{"id":"https://openalex.org/W4411151712","doi":"https://doi.org/10.3390/sym17060902","title":"FGeo-Eval: Evaluation System for Plane Geometry Problem Solving","display_name":"FGeo-Eval: Evaluation System for Plane Geometry Problem Solving","publication_year":2025,"publication_date":"2025-06-07","ids":{"openalex":"https://openalex.org/W4411151712","doi":"https://doi.org/10.3390/sym17060902"},"language":"en","primary_location":{"id":"doi:10.3390/sym17060902","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17060902","pdf_url":"https://www.mdpi.com/2073-8994/17/6/902/pdf?version=1749286224","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/17/6/902/pdf?version=1749286224","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101074146","display_name":"Qike Huang","orcid":null},"institutions":[{"id":"https://openalex.org/I113940042","display_name":"Shanghai University","ror":"https://ror.org/006teas31","country_code":"CN","type":"education","lineage":["https://openalex.org/I113940042"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qike Huang","raw_affiliation_strings":["Institute of Artificial Intelligence, Shanghai University, Shanghai 200444, China"],"raw_orcid":"https://orcid.org/0009-0007-6016-7741","affiliations":[{"raw_affiliation_string":"Institute of Artificial Intelligence, Shanghai University, Shanghai 200444, China","institution_ids":["https://openalex.org/I113940042"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101865974","display_name":"Xiaokai Zhang","orcid":"https://orcid.org/0000-0002-5678-7485"},"institutions":[{"id":"https://openalex.org/I141962983","display_name":"Shanghai University of Engineering Science","ror":"https://ror.org/0557b9y08","country_code":"CN","type":"education","lineage":["https://openalex.org/I141962983"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaokai Zhang","raw_affiliation_strings":["School of Computer Engineering and Science, Shanghai University, Shanghai 200444, China"],"raw_orcid":"https://orcid.org/0000-0002-5678-7485","affiliations":[{"raw_affiliation_string":"School of Computer Engineering and Science, Shanghai University, Shanghai 200444, China","institution_ids":["https://openalex.org/I141962983"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028312989","display_name":"Na Zhu","orcid":"https://orcid.org/0009-0000-2513-7060"},"institutions":[{"id":"https://openalex.org/I113940042","display_name":"Shanghai University","ror":"https://ror.org/006teas31","country_code":"CN","type":"education","lineage":["https://openalex.org/I113940042"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Na Zhu","raw_affiliation_strings":["Institute of Artificial Intelligence, Shanghai University, Shanghai 200444, China"],"raw_orcid":"https://orcid.org/0009-0000-2513-7060","affiliations":[{"raw_affiliation_string":"Institute of Artificial Intelligence, Shanghai University, Shanghai 200444, China","institution_ids":["https://openalex.org/I113940042"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100865454","display_name":"Fangzhen Zhu","orcid":null},"institutions":[{"id":"https://openalex.org/I141962983","display_name":"Shanghai University of Engineering Science","ror":"https://ror.org/0557b9y08","country_code":"CN","type":"education","lineage":["https://openalex.org/I141962983"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Fangzhen Zhu","raw_affiliation_strings":["School of Computer Engineering and Science, Shanghai University, Shanghai 200444, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Engineering and Science, Shanghai University, Shanghai 200444, China","institution_ids":["https://openalex.org/I141962983"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066842145","display_name":"Tuo Leng","orcid":"https://orcid.org/0000-0002-2921-3291"},"institutions":[{"id":"https://openalex.org/I113940042","display_name":"Shanghai University","ror":"https://ror.org/006teas31","country_code":"CN","type":"education","lineage":["https://openalex.org/I113940042"]},{"id":"https://openalex.org/I141962983","display_name":"Shanghai University of Engineering Science","ror":"https://ror.org/0557b9y08","country_code":"CN","type":"education","lineage":["https://openalex.org/I141962983"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Tuo Leng","raw_affiliation_strings":["Institute of Artificial Intelligence, Shanghai University, Shanghai 200444, China","School of Computer Engineering and Science, Shanghai University, Shanghai 200444, China"],"raw_orcid":"https://orcid.org/0000-0002-2921-3291","affiliations":[{"raw_affiliation_string":"Institute of Artificial Intelligence, Shanghai University, Shanghai 200444, China","institution_ids":["https://openalex.org/I113940042"]},{"raw_affiliation_string":"School of Computer Engineering and Science, Shanghai University, Shanghai 200444, China","institution_ids":["https://openalex.org/I141962983"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5066842145"],"corresponding_institution_ids":["https://openalex.org/I113940042","https://openalex.org/I141962983"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.23786595,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"17","issue":"6","first_page":"902","last_page":"902"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9828000068664551,"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"}},"topics":[{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9828000068664551,"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/T10533","display_name":"Teaching and Learning Programming","score":0.9668999910354614,"subfield":{"id":"https://openalex.org/subfields/1706","display_name":"Computer Science Applications"},"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/T11450","display_name":"Model-Driven Software Engineering