{"id":"https://openalex.org/W3019721189","doi":"https://doi.org/10.1080/00029890.2020.1722019","title":"The Inverse Caustic Problem","display_name":"The Inverse Caustic Problem","publication_year":2020,"publication_date":"2020-04-23","ids":{"openalex":"https://openalex.org/W3019721189","doi":"https://doi.org/10.1080/00029890.2020.1722019","mag":"3019721189"},"language":"en","primary_location":{"id":"doi:10.1080/00029890.2020.1722019","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.2020.1722019","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/A5051847827","display_name":"Norbert Hungerb\u00fchler","orcid":"https://orcid.org/0000-0001-6191-0022"},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":true,"raw_author_name":"Norbert Hungerb\u00fchler","raw_affiliation_strings":["Department of Mathematics, ETH Z\u00fcrich","Department of Mathematics, ETH Z\u00fcrich, 8092 Z\u00fcrich, Switzerland"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, ETH Z\u00fcrich","institution_ids":["https://openalex.org/I35440088"]},{"raw_affiliation_string":"Department of Mathematics, ETH Z\u00fcrich, 8092 Z\u00fcrich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5051847827"],"corresponding_institution_ids":["https://openalex.org/I35440088"],"apc_list":null,"apc_paid":null,"fwci":0.3852,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.55401722,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"127","issue":"5","first_page":"387","last_page":"400"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.9965000152587891,"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":0.9965000152587891,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9876999855041504,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"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":0.9703999757766724,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/caustic","display_name":"Caustic (mathematics)","score":0.9878903031349182},{"id":"https://openalex.org/keywords/string","display_name":"String (physics)","score":0.6184555292129517},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.5219718217849731},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4573303163051605},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.44821611046791077},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4412737190723419},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.35396409034729004},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2761490046977997},{"id":"https://openalex.org/keywords/theoretical-physics","display_name":"Theoretical physics","score":0.2597656548023224}],"concepts":[{"id":"https://openalex.org/C2779567845","wikidata":"https://www.wikidata.org/wiki/Q3492725","display_name":"Caustic (mathematics)","level":2,"score":0.9878903031349182},{"id":"https://openalex.org/C157486923","wikidata":"https://www.wikidata.org/wiki/Q1376436","display_name":"String (physics)","level":2,"score":0.6184555292129517},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.5219718217849731},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4573303163051605},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.44821611046791077},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4412737190723419},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.35396409034729004},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2761490046977997},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.2597656548023224},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00029890.2020.1722019","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.2020.1722019","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":[{"id":"https://metadata.un.org/sdg/11","score":0.5899999737739563,"display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W388188966","https://openalex.org/W563274145","https://openalex.org/W1981048687","https://openalex.org/W2052642155","https://openalex.org/W2074006886","https://openalex.org/W2326794987","https://openalex.org/W2901140998","https://openalex.org/W2962730580","https://openalex.org/W2962879977","https://openalex.org/W4238671068","https://openalex.org/W4302082819"],"related_works":["https://openalex.org/W2275922919","https://openalex.org/W2116544824","https://openalex.org/W2019997658","https://openalex.org/W2119139662","https://openalex.org/W2332325091","https://openalex.org/W3123729244","https://openalex.org/W2618423235","https://openalex.org/W1507928521","https://openalex.org/W2295362318","https://openalex.org/W2089249808"],"abstract_inverted_index":{"For":[0],"a":[1,14,23,28,59,65],"family":[2],"of":[3,12,40,64],"parallel":[4],"incoming":[5],"light":[6],"rays,":[7],"we":[8],"consider":[9],"the":[10,37,41,62],"problem":[11],"finding":[13],"reflecting":[15],"curve":[16,25,42],"\u0393":[17,33,43],"that":[18],"has":[19],"as":[20],"its":[21,47],"caustic":[22],"given":[24],"\u03b3.":[26],"First,":[27],"geometric":[29],"string":[30],"construction":[31],"for":[32],"is":[34,44],"presented.":[35],"Then":[36],"differential":[38],"equation":[39],"derived":[45],"and":[46,58],"analytical":[48],"properties":[49],"are":[50],"discussed.":[51],"We":[52],"conclude":[53],"with":[54],"two":[55],"concrete":[56],"examples,":[57],"remark":[60],"about":[61],"cusps":[63],"caustic.":[66]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2026-02-01T03:34:12.195049","created_date":"2025-10-10T00:00:00"}
