{"id":"https://openalex.org/W2035891306","doi":"https://doi.org/10.1145/585905.585915","title":"Lines through a cure and tic-tac-toe","display_name":"Lines through a cure and tic-tac-toe","publication_year":1972,"publication_date":"1972-09-01","ids":{"openalex":"https://openalex.org/W2035891306","doi":"https://doi.org/10.1145/585905.585915","mag":"2035891306"},"language":"en","primary_location":{"id":"doi:10.1145/585905.585915","is_oa":true,"landing_page_url":"https://doi.org/10.1145/585905.585915","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/585905.585915","source":{"id":"https://openalex.org/S4210186172","display_name":"ACM SIGAPL APL Quote Quad","issn_l":"0163-6006","issn":["0163-6006","1558-3392"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM SIGAPL APL Quote Quad","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://dl.acm.org/doi/pdf/10.1145/585905.585915","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5040406257","display_name":"K. W. Smillie","orcid":null},"institutions":[{"id":"https://openalex.org/I154425047","display_name":"University of Alberta","ror":"https://ror.org/0160cpw27","country_code":"CA","type":"education","lineage":["https://openalex.org/I154425047"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"K. W. Smillie","raw_affiliation_strings":["University of Alberta, Edmonton, Alberta","University of Alberta. Edmonton. Alberta"],"affiliations":[{"raw_affiliation_string":"University of Alberta, Edmonton, Alberta","institution_ids":["https://openalex.org/I154425047"]},{"raw_affiliation_string":"University of Alberta. Edmonton. Alberta","institution_ids":["https://openalex.org/I154425047"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5040406257"],"corresponding_institution_ids":["https://openalex.org/I154425047"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.23320158,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"4","issue":"1","first_page":"18","last_page":"28"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9743000268936157,"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":0.9743000268936157,"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/T12504","display_name":"Mathematics and Applications","score":0.9664000272750854,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9401999711990356,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/transpose","display_name":"Transpose","score":0.895756721496582},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.7955977916717529},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.7132607698440552},{"id":"https://openalex.org/keywords/cube","display_name":"Cube (algebra)","score":0.6180371046066284},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5525420904159546},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.49542343616485596},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.35681208968162537},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3069996237754822},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.28445661067962646},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.18483403325080872},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13960498571395874},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.08902207016944885},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.06321576237678528},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.05157718062400818}],"concepts":[{"id":"https://openalex.org/C200106649","wikidata":"https://www.wikidata.org/wiki/Q223683","display_name":"Transpose","level":3,"score":0.895756721496582},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.7955977916717529},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.7132607698440552},{"id":"https://openalex.org/C53051483","wikidata":"https://www.wikidata.org/wiki/Q861555","display_name":"Cube (algebra)","level":2,"score":0.6180371046066284},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5525420904159546},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.49542343616485596},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.35681208968162537},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3069996237754822},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.28445661067962646},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.18483403325080872},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13960498571395874},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.08902207016944885},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.06321576237678528},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.05157718062400818},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/585905.585915","is_oa":true,"landing_page_url":"https://doi.org/10.1145/585905.585915","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/585905.585915","source":{"id":"https://openalex.org/S4210186172","display_name":"ACM SIGAPL APL Quote Quad","issn_l":"0163-6006","issn":["0163-6006","1558-3392"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM SIGAPL APL Quote Quad","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1145/585905.585915","is_oa":true,"landing_page_url":"https://doi.org/10.1145/585905.585915","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/585905.585915","source":{"id":"https://openalex.org/S4210186172","display_name":"ACM SIGAPL APL Quote Quad","issn_l":"0163-6006","issn":["0163-6006","1558-3392"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM SIGAPL APL Quote Quad","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2035891306.pdf","grobid_xml":"https://content.openalex.org/works/W2035891306.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W2046856528"],"related_works":["https://openalex.org/W2003786218","https://openalex.org/W4313549635","https://openalex.org/W2376104713","https://openalex.org/W2356636683","https://openalex.org/W4205331489","https://openalex.org/W4385493077","https://openalex.org/W2009510026","https://openalex.org/W2189595417","https://openalex.org/W201246341","https://openalex.org/W2176391467"],"abstract_inverted_index":{"This":[0],"paper":[1],"discusses":[2],"the":[3,6,12,18,37],"use":[4],"of":[5,20,27,39],"primitive":[7],"transpose":[8],"function":[9],"to":[10],"enumerate":[11],"76":[13],"diagonal":[14],"lines":[15,29],"passing":[16],"through":[17],"cells":[19],"a":[21,40,48],"4\u00d74\u00d74":[22],"cube.":[23],"Some":[24],"simple":[25,41],"properties":[26],"these":[28],"are":[30,34],"derived.":[31],"The":[32],"results":[33],"used":[35],"for":[36,43],"construction":[38],"algorithm":[42],"playing":[44],"three-dimensional":[45],"tic-tac-toe":[46],"with":[47],"computer":[49],"and":[50],"its":[51],"implementation":[52],"in":[53],"APL\\360.":[54]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