Techniques","score":0.9466000199317932,"subfield":{"id":"https://openalex.org/subfields/1712","display_name":"Software"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.6676244139671326},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4980621337890625},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.44299110770225525},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.35599133372306824}],"concepts":[{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.6676244139671326},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4980621337890625},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.44299110770225525},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.35599133372306824}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3390/sym17060902","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17060902","pdf_url":"https://www.mdpi.com/2073-8994/17/6/902/pdf?version=1749286224","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.3390/sym17060902","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17060902","pdf_url":"https://www.mdpi.com/2073-8994/17/6/902/pdf?version=1749286224","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4772063613","display_name":"\u82e5\u5e72\u79bb\u6563\u51e0\u4f55\u95ee\u9898\u53ca\u53cd\u95ee\u9898\u7684\u673a\u5668\u8bc1\u660e\u4e0e\u53ef\u89e3\u91ca\u6027\u7814\u7a76","funder_award_id":"12071282","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4411151712.pdf","grobid_xml":"https://content.openalex.org/works/W4411151712.grobid-xml"},"referenced_works_count":40,"referenced_works":["https://openalex.org/W7934914","https://openalex.org/W27914859","https://openalex.org/W109897293","https://openalex.org/W1479887426","https://openalex.org/W2068101968","https://openalex.org/W2077378514","https://openalex.org/W2079751248","https://openalex.org/W2084007313","https://openalex.org/W2091926481","https://openalex.org/W2134647504","https://openalex.org/W2160410991","https://openalex.org/W2250564385","https://openalex.org/W2359541546","https://openalex.org/W2667333411","https://openalex.org/W2740314591","https://openalex.org/W2757050214","https://openalex.org/W2898429904","https://openalex.org/W2898599002","https://openalex.org/W2965735863","https://openalex.org/W2979899153","https://openalex.org/W3173260995","https://openalex.org/W3176186248","https://openalex.org/W3176371077","https://openalex.org/W4225105060","https://openalex.org/W4312834975","https://openalex.org/W4385572160","https://openalex.org/W4385572852","https://openalex.org/W4385768252","https://openalex.org/W4388190426","https://openalex.org/W4389520727","https://openalex.org/W4390940921","https://openalex.org/W4393357623","https://openalex.org/W4393871228","https://openalex.org/W4393993850","https://openalex.org/W4399937324","https://openalex.org/W4401024948","https://openalex.org/W4402670709","https://openalex.org/W4402774456","https://openalex.org/W4405737871","https://openalex.org/W6798353961"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027"],"abstract_inverted_index":{"Plane":[0],"geometry":[1,70,200],"problem":[2,71,89,115,156],"solving":[3],"has":[4,32],"been":[5],"a":[6,64,88,106],"long-term":[7],"challenge":[8],"in":[9],"mathematical":[10],"reasoning":[11,111,201],"and":[12,28,38,52,73,105,117,126,145,158,209],"symbolic":[13],"artificial":[14],"intelligence.":[15],"With":[16,162],"the":[17,23,75,133,151,163,166,175,184],"continued":[18],"advancement":[19],"of":[20,212],"automated":[21],"methods,":[22],"need":[24],"for":[25,36,68,174,197,206],"large-scale":[26],"datasets":[27],"rigorous":[29],"evaluation":[30,55,66,85],"frameworks":[31],"become":[33],"increasingly":[34],"critical":[35],"benchmarking":[37],"guiding":[39,210],"system":[40,67,86,121],"development.":[41],"However,":[42],"existing":[43],"resources":[44],"often":[45],"lack":[46],"sufficient":[47],"scale,":[48],"systematic":[49],"difficulty":[50,107,124,157,172],"modeling,":[51],"quantifiable,":[53],"process-based":[54],"metrics.":[56],"To":[57],"address":[58],"these":[59],"limitations,":[60],"we":[61],"propose":[62],"FGeo-Eval,":[63],"comprehensive":[65],"plane":[69,199],"solving,":[72],"introduce":[74],"FormalGeo30K":[76,131],"dataset,":[77,165],"an":[78],"extended":[79],"dataset":[80,134],"derived":[81],"from":[82,179,188],"FormalGeo7K.":[83],"The":[84],"includes":[87],"completion":[90],"rate":[91,169],"metric":[92],"PCR":[93,186],"to":[94,101,135,181,190],"assess":[95,159],"partial":[96],"progress,":[97],"theorem":[98],"weight":[99],"computation":[100],"quantify":[102],"knowledge":[103],"importance,":[104],"coefficient":[108],"based":[109],"on":[110],"complexity.":[112],"By":[113],"analyzing":[114],"structures":[116],"solution":[118],"dependencies,":[119],"this":[120],"enables":[122],"fine-grained":[123],"stratification":[125],"objective":[127],"performance":[128],"measurement.":[129],"Concurrently,":[130],"expands":[132],"30,540":[136],"formally":[137],"annotated":[138],"problems,":[139],"supporting":[140],"more":[141],"robust":[142],"model":[143,177,207],"training":[144],"evaluation.":[146],"Experimental":[147],"results":[148],"demonstrate":[149],"that":[150],"proposed":[152],"metrics":[153],"effectively":[154],"evaluate":[155],"solver":[160],"capabilities.":[161],"augmented":[164],"average":[167,185],"success":[168],"across":[170],"all":[171],"levels":[173],"FGeo-HyperGNet":[176],"increases":[178,187],"77.43%":[180],"85.01%,":[182],"while":[183],"88.57%":[189],"91.79%.":[191],"These":[192],"contributions":[193],"provide":[194],"essential":[195],"infrastructure":[196],"advancing":[198],"systems,":[202],"offering":[203],"standardized":[204],"benchmarks":[205],"development":[208],"optimization":[211],"geometry-solving":[213],"models.":[214]},"counts_by_year":[],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}