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Triangulation 3-coloring
In trigonometry and geometry, triangulation is the process of determining the location of a point by forming triangles to the point from known points. Applications In surveying Specifically in surveying, triangulation involves only angle measurements at known points, rather than measuring distances to the point directly as in trilateration; the use of both angles and distance measurements is referred to as triangulateration. In computer vision Computer stereo vision and optical 3D measuring 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 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 ''b'' and must be known. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trigonometry
Trigonometry () is a branch of mathematics that studies relationships between side lengths and angles of triangles. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies. The Greeks focused on the calculation of chords, while mathematicians in India created the earliest-known tables of values for trigonometric ratios (also called trigonometric functions) such as sine. Throughout history, trigonometry has been applied in areas such as geodesy, surveying, celestial mechanics, and navigation. Trigonometry is known for its many identities. These trigonometric identities are commonly used for rewriting trigonometrical expressions with the aim to simplify an expression, to find a more useful form of an expression, or to solve an equation. History Sumerian astronomers studied angle measure, using a division of circles into 360 degrees. They, and later the Babylonians, studied the ratios of the sides of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ptolemaic Dynasty
The Ptolemaic dynasty (; grc, Πτολεμαῖοι, ''Ptolemaioi''), sometimes referred to as the Lagid dynasty (Λαγίδαι, ''Lagidae;'' after Ptolemy I's father, Lagus), was a Macedonian Greek royal dynasty which ruled the Ptolemaic Kingdom in Ancient Egypt during the Hellenistic period. Their rule lasted for 275 years, from 305 to 30 BC. The Ptolemaic was the last dynasty of ancient Egypt. Ptolemy, one of the seven somatophylakes (bodyguard companions), a general and possible half-brother of Alexander the Great, was appointed satrap of Egypt after Alexander's death in 323 BC. In 305 BC, he declared himself Pharaoh Ptolemy I, later known as ''Sōter'' "Saviour". The Egyptians soon accepted the Ptolemies as the successors to the pharaohs of independent Egypt. Ptolemy's family ruled Egypt until the Roman conquest of 30 BC. Like the earlier dynasties of ancient Egypt, the Ptolemaic dynasty practiced inbreeding including sibling marriage, but this did not start ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Willebrord Snellius
Willebrord Snellius (born Willebrord Snel van Royen) (13 June 158030 October 1626) was a Dutch astronomer and mathematician, Snell. His name is usually associated with the law of refraction of light known as Snell's law. The lunar crater Snellius is named after Willebrord Snellius. The Royal Netherlands Navy has named three survey ships after Snellius, including a currently-serving vessel. Biography Willebrord Snellius was born in Leiden, Netherlands. In 1613 he succeeded his father, Rudolph Snel van Royen (1546–1613) as professor of mathematics at the University of Leiden. Snellius' triangulation In 1615, Snellius, after the work of Eratosthenes in Ptolemaic Egypt in the 3rd century BC, probably was the first to try to do a large-scale experiment to measure the circumference of the earth using triangulation. He was helped in his measurements by two of his students, the Austrian barons Erasmus and Casparus Sterrenberg. In several cities he also received su ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hero Of Alexandria
Hero of Alexandria (; grc-gre, Ἥρων ὁ Ἀλεξανδρεύς, ''Heron ho Alexandreus'', also known as Heron of Alexandria ; 60 AD) was a Greece, Greek mathematician and engineer who was active in his native city of Alexandria, Roman Egypt. He is often considered the greatest experimenter of antiquity and his work is representative of the Hellenistic civilization, Hellenistic scientific tradition. Hero published a well-recognized description of a Steam engine, steam-powered device called an ''aeolipile'' (sometimes called a "Hero engine"). Among his most famous inventions was a windmill, windwheel, constituting the earliest instance of Wind power, wind harnessing on land. He is said to have been a follower of the atomism, atomists. In his work ''Mechanics'', he described pantographs. Some of his ideas were derived from the works of Ctesibius. In mathematics he is mostly remembered for Heron's formula, a way to calculate the area of a triangle using only the lengths of it ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alidade
An alidade () (archaic forms include alhidade, alhidad, alidad) or a turning board is a device that allows one to sight a distant object and use the line of sight to perform a task. This task can be, for example, to triangulate a scale map on site using a plane table drawing of intersecting lines in the direction of the object from two or more points or to measure the angle and horizontal distance to the object from some reference point's polar measurement. Angles measured can be horizontal, vertical or in any chosen plane. The alidade sighting ruler was originally a part of many types of scientific and astronomical instrument. At one time, some alidades, particularly using circular graduations as on astrolabes, were also called ''diopters''. With modern technology, the name is applied to complete instruments such as the 'plane table alidade'. Origins The word in Arabic ( , "the ruler"), signifies the same device. In Greek and Latin, it is respectively called , "''dioptra''" ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dioptra
