View source for Triangulation

==English==
{{was wotd|2019|March|3}}

===Etymology===
{{multiple images
|direction = vertical
|image1 = CD006-Triangulation 16th century.png
|caption1 = People determining the width of a river by triangulation ''(sense 1)''{{refn|group=n|name=n1|An engraving from a 16th-century treatise by {{w|Levinus Hulsius}} (1546–1606).}}
|image2 = A triangulation of the torus, with bounding box fixed.svg
|caption2 = A triangulation ''(sense 4)'' of the surface of a [[torus]]
}}

From {{der|en|ML.|triangulātiōnem||triangulation}}, from {{m|la|triangulāre||to triangulate}} + {{m|la|-tiōnem|pos=''suffix forming nouns relating to some actions or the results of actions''}}. ''Triangulāre'' is derived from {{m|la|triangulāris||triangular}}, from {{m|la|triangulus||triangular; triangle}}, from {{m|la|trēs||three}} + {{m|la|angulus||angle; corner}}. The English word is analysable as {{suffix|en|triangulate|ion}}, and is cognate with {{cog|fr|triangulation}}.<ref>{{R:OED Online|pos=n|id=205691|date=1914|nodot=yes}}; {{R:Lexico}}</ref>

===Pronunciation===
* {{IPA|en|/tɹʌɪaŋɡjʊˈleɪʃn̩/|a=RP}}
* {{IPA|en|/ˌtɹaɪˌæŋɡjəˈleɪʃən/|a=GA}}
* {{audio|en|en-au-triangulation.ogg|a=AU}}
* {{rhymes|en|eɪʃən|s=5}}
* {{hyphenation|en|tri|an|gu|lat|ion}}

