Triangulation Survey
Today triangulation surveying, navigation, metrology, astrometry, binocular vision, model rockets and weapons including guns direction is used for many purposes.
Used to estimate the distance of the triangle goes back to ancient times. Thales same time, the length of his shadow and by their own measure to estimate the height of the pyramid using similar triangles, and its height (intercept theorem) as compared to the percentage recorded in the 6th century BC Greek philosopher is, [1] and from the clifftop, line-of-sight to fall from a known fixed horizontal distance measurement, and scaling the mountain height of eye ships at sea estimated distance [2] such techniques are known to the ancient Egyptians. 57 Papyrus issue and found wallet, a thousand years ago, seqt defines a shield to increase the number of runs as the ratio seked, measured as the reciprocal of the gradients. Slopes and angles Greeks a dioptra, Arabic is called the forerunner of alidade that were measured using a sighting rod. Use this tool to determine a distance range of construction is known a detailed contemporary collection, which survived in Arabic translation of Alexandria (c. 10-70 AD.), The hero Dioptra; but knowledge in Europe became lost. China, Pei Xiu's I (224-271) must identify accurately set the distance for accurate mapping fifth of his six principles, as "right-angle and acute angle measurement"; [3 ] Liu Hui (. c. 263), while the perpendicular distance measurements in inaccessible places a version of the above calculation. [4] [5]
In the field, triangulation methods apparently Roman specialist land surveyors, agromensores been used by, but Ibn al-Saffar (d. 1035) by Arabic treatise on the astrolabe as, through the Middle Ages introduced in Spain a. [6] Abu Rayhan Biruni (d. 1048) introduced the technique of triangulation to measure the size of the earth and the distance between different locations. [7] simplified the Roman techniques used by professional surveyors with more sophisticated techniques seem to co-exist. To provide such methods in Latin but it was rare (a manual on geometry, Geomatria incerti author eleventh century is a rare exception), and in other parts of Europe such techniques show only slowly percolated. [6] awareness and use of such techniques in Spain, which dates from about 1300, especially for measuring the angle used by the Middle Ages, Jacob's staff can be verified; and Portolan charts oldest living accurately survey the appearance of coastline, is dated 1296.
Gemma Frisius to mapmaking and triangulation [Edit]
On the ground, cartographer Gemma Frisius of far-away places for accurately mapping the position suggested using triangulation his Libellus de Locorum describendorum ratione the new 1533 brochure as a supplement is required, which (one way of describing the locations booklet) Peter Apian's edition of the best-selling 1524 Cosmographica. It became very influential, and techniques Germany, Austria and the Netherlands spread. Astronomer Tycho Brahe 1584 the island in the production of an estate plan, the Observatory of the important landmarks on both sides of Öresund, where was based on Hven, the island in 1579 to complete a detailed triangulation, Scandinavia the method is applied. [8] In England, William Cuningham's Cosmographical glasse method of Frisius (1559), all kinds of land (1562) Leigh Valentine's measurement of the treatise, including William, which appeared in the middle of the century books on surveying was added in increasing numbers Navigation (1571), Thomas Digges geometric rules to practice Pantometria (1571), and John Norden's surveyor's dialogue (1607) called. This map features in their county of Christopher Saxton 1570s to replace the rough-and-ready that can be used for triangulation has been suggested, but from the vantage points of the key features of others to get some bearings after that, they just guesswork by their distance can be estimated. [9]
Willebrord Snell and modern triangulation networks [Edit]
In 1615 the systematic use of triangulation networks Bergen op Zoom distance from Alkmaar to the Dutch mathematician Willebrord Snell of survey work, stems from, all of the 33 triangles using a series of quadrangles approximately 70 miles (110 km). Book Eratosthenes Batavus (Dutch Eratosthenes) observed a feat in the title published in 1617, - measuring the circumference of the earth, was able to calculate a value for the two cities, separated by a degree on the meridian were doing. Snell's planar formulas to allow for the curvature of the earth can be accurately calculated how. They also, unknown cast angle between the vertices of a triangle using the position of a point in the resection, or shown how to calculate. It depends on the vertices of a compass bearings, much more than can be measured accurately. The first control point surveying a large-scale core network, and then within the core network, the main idea of locating points in the secondary subsidiary established.
Methods of France near Snell in 1669-70, Sourdon stretching north from the Clock Tower in Paris thirteen triangles using a series of one degree of latitude with the meridian of Paris to the survey was Jean-Packard . Devices and thanks to improvements in accuracy, Picard first reasonably accurate measurement of the radius of the earth is classified as. His most important work by Cassini family was extended during the next century: Jean-Dominique Cassini and his son Jacques Cassini between 1683 and 1718, the survey of the Paris meridian from Dunkirk to Perpignan. And between 1733 and 1740 Jacques Cassini and his son Caesar built on strict principles of France as a result of the publication in 1745 of the first map, the meridian arc re-surveying the entire country, including the triangulation, taken in hand.
triangulation methods are now well established for local mapmaking, but the only other countries detailed maps of the countries surveyed to establish triangulation network that began towards the end of the 18th century. Is not completed until 1853, although the United Kingdom's principal triangulation, 1783 by Ordnance Survey was launched, and eventually Mount Everest and other Himalayan peaks named and mapped in the India, the Great Trigonometric Survey, Napoleon French state began in 1801. for, after the French full of triangulation, the German Rhineland in 1801, was extended by Jean-Joseph Tranchot Prussian general Carl von since 1815 by Müffling. Meanwhile, the famous mathematician Carl Friedrich Gauss was more real- problems of large systems of simultaneous equations to find the best fit for the solution of the least squares method is developed for the triangulation of the kingdom of Hanover, as well 1825 1821 entrusted the measure
