{"id":"https://openalex.org/W2045935043","doi":"https://doi.org/10.1007/s00454-002-0748-5","title":"Congruence by Dissection of Topological Discs\u2014An Elementary Approach to Tarski's Circle Squaring Problem","display_name":"Congruence by Dissection of Topological Discs\u2014An Elementary Approach to Tarski's Circle Squaring Problem","publication_year":2002,"publication_date":"2002-08-01","ids":{"openalex":"https://openalex.org/W2045935043","doi":"https://doi.org/10.1007/s00454-002-0748-5","mag":"2045935043"},"language":"en","primary_location":{"id":"doi:10.1007/s00454-002-0748-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-002-0748-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-002-0748-5.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete & Computational Geometry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://link.springer.com/content/pdf/10.1007/s00454-002-0748-5.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5097639896","display_name":"Richter","orcid":null},"institutions":[{"id":"https://openalex.org/I76198965","display_name":"Friedrich Schiller University Jena","ror":"https://ror.org/05qpz1x62","country_code":"DE","type":"education","lineage":["https://openalex.org/I76198965"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Richter","raw_affiliation_strings":["Mathematisches Institut, Friedrich-Schiller-Universit\u00e4t Jena, D-07740 Jena, Germany richterc@minet.uni-jena.de, Germany","University of Jena"],"affiliations":[{"raw_affiliation_string":"Mathematisches Institut, Friedrich-Schiller-Universit\u00e4t Jena, D-07740 Jena, Germany richterc@minet.uni-jena.de, Germany","institution_ids":["https://openalex.org/I76198965"]},{"raw_affiliation_string":"University of Jena","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5097639896"],"corresponding_institution_ids":["https://openalex.org/I76198965"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":0.501,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.6205574,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"28","issue":"3","first_page":"427","last_page":"442"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.9941999912261963,"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":0.9941999912261963,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.9883999824523926,"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/T12170","display_name":"History and Theory of Mathematics","score":0.98089998960495,"subfield":{"id":"https://openalex.org/subfields/2614","display_name":"Theoretical Computer Science"},"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/mathematics","display_name":"Mathematics","score":0.8604676723480225},{"id":"https://openalex.org/keywords/congruence","display_name":"Congruence (geometry)","score":0.7245738506317139},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5836824178695679},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.5359559655189514},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5270056128501892},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.4665507972240448},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4118787944316864},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.40660563111305237},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.22052091360092163},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2164013385772705}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8604676723480225},{"id":"https://openalex.org/C132074034","wikidata":"https://www.wikidata.org/wiki/Q154210","display_name":"Congruence (geometry)","level":2,"score":0.7245738506317139},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5836824178695679},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.5359559655189514},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5270056128501892},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.4665507972240448},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4118787944316864},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.40660563111305237},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.22052091360092163},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2164013385772705}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00454-002-0748-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-002-0748-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-002-0748-5.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete & Computational Geometry","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s00454-002-0748-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-002-0748-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-002-0748-5.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete & Computational Geometry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2045935043.pdf","grobid_xml":"https://content.openalex.org/works/W2045935043.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W212595457","https://openalex.org/W1497035321","https://openalex.org/W2294079176"],"related_works":["https://openalex.org/W2388471861","https://openalex.org/W2354789018","https://openalex.org/W2391316944","https://openalex.org/W2065462305","https://openalex.org/W4380684998","https://openalex.org/W4226251895","https://openalex.org/W2988866178","https://openalex.org/W4286857063","https://openalex.org/W3040895870","https://openalex.org/W2794564760"],"abstract_inverted_index":null,"counts_by_year":[{"year":2017,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}