===Noun===
{{en-noun|~}}

# {{lb|en|uncountable|surveying}} A technique in which [[distance]]s and [[direction]]s are [[estimate#Verb|estimated]] from an [[accurately]] [[measured#Adjective|measured]] [[baseline]] and the [[principle]]s of [[trigonometry]]; {{lb|en|countable}} an instance of the use of this technique.
#* {{quote-journal|en|author=T. B. Jervis|title=IV. Some Account of the Progress of the Trigonometrical Survey Now Carrying On in India. Extracted from the Correspondence of Colonel Everest, and Communicated by Major T. B. Jervis.|journal=[[w:Monthly Notices of the Royal Astronomical Society|Monthly Notices of the Royal Astronomical Society,{{nb...|Containing Abstracts of Papers, and Reports of the Proceedings of the Society}}]]|location=London|publisher=Printed by Moyes and Barclay,{{nb...|Castle Street, Leicester Square.}}|date=14 June 1839|volume=IV|issue=24|page=208|pageurl=https://books.google.com/books?id=BUI0AQAAIAAJ&pg=RA1-PA208|oclc=637567819|passage=The season of 1835–36 was employed in carrying on the '''triangulation'''; in which Colonel [[w:George Everest|[George] Everest]] was much impeded by a long continuance of hazy and cloudy weather. It appears, however, that the principal '''triangulation''' was brought down to the line from Juktipura to Pagara; {{...}}}}
#* {{quote-book|en|author=John B. Aycrigg|chapter=Notes|title=Report of John B. Aycrigg, (Made to the House of Representatives on the 9th February, 1843,) Submitted as an Individual Member of the Committee on the Coast Survey,{{nb...|(Composed of Messrs. Mallory, Wise, Cushing, Aycrigg, and Holmes.)}}|series=Report No. 170|location=Washington, D.C.|publisher=Printed at the {{w|National Intelligencer}} Office|date=9 February 1843|year_published=19 February 1843|section=note 19|pages=32–33|pageurl=https://books.google.com/books?id=6DhYAAAAYAAJ&pg=PA33|oclc=31085054|passage=Russia began under [[w:Catherine the Great|Catherine II]], and has since constantly either taken up at different points or extended the '''triangulations''' successively made, with always more perfection of men of science. Now, these '''triangulations''' form a fully connected series from north of the arctic circle to south of Dorpat.}}
#* {{quote-journal|en|title=Stated Meeting, January 19|journal=[[w:Proceedings of the American Philosophical Society|Proceedings of the American Philosophical Society,{{nb...|Held at Philadelphia, for Promoting Useful Knowledge}}]]|location=Philadelphia, Pa.|publisher=Published for the [[w:American Philosophical Society|[American Philosophical] Society]], [b]y John C. Clark,{{nb...|68 Dock Street.}}|month=January–March|year=1849|year_published=1854|volume=V|issue=42|pages=57–58|pageurl=https://books.google.com/books?id=ng5LAAAAYAAJ&pg=PA58|issn=0003-049X|oclc=299393900|passage=The original base lines, which form the starting points of the survey, require to be measured by apparatus of the most delicate nature, since any error, committed in the early part of this work, will necessarily be multiplied throughout the series of '''triangulations''' which rest upon it. {{...}} Nor is less precision necessary in the measurement of the angles of the primary and secondary '''triangulations''', which serve as checks upon each other, since the position of any point in the former is determined by each of these series.}}
# {{lb|en|countable|surveying}} The [[network#Noun|network]] of [[triangle]]s so obtained, that are the basis of a [[chart#Noun|chart]] or [[map#Noun|map]].
#* {{quote-book|en|author=[[w:Henry James (British Army officer)|Henry James]]|chapter=Appendix. [Official Correspondence, Letter C.]|title=Extension of the Triangulation of the Ordnance Survey into France and Belgium{{nb...|with the Measurement of an Arc of Parallel in Latitude 52° N. from Valentia in Ireland to Mount Kemmel in Belgium. Published by Order of the Right Hon. Sir George C. Lewis, Bart. Secretary of State for War.}}|location=London|publisher=Printed by [[w:Eyre & Spottiswoode|George Edward Eyre and William Spottiswoode]],{{nb...|printers to the Queen’s Most Excellent Majesty}}, for [[w:Office of Public Sector Information|Her Majesty’s Stationery Office]]|date=29 November 1860|year_published=1863|section=paragraphs 1–2|pages=57–58|pageurl=https://books.google.com/books?id=3V0_AAAAcAAJ&pg=PA58|oclc=913570822|passage={{...}} I have placed myself in communication with the Astronomer Royal, for the purpose of considering the steps necessary to be taken to effect the connexion required, between the '''triangulation''' of Great Britain and that of Belgium. {{...}} I have also placed myself in communication with General Nerenburger, Director of the Dêpot de la Guerre at Brussels, and have received from him the diagram of the Belgian '''triangulation''', with descriptions of the stations with which it is necessary to connect our '''triangulation''', and we possess a copy of the '''triangulation''' of France.}}
# {{lb|en|countable|chess}} A [[delaying#Adjective|delaying]] [[move#Noun|move]] in which the [[king#Noun|king]] moves in a [[triangular]] [[path]] to force the [[advance#Noun|advance]] of a [[pawn]].
#* {{quote-book|en|author=w:Gerald Abrahams|chapter=Kings and Ascending Pawns|title=Technique in Chess|location=London|publisher=[[w:George Bell & Sons|G[eorge] Bell and Sons]]|year=1961|oclc=936938891|location2=New York, N.Y.|publisher2=w:Dover Publications|year2=1973|pages2=76 and 77|pageurl2=https://books.google.com/books?id=0xACg6Z6T6wC&pg=RA1-PA76|isbn2=978-0-486-22953-9|passage=&#91;[https://books.google.com/books?id=0xACg6Z6T6wC&pg=RA1-PA76 page 76]&#93; At this point, it may be useful to refer to a word that has been used in connection with earlier examples. The King has been said to indulge in a process called '''Triangulation'''. The word is harder than the idea. The basic fact is that the King can move to an adjacent square in one move, two moves or three moves, without returning to its point of origin. {{...}} &#91;[https://books.google.com/books?id=0xACg6Z6T6wC&pg=RA1-PA77 page 77]&#93; This diagram {{...}} shows a position where the '''triangulation''' is vital.}}
# {{lb|en|countable|geometry}} A [[subdivision]] of a [[planar]] [[object#Noun|object]] into [[triangle]]s, and by extension the subdivision of a higher-[[dimension]] [[geometric#Adjective|geometric]] object into [[simplex#Noun|simplices]].
#* {{quote-journal|en|author=[[w:Francisco Santos Leal|Francisco Santos]]|title=Triangulations of Oriented Matroids|journal=w:Memoirs of the American Mathematical Society|location=Providence, R.I.|publisher=w:American Mathematical Society|month=March|year=2002|volume=156|issue=741|section=chapter 5 (Lifting Triangulations)|page=59|pageurl=https://books.google.com/books?id=F7TUCQAAQBAJ&pg=PA59|issn=0065-9266|oclc=1066893094|passage=Regular '''triangulations''' are a class in-between lifting and lexicographic '''triangulations'''. Their main draw-back in the context of this paper is that regularity depends on the specific realization and not only on the oriented matroid.}}
