{"id":"https://openalex.org/W3112806242","doi":"https://doi.org/10.1080/00029890.2020.1825588","title":"Using Embedding Diagrams to Visualize Curvature","display_name":"Using Embedding Diagrams to Visualize Curvature","publication_year":2020,"publication_date":"2020-11-25","ids":{"openalex":"https://openalex.org/W3112806242","doi":"https://doi.org/10.1080/00029890.2020.1825588","mag":"3112806242"},"language":"en","primary_location":{"id":"doi:10.1080/00029890.2020.1825588","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.2020.1825588","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/A5018652045","display_name":"Tevian Dray","orcid":"https://orcid.org/0000-0001-8692-7963"},"institutions":[{"id":"https://openalex.org/I131249849","display_name":"Oregon State University","ror":"https://ror.org/00ysfqy60","country_code":"US","type":"education","lineage":["https://openalex.org/I131249849"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Tevian Dray","raw_affiliation_strings":["Department of Mathematics, Oregon State University","Department of Mathematics, Oregon State University, Corvallis, OR 97331"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Oregon State University","institution_ids":["https://openalex.org/I131249849"]},{"raw_affiliation_string":"Department of Mathematics, Oregon State University, Corvallis, OR 97331","institution_ids":["https://openalex.org/I131249849"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5018652045"],"corresponding_institution_ids":["https://openalex.org/I131249849"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.2659715,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"127","issue":"10","first_page":"867","last_page":"879"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.9983000159263611,"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":0.9983000159263611,"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":0.991599977016449,"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"}},{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.958899974822998,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/embedding","display_name":"Embedding","score":0.8003674745559692},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.7710409164428711},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.5198019742965698},{"id":"https://openalex.org/keywords/schwarzschild-radius","display_name":"Schwarzschild radius","score":0.48482242226600647},{"id":"https://openalex.org/keywords/diagram","display_name":"Diagram","score":0.44807836413383484},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.40653544664382935},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.4024249315261841},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3915793001651764},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2912237346172333},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.249471515417099},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.20369237661361694},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.11569184064865112},{"id":"https://openalex.org/keywords/gravitation","display_name":"Gravitation","score":0.11463585495948792}],"concepts":[{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.8003674745559692},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.7710409164428711},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.5198019742965698},{"id":"https://openalex.org/C115304011","wikidata":"https://www.wikidata.org/wiki/Q72755","display_name":"Schwarzschild radius","level":3,"score":0.48482242226600647},{"id":"https://openalex.org/C186399060","wikidata":"https://www.wikidata.org/wiki/Q959962","display_name":"Diagram","level":2,"score":0.44807836413383484},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.40653544664382935},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.4024249315261841},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3915793001651764},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2912237346172333},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.249471515417099},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.20369237661361694},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.11569184064865112},{"id":"https://openalex.org/C124017977","wikidata":"https://www.wikidata.org/wiki/Q11412","display_name":"Gravitation","level":2,"score":0.11463585495948792},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00029890.2020.1825588","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.2020.1825588","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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W165787586","https://openalex.org/W225012726","https://openalex.org/W619507912","https://openalex.org/W1667086166","https://openalex.org/W1916666649","https://openalex.org/W1969173702","https://openalex.org/W1977702809","https://openalex.org/W1991551016","https://openalex.org/W2033551585","https://openalex.org/W2060745302","https://openalex.org/W2114722947","https://openalex.org/W2127765040","https://openalex.org/W2135318662","https://openalex.org/W2259370121","https://openalex.org/W2480735324","https://openalex.org/W3098361935","https://openalex.org/W3103820297","https://openalex.org/W3108917569","https://openalex.org/W3145411641","https://openalex.org/W4249224101"],"related_works":["https://openalex.org/W2081900870","https://openalex.org/W2739424431","https://openalex.org/W4366702998","https://openalex.org/W2952218778","https://openalex.org/W4298061302","https://openalex.org/W4241212870","https://openalex.org/W2067832842","https://openalex.org/W2594050709","https://openalex.org/W2474734932","https://openalex.org/W55883722"],"abstract_inverted_index":{"We":[0,25],"give":[1],"an":[2,22],"elementary":[3],"treatment":[4],"of":[5,8,10,15,30,45],"the":[6,13,43,46],"curvature":[7,31],"surfaces":[9],"revolution":[11],"in":[12],"language":[14],"vector":[16],"calculus,":[17],"using":[18,32],"differentials":[19],"rather":[20],"than":[21],"explicit":[23],"parameterization.":[24],"illustrate":[26],"some":[27],"basic":[28],"features":[29],"embedding":[33],"diagrams,":[34],"and":[35],"then":[36],"use":[37],"such":[38],"a":[39],"diagram":[40],"to":[41],"analyze":[42],"geometry":[44],"Schwarzschild":[47],"black":[48],"hole.":[49]},"counts_by_year":[],"updated_date":"2026-03-07T13:37:22.277990","created_date":"2025-10-10T00:00:00"}