{"id":"https://openalex.org/W2397614047","doi":"https://doi.org/10.4169/amer.math.monthly.121.01.018","title":"On Equidistant Sets and Generalized Conics: The Old and the New","display_name":"On Equidistant Sets and Generalized Conics: The Old and the New","publication_year":2013,"publication_date":"2013-12-08","ids":{"openalex":"https://openalex.org/W2397614047","doi":"https://doi.org/10.4169/amer.math.monthly.121.01.018","mag":"2397614047"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.4169/amer.math.monthly.121.01.018","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":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"journal-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/A5102722643","display_name":"Mario Ponce","orcid":"https://orcid.org/0000-0002-6617-3145"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"None Mario Ponce","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5113488396","display_name":"Patricio Santib\u00e1\u00f1ez","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"None Patricio Santib\u00e1\u00f1ez","raw_affiliation_strings":[],"affiliations":[]}],"institution_assertions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.851,"has_fulltext":true,"fulltext_origin":"ngrams","cited_by_count":15,"citation_normalized_percentile":{"value":0.879185,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":89},"biblio":{"volume":"121","issue":"1","first_page":"18","last_page":"18"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T12504","display_name":"Foundations of Geometric Mathematics","score":0.9959,"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":"Foundations of Geometric Mathematics","score":0.9959,"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":"Isogeometric Analysis in Computational Engineering","score":0.9883,"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/T10996","display_name":"Mesh Generation Algorithms","score":0.9845,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/equidistant","display_name":"Equidistant","score":0.9628399},{"id":"https://openalex.org/keywords/conic-section","display_name":"Conic section","score":0.630662},{"id":"https://openalex.org/keywords/computational-geometry","display_name":"Computational Geometry","score":0.490951}],"concepts":[{"id":"https://openalex.org/C158245278","wikidata":"https://www.wikidata.org/wiki/Q4386982","display_name":"Equidistant","level":2,"score":0.9628399},{"id":"https://openalex.org/C108598597","wikidata":"https://www.wikidata.org/wiki/Q124255","display_name":"Conic section","level":2,"score":0.630662},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.52250224},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.445788},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4436122},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.4407036},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.42503273},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.42351857},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.34819937},{"id":"https://openalex.org/C145420912","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics education","level":1,"score":0.34554446},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3238924},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2918777},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.21525714},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.4169/amer.math.monthly.121.01.018","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":null,"is_accepted":false,"is_published":false}],"best_oa_location":null,"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":12,"referenced_works":["https://openalex.org/W1603515630","https://openalex.org/W1974689301","https://openalex.org/W1984358176","https://openalex.org/W1995148792","https://openalex.org/W2012588304","https://openalex.org/W2041449763","https://openalex.org/W2047568926","https://openalex.org/W2062547374","https://openalex.org/W2285371954","https://openalex.org/W2548798027","https://openalex.org/W2565817293","https://openalex.org/W4240893236"],"related_works":["https://openalex.org/W2836992267","https://openalex.org/W2528752197","https://openalex.org/W2385837322","https://openalex.org/W2373708349","https://openalex.org/W2370379095","https://openalex.org/W2313824579","https://openalex.org/W2122029179","https://openalex.org/W2075445622","https://openalex.org/W2064284991","https://openalex.org/W2055230676"],"abstract_inverted_index":{"AbstractThis":[0],"article":[1],"is":[2,165,196,212],"devoted":[3],"to":[4,215],"the":[5,17,29,104,129,149,158,170,186,190,201,206],"study":[6],"of":[7,22,28,68,74,91,108,160,203,205],"classical":[8,109],"and":[9,19,40,145,184],"new":[10,44],"results":[11],"concerning":[12],"equidistant":[13,50,69,86,117],"sets,":[14],"both":[15],"from":[16,114,128,137,148],"topological":[18],"metric":[20],"point":[21],"view.":[23],"We":[24,58],"include":[25],"a":[26,82,93,217],"review":[27],"most":[30],"interesting":[31],"known":[32],"facts":[33],"about":[34,65],"these":[35,99],"sets":[36,51,70,87],"in":[37,84,133,143,155,181,200],"Euclidean":[38],"space":[39],"we":[41,47,80,101],"prove":[42,60],"two":[43],"results.":[45],"First,":[46],"show":[48,102],"that":[49,71,103],"vary":[52],"continuously":[53],"with":[54],"their":[55],"focal":[56],"sets.":[57,118],"also":[59],"an":[61,166,197],"error":[62],"estimate":[63],"result":[64],"approximative":[66],"versions":[67],"should":[72],"be":[73,89,112],"interest":[75],"for":[76,96,189,221],"computer":[77],"simulations.":[78],"Moreover,":[79],"offer":[81],"viewpoint":[83],"which":[85],"can":[88,111],"thought":[90],"as":[92],"natural":[94],"generalization":[95],"conics.":[97],"Along":[98],"lines,":[100],"main":[105,176],"geometric":[106],"features":[107],"conics":[110],"retrieved":[113],"more":[115],"general":[116],"Additional":[119],"informationNotes":[120],"on":[121],"contributorsMario":[122],"PonceMARIO":[123],"PONCE":[124],"received":[125],"his":[126,135,146],"B.A.":[127],"Universidad":[130,171,207],"de":[131,140,173,209],"Chile":[132],"2001,":[134],"Mestrado":[136],"IMPA":[138],"(Rio":[139],"Janeiro,":[141],"Brazil)":[142],"2003,":[144],"Doctorat":[147],"Universit\u00e9":[150],"Paris":[151],"Sud":[152],"(Orsay,":[153],"France)":[154],"2007,":[156],"under":[157],"supervision":[159],"Jean-Christophe":[161],"Yoccoz.":[162],"Currently":[163],"he":[164],"assistant":[167],"professor":[168],"at":[169],"Cat\u00f3lica":[172,208],"Chile.":[174,210],"His":[175],"mathematical":[177,192],"interests":[178],"are":[179],"research":[180],"dynamical":[182],"systems":[183],"coordinating":[185],"academic":[187],"committee":[188],"Chilean":[191],"olympiad.Patricio":[193],"Santib\u00e1\u00f1ezPATRICIO":[194],"SANTIB\u00c1\u00d1EZ":[195],"undergraduate":[198],"student":[199],"faculty":[202],"mathematics":[204],"He":[211],"preparing":[213],"himself":[214],"become":[216],"very":[218],"good":[219],"teacher":[220],"secondary":[222],"students.":[223]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W2397614047","counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":2},{"year":2014,"cited_by_count":1}],"updated_date":"2024-11-18T12:57:05.098052","created_date":"2016-06-24"}