#* {{quote-book|en|author=[[w:Jesús A. De Loera|Jésus A[ntonio] De Loera]]; Jörg Rambau; [[w:Francisco Santos Leal|Francisco Santos]]|chapter=Triangulations in Mathematics|title=Triangulations: Structures for Algorithms and Applications|series=Algorithms and Computation in Mathematics|seriesvolume=25|location=Heidelberg; Dordrecht|publisher=[[w:Springer Science+Business Media|Springer Verlag]]|year=2010|section=definition 1.0.1|page=1|pageurl=https://books.google.com/books?id=SxY1Xrr12DwC&pg=PA1|doi=10.1007/978-3-642-12971-1|isbn=978-3-642-12970-4|issn=1431-1550|passage=A '''''triangulation''''' of a point configuration <math>\mathbf{A} \in \mathbb{R}^d</math> is a collection  of ''d''-simplices all of whose vertices are points in <math>\mathbf{A}</math> that satisfies the following two properties: 1. &nbsp;The union of all these simplices equals conv<math>(\mathbf{A})</math>. (''Union Property'') 2.&nbsp;Any pair of these simplices intersects in a common face (possibly empty). (''Intersection Property'')}}
# {{lb|en|uncountable|navigation|seismology}} A process by which an [[unknown]] [[location]] is found using three [[known#Adjective|known]] [[distance#Noun|distances]] from known locations.
#* {{quote-journal|en|title=News Notes: Army Weather Radar Tracks Nuclear Clouds|editor=William H. Zierdt Jr.|magazine=[[w:Armor (magazine)|Armor: The Magazine of Mobile Warfare]]|location=Washington, D.C.|publisher=w:United States Armor Association|month=November–December|year=1958|volume=LXVII|issue=6|page=58|pageurl=https://books.google.com/books?id=LRhMtZiFEvsC&pg=RA5-PA58|column=2|issn=0004-2420|oclc=809188389|passage=A special advantage of radar is that it works during darkness and other periods of low visibility, which prevent visual '''triangulation''' and aircraft techniques for measuring nuclear clouds.}}
# {{lb|en|uncountable|politics}} The practice of [[reposition]]ing one's group or oneself on the [[political]] [[spectrum]] in an attempt to [[capture#Verb|capture]] the [[centre#Noun|centre]].
#* {{quote-book|en|author=[[w:Stanley Renshon|Stanley A[llen] Renshon]]|chapter=The Politics of Transformation|title=In His Father’s Shadow: The Transformations of {{w|George W. Bush}}|location=New York, N.Y.|publisher=w:Palgrave Macmillan|year=2004|isbn=978-1-4039-6546-2|edition2=paperback|location2=New York, N.Y.; Basingstoke, Hampshire|publisher2=Palgrave Macmillan|year2=November 2005|section2=section V (A Transforming President in Perspective)|page2=197|pageurl2=https://books.google.com/books?id=12JpBgAAQBAJ&pg=PA197|isbn2=978-1-4039-7048-0|passage='''Triangulation''' was a presidential leadership strategy that presented the president as having borrowed elements of both the right and the left to develop some form of center policy amalgam.}}
#* {{quote-book|en|author=Tamar W. Carroll|chapter=It Saved My Life: Creating Queer Politics|title=Mobilizing New York: AIDS, Antipoverty, and Feminist Activism|location=Chapel Hill, N.C.|publisher=w:University of North Carolina Press|year=2015|page=181|pageurl=https://books.google.com/books?id=rzHtBgAAQBAJ&pg=PA181|isbn=978-1-4696-1988-0|passage=Increased security for women's health clinics was part of [[w:Bill Clinton|[Bill] Clinton]]'s "third way," a politics of '''triangulation''' that moved the Democratic Party closer to the right and embraced neoliberal economic policies while offering comparatively moderate social positions.}}
# {{lb|en|uncountable|qualitative research}} The use of three (or more) [[researcher]]s to [[interview#Verb|interview]] the same people or to [[evaluate]] the same [[evidence#Noun|evidence]] to [[reduce]] the [[impact#Noun|impact]] of [[individual#Adjective|individual]] [[bias#Noun|bias]].
#* {{quote-book|en|author=Carol Grbich|chapter=Qualitative Research: An Introduction|title=Qualitative Research in Health: An Introduction|location=Crows Nest, N.S.W.|publisher=w:Allen & Unwin|year=1999|section=part 1 (Theory and Design)|pages=17–18|pageurl=https://books.google.com/books?id=UPJ_BRWJ6b8C&pg=PA18|isbn=978-1-86448-568-4|passage=One recent attempt to combine both forms of data collection {{...}} was based on a parallel methods approach, in which the results of two similar but separately located studies were triangulated. '''''Triangulation''''' entails overlapping the results at several points to enhance reliability. {{...}} Other documented research has attempted to gain a broader view through the '''triangulation''' of two sets of data (quantitative and qualitative) on the same question, taken from the same respondents in a single study.}}
#* {{quote-journal|en|author=Nahid Golafshani|title=Understanding Reliability and Validity in Qualitative Research|url=https://nsuworks.nova.edu/tqr/vol8/iss4/6/|journal=The Qualitative Report|date=1 December 2003|volume=8|number=4|page=603|passage=Even though '''triangulation''' is used in quantitative paradigm for confirmation and generalization of a research, Barbour (1998) does not disregard the notion of '''triangulation''' in qualitative paradigm and she states the need to define '''triangulation''' from a qualitative research's perspective in each paradigm. For example, in using '''triangulation''' of several data sources in quantitative research, any exception may lead to a disconfirmation of the hypothesis where exceptions in qualitative research are dealt to modify the theories and are fruitful.}}
#* {{quote-book|en|author=Alexander Cárdenas|chapter=Introduction|title=Football: Origins, Paths and New Dimensions: Master’s Thesis|location=[Munich]|publisher=GRIN Verlag|year=2014|section=section 1.2 (Research Methods)|page=4|pageurl=https://books.google.com/books?id=WbnSAgAAQBAJ&pg=PA4|isbn=978-3-656-59019-4|passage=Multiple sources of data were used to create a '''triangulation''' of evidence: books, documentation, archival records and relevant publications by key actors, particularly in the development field, open ended interviews, participant-observation conducted during field work and a case study. {{...}} '''Triangulation''' was initially conceptualized as a strategy to validating results achieved with individual research methods. The focus of this research strategy, however, has increasingly shifted towards enriching and complementing knowledge and towards expanding and furthering the potential of individual methods.}}