A dioptra (sometimes also named dioptre or diopter, from el, διόπτρα) is a classical astronomical and surveying instrument, dating from the 3rd century BC. The dioptra was a sighting tube or, alternatively, a rod with a sight at both ends, attached to a stand. If fitted with protractors, it could be used to measure angles. Use Greek astronomers used the dioptra to measure the positions of stars; both Euclid and Geminus refer to the dioptra in their astronomical works. It continued in use as an effective surveying tool. Adapted to surveying, the dioptra is similar to the theodolite, or surveyor's transit, which dates to the sixteenth century. It is a more accurate version of the groma. There is some speculation that it may have been used to build the Eupalinian aqueduct. Called "one of the greatest engineering achievements of ancient times," it is a tunnel 1,036 meters (4,000 ft) long, "excavated through Mount Kastro on the Greek island of Samos, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Slope
In mathematics, the slope or gradient of a line is a number that describes both the ''direction'' and the ''steepness'' of the line. Slope is often denoted by the letter ''m''; there is no clear answer to the question why the letter ''m'' is used for slope, but its earliest use in English appears in O'Brien (1844) who wrote the equation of a straight line as and it can also be found in Todhunter (1888) who wrote it as "''y'' = ''mx'' + ''c''". Slope is calculated by finding the ratio of the "vertical change" to the "horizontal change" between (any) two distinct points on a line. Sometimes the ratio is expressed as a quotient ("rise over run"), giving the same number for every two distinct points on the same line. A line that is decreasing has a negative "rise". The line may be practical – as set by a road surveyor, or in a diagram that models a road or a roof either as a description or as a plan. The ''steepness'', incline, or grade of a line is measured by the absolute ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Seked
Seked (or seqed) is an ancient Egyptian term describing the inclination of the triangular faces of a right pyramid. The system was based on the Egyptians' length measure known as the royal cubit. It was subdivided into seven ''palms'', each of which was sub-divided into four ''digits''. The inclination of measured slopes was therefore expressed as the number of horizontal palms and digits relative to each royal cubit rise. The seked is proportional to the reciprocal of our modern measure of slope or gradient, and to the cotangent of the angle of elevation.Gillings: Mathematics in the Time of the Pharaohs 1982: pp 212 Specifically, if ''s'' is the seked, ''m'' the slope (rise over run), and \phi the angle of elevation from horizontal, then: :s = \frac = 7\cot(\phi). The most famous example of a seked slope is of the Great Pyramid of Giza in Egypt built around 2550 BC. Based on modern surveys, the faces of this monument had a seked of 5½, or 5 palms and 2 digits, in modern terms eq ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rhind Papyrus
The Rhind Mathematical Papyrus (RMP; also designated as papyrus British Museum 10057 and pBM 10058) is one of the best known examples of ancient Egyptian mathematics. It is named after Alexander Henry Rhind, a Scottish antiquarian, who purchased the papyrus in 1858 in Luxor, Egypt; it was apparently found during illegal excavations in or near the Ramesseum. It dates to around 1550 BC. The British Museum, where the majority of the papyrus is now kept, acquired it in 1865 along with the Egyptian Mathematical Leather Roll, also owned by Henry Rhind. There are a few small fragments held by the Brooklyn Museum in New York City and an central section is missing. It is one of the two well-known Mathematical Papyri along with the Moscow Mathematical Papyrus. The Rhind Papyrus is larger than the Moscow Mathematical Papyrus, while the latter is older. The Rhind Mathematical Papyrus dates to the Second Intermediate Period of Egypt. It was copied by the scribe Ahmes (i.e., Ahmose; ''Ahmes'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proclus
Proclus Lycius (; 8 February 412 – 17 April 485), called Proclus the Successor ( grc-gre, Πρόκλος ὁ Διάδοχος, ''Próklos ho Diádokhos''), was a Greek Neoplatonist philosopher, one of the last major classical philosophers of late antiquity. He set forth one of the most elaborate and fully developed systems of Neoplatonism and, through later interpreters and translators, exerted an influence on Byzantine philosophy, Early Islamic philosophy, and Scholastic philosophy. Biography The primary source for the life of Proclus is the eulogy ''Proclus, or On Happiness'' that was written for him upon his death by his successor, Marinus, Marinus' biography set out to prove that Proclus reached the peak of virtue and attained eudaimonia. There are also a few details about the time in which he lived in the similarly structured ''Life of Isidore'' written by the philosopher Damascius in the following century. According to Marinus, Proclus was born in 412 AD in Cons ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Intercept Theorem
The intercept theorem, also known as Thales's theorem, basic proportionality theorem or side splitter theorem is an important theorem in elementary geometry about the ratios of various line segments that are created if two intersecting lines are intercepted by a pair of parallels. It is equivalent to the theorem about ratios in similar triangles. It is traditionally attributed to Greek mathematician Thales. It was known to the ancient Babylonians and Egyptians, although its first known proof appears in Euclid's '' Elements''. Formulation Suppose S is the intersection point of two lines and A, B are the intersections of the first line with the two parallels, such that B is further away from S than A, and similarly C, D are the intersections of the second line with the two parallels such that D is further away from S than C. # The ratio of any two segments on the first line equals the ratio of the according segments on the second line: , SA , : , AB , =, SC , : , CD , , ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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