[94],"continue":[95],"to":[96],"ensure":[97],"continuous":[99],"appearance":[100],"discoveries.":[104],"integration":[106],"into":[112],"advanced":[113],"computational":[114],"techniques":[115],"fields":[117],"artificial":[119],"intelligence":[120],"exemplifies":[121],"driving":[125],"innovation.":[127]},"counts_by_year":[],"updated_date":"2025-12-19T19:40:27.379048","created_date":"2025-03-01T00:00:00"}