====Hypernyms====
* {{l|en|polygonation}}

====Coordinate terms====
* {{l|en|quadrangulation}}

====Derived terms====
{{col3|en| Delaunay triangulation|triangulation station
|phototriangulation
|pseudotriangulation|Schur triangulation
|triangulation pillar
|retriangulation
|triangulational
|triangulation point
|triangulation number
|triangulateration}}

====Related terms====
{{col3|en|triangle|triangular|triangulate}}

====Translations====
{{trans-top|surveying technique}}
* Bulgarian: {{t+|bg|триангулация|f}}
* Catalan: {{t+|ca|triangulació|f}}
* Chinese:
*: Mandarin: {{t+|cmn|三角測量|tr=sānjiǎo cèliáng}}
* Czech: {{t|cs|triangulace|f}}
* Dutch: {{t+|nl|driehoeksmeting|f}}, {{t+|nl|triangulatie|f}}
* Finnish: {{t+|fi|kolmiomittaus}}
* French: {{t+|fr|triangulation|f}}
* Greek: {{t+|el|τριγωνισμός|m}}
* Hebrew: {{t|he|שילוש|m|tr=shilúsh}}
* Hungarian: {{t+|hu|háromszögelés}}, {{t|hu|trianguláció}}
* Irish: {{t-check|ga|triantánú|m}}, {{t-check|ga|triantánacht|f}}
* Italian: {{t|it|triangolazione|f}}
* Japanese: {{t+|ja|三角測量|tr=さんかくそくりょう, sankakusokuryō}}
* Kazakh: {{t|kk|триангуляция}}
* Kyrgyz: {{t|ky|триангуляция}}
* Norwegian: {{t+|no|triangulering|m|f}}
* Polish: {{t|pl|triangulacja|f}}
* Portuguese: {{t+|pt|triangulação|f}}
* Russian: {{t+|ru|триангуляция|f}}, {{t+|ru|триангуля́ция|f}}
* Scottish Gaelic: {{t|gd|triantanachadh|m}}
* Swedish: {{t+|sv|triangulering|c}}
* Turkish: {{t+|tr|nirengi}}
* Welsh: {{t+|cy|triongl|m|f}}
{{trans-bottom}}

===Notes===
{{reflist|group=n}}

===References===
<references />

===Further reading===
* {{pedia|triangulation}}
* {{pedia|triangulation (chess)}}
* {{pedia|triangulation (geometry)}}
* {{pedia|triangulation (politics)}}
* {{pedia|triangulation (social science)}}
* {{pedia|triangulation (surveying)}}
* {{pedia|triangulation (topology)}}
* {{pedia|triangulation (disambiguation)}}

{{cln|en|terms prefixed with tri-|sort=angulation}}
{{C|en|Three}}

==French==

===Pronunciation===
* {{audio|fr|LL-Q150 (fra)-WikiLucas00-triangulation.wav}}

===Noun===
{{fr-noun|f}}

# {{l|en|triangulation}}

===Further reading===
* {{R:fr:TLFi}}