42:
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34:
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212:). Thales also estimated the distances to ships at sea as seen from a clifftop by measuring the horizontal distance traversed by the line-of-sight for a known fall, and scaling up to the height of the whole cliff. Such techniques would have been familiar to the ancient Egyptians. Problem 57 of the
133:
systems use this principle to determine the spatial dimensions and the geometry of an item. Basically, the configuration consists of two sensors observing the item. One of the sensors is typically a digital camera device, and the other one can also be a camera or a light projector. The projection
138:
and must be known. By determining the angles between the projection rays of the sensors and the basis, the intersection point, and thus the 3D coordinate, is calculated from the triangular relations.
271:(224–271) identified "measuring right angles and acute angles" as the fifth of his six principles for accurate map-making, necessary to accurately establish distances, while
41:
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centers of the sensors and the considered point on the object's surface define a (spatial) triangle. Within this triangle, the distance between the sensors is the base
902:
542:
550:
965:
244:. A detailed contemporary collection of constructions for the determination of lengths from a distance using this instrument is known, the
918:
533:
188:
The use of triangles to estimate distances dates to antiquity. In the 6th century BC, about 250 years prior to the establishment of the
910:
234:
the reciprocal of gradients as measured today. The slopes and angles were measured using a sighting rod that the Greeks called a
208:. He measured the length of the pyramids' shadows and that of his own at the same moment, and compared the ratios to his height (
146:
382:
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Finding the position of a distant object B with the angles observed from points A and C and the baseline b between them
372:
502:
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121:
708:
631:
20:
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816:
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282:) gives a version of the calculation above, for measuring perpendicular distances to inaccessible places.
1016:
867:
677:
497:, Proceedings of a conference held July, 1997, Mathematisches Forschungsinstitut, Oberwolfach, Germany.
519:
457:
Science and
Civilization in China: Volume 3, Mathematics and the Sciences of the Heavens and the Earth
259:–70 AD), which survived in Arabic translation; but the knowledge became lost in Europe until in 1615
91:
775:
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1021:
312:
353:
934:
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333:
126:
267:, reworked the technique for an attempt to measure the circumference of the earth. In China,
109:
402:
304:, where a point is calculated using the time-difference-of-arrival between other known points
46:
486:
749:
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398:
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and, in the military, the gun direction, the trajectory and distribution of fire power of
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measurements at known points, rather than measuring distances to the point directly as in
8:
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This article is about measurement by the use of triangles. For other uses, see
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Thomas
Luhmann; Stuart Robson; Stephen Kyle; Jan Boehm (27 November 2013).
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108:; the use of both angles and distance measurements is referred to as
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356:[what is in the picture? (Answer: Triangulation Point)].
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is the process of determining the location of a point by forming
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Triangulation today is used for many purposes, including
543:
Geography and cartography in the medieval
Islamic world
37:
Estimating the height of a mountain using triangulation
998:
364:
487:A Surveying Problem Travels from China to Paris
404:The Lives and Opinions of Eminent Philosophers
527:
397:
391:
150:Measuring the height of a building with an
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374:Close-Range Photogrammetry and 3D Imaging
226:as the ratio of the run to the rise of a
216:, a thousand years earlier, defines the
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40:
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354:"מה בתמונה? (תשובה: נקודת טריאנגולציה)"
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459:. Taipei: Caves Books Ltd. pp. 539–540
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325:, covering a polygon with triangles
13:
14:
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617:Abu Muhammad al-Hasan al-Hamdani
69:to the point from known points.
16:Method of determining a location
240:, the forerunner of the Arabic
122:Triangulation (computer vision)
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632:Khashkhash Ibn Saeed Ibn Aswad
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200:to estimate the height of the
100:, triangulation involves only
21:Triangulation (disambiguation)
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868:Mir Ahmed Nasrallah Thattvi
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920:Book of Roads and Kingdoms
912:Book of Roads and Kingdoms
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485:Kurt Vogel (1983; 1997),
92:Triangulation (surveying)
817:Abd-al-Razzāq Samarqandī
423:: CS1 maint: location (
360:(in Hebrew). 2007-07-08.
192:, the Greek philosopher
26:Not to be confused with
313:Resection (orientation)
935:Kitab al-Rawd al-Mitar
822:Ghiyāth al-dīn Naqqāsh
491:Yvonne Dold-Samplonius
334:Wireless triangulation
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127:Computer stereo vision
82:
50:
38:
719:Abu'l Abbas al-Hijazi
196:is recorded as using
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47:triangulation station
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750:Ibn Said al-Maghribi
401:, "Life of Thales",
263:, after the work of
131:optical 3D measuring
1012:Elementary geometry
954:The Meadows of Gold
571:Abu Hanifa Dinawari
495:From China to Paris
358:Jeepolog.com forums
1017:Euclidean geometry
791:Hamdallah Mustawfi
714:Muhammad al-Idrisi
688:Mahmud al-Kashgari
612:Abu Zayd al-Balkhi
250:Hero of Alexandria
155:
116:In computer vision
83:
51:
49:signed by iron rod
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858:Sulaiman Al Mahri
678:Abu Saʿīd Gardēzī
657:Qudama ibn Ja'far
581:Sulaiman al-Tajir
399:Diogenes Laërtius
384:978-3-11-030278-3
292:Direction finding
210:intercept theorem
198:similar triangles
190:Ptolemaic dynasty
110:triangulateration
1029:
942:Mu'jam Al-Buldan
928:Tabula Rogeriana
922:(ibn Khordadbeh)
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28:Trilateration
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882:17th century
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786:Ibn al-Wardi
769:14th century
755:Ibn al-Nafis
728:13th century
702:12th century
666:11th century
647:Al-Muqaddasi
642:Ibn al-Faqih
590:10th century
566:Al-Khwarizmi
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265:Eratosthenes
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152:inclinometer
135:
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86:In surveying
73:Applications
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796:Ibn Battuta
776:Al-Dimashqi
559:9th century
551:Geographers
442:In Euclidem
1001:Categories
976:Influences
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781:Abu'l-Fida
735:Ibn Jubayr
637:Ibn Hawqal
411:2008-02-22
340:References
329:Trig point
318:Stereopsis
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171:astrometry
163:navigation
986:(Ptolemy)
984:Geography
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863:Piri Reis
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419:citation
308:Parallax
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837:Ma Huan
693:Domiyat
576:Ya'qubi
493:(ed.),
469:Liu Hui
438:Proclus
407:, I, 27
273:Liu Hui
269:Pei Xiu
246:Dioptra
242:alidade
237:dioptra
183:weapons
142:History
801:Lin Nu
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