1.
Trilateration
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In geometry, trilateration is the process of determining absolute or relative locations of points by measurement of distances, using the geometry of circles, spheres or triangles. In addition to its interest as a problem, trilateration does have practical applications in surveying and navigation. In contrast to triangulation, it does not involve the measurement of angles, in two-dimensional geometry, it is known that if a point lies on two circles, then the circle centers and the two radii provide sufficient information to narrow the possible locations down to two. Additional information may narrow the possibilities down to one unique location and this article describes a method for determining the intersections of three sphere surfaces given the centers and radii of the three spheres. The intersections of the surfaces of three spheres is found by formulating the equations for the three surfaces and then solving the three equations for the three unknowns, x, y, and z. To simplify the calculations, the equations are formulated so that the centers of the spheres are on the z =0 plane, also, the formulation is such that one center is at the origin, and one other is on the x-axis. It is possible to formulate the equations in this manner since any three points lie on a unique plane. After finding the solution, it can be transformed back to the three dimensional Cartesian coordinate system. You have to subtract it from x to get the length of the base of the triangle between the intersection and r2 and we need to find a point located at that satisfies all three equations. Assuming that the first two spheres intersect in more than one point, that is that d − r 1 < r 2 < d + r 1. Now that the x- and y-coordinates of the point are found. Now the solution to all three points x, y and z is found, because z is expressed as the positive or negative square root, it is possible for there to be zero, one or two solutions to the problem. This last part can be visualized as taking the circle found from intersecting the first and second sphere, if that circle falls entirely outside or inside of the sphere, z is equal to the square root of a negative number, no real solution exists. If that circle touches the sphere on one point, z is equal to zero. If that circle touches the surface of the sphere at two points, then z is equal to plus or minus the square root of a positive number, in general the problem will not be given in a form such that these requirements are met. This problem can be overcome as described below where the points, P1, P2, P1, P2, and P3 are of course expressed in the original coordinate system. E ^ x = P2 − P1 ∥ P2 − P1 ∥ is the vector in the direction from P1 to P2. I = e ^ x ⋅ is the magnitude of the x component, in the figure 1 coordinate system
2.
Trigonometry
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Trigonometry is a branch of mathematics that studies relationships involving lengths and angles of triangles. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies, Trigonometry is also the foundation of surveying. Trigonometry is most simply associated with planar right-angle triangles, thus the majority of applications relate to right-angle triangles. One exception to this is spherical trigonometry, the study of triangles on spheres, surfaces of constant positive curvature, Trigonometry on surfaces of negative curvature is part of hyperbolic geometry. Trigonometry basics are often taught in schools, either as a course or as a part of a precalculus course. Sumerian astronomers studied angle measure, using a division of circles into 360 degrees, the ancient Nubians used a similar method. In 140 BC, Hipparchus gave the first tables of chords, analogous to modern tables of sine values, in the 2nd century AD, the Greco-Egyptian astronomer Ptolemy printed detailed trigonometric tables in Book 1, chapter 11 of his Almagest. Ptolemy used chord length to define his trigonometric functions, a difference from the sine convention we use today. The modern sine convention is first attested in the Surya Siddhanta and these Greek and Indian works were translated and expanded by medieval Islamic mathematicians. By the 10th century, Islamic mathematicians were using all six trigonometric functions, had tabulated their values, at about the same time, Chinese mathematicians developed trigonometry independently, although it was not a major field of study for them. At the same time, another translation of the Almagest from Greek into Latin was completed by the Cretan George of Trebizond, Trigonometry was still so little known in 16th-century northern Europe that Nicolaus Copernicus devoted two chapters of De revolutionibus orbium coelestium to explain its basic concepts. Driven by the demands of navigation and the growing need for maps of large geographic areas. Bartholomaeus Pitiscus was the first to use the word, publishing his Trigonometria in 1595, gemma Frisius described for the first time the method of triangulation still used today in surveying. It was Leonhard Euler who fully incorporated complex numbers into trigonometry, the works of the Scottish mathematicians James Gregory in the 17th century and Colin Maclaurin in the 18th century were influential in the development of trigonometric series. Also in the 18th century, Brook Taylor defined the general Taylor series, if one angle of a triangle is 90 degrees and one of the other angles is known, the third is thereby fixed, because the three angles of any triangle add up to 180 degrees. The two acute angles therefore add up to 90 degrees, they are complementary angles, the shape of a triangle is completely determined, except for similarity, by the angles. Once the angles are known, the ratios of the sides are determined, if the length of one of the sides is known, the other two are determined. Sin A = opposite hypotenuse = a c, Cosine function, defined as the ratio of the adjacent leg to the hypotenuse
3.
Geometry
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Geometry is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. A mathematician who works in the field of geometry is called a geometer, Geometry arose independently in a number of early cultures as a practical way for dealing with lengths, areas, and volumes. Geometry began to see elements of mathematical science emerging in the West as early as the 6th century BC. By the 3rd century BC, geometry was put into a form by Euclid, whose treatment, Euclids Elements. Geometry arose independently in India, with texts providing rules for geometric constructions appearing as early as the 3rd century BC, islamic scientists preserved Greek ideas and expanded on them during the Middle Ages. By the early 17th century, geometry had been put on a solid footing by mathematicians such as René Descartes. Since then, and into modern times, geometry has expanded into non-Euclidean geometry and manifolds, while geometry has evolved significantly throughout the years, there are some general concepts that are more or less fundamental to geometry. These include the concepts of points, lines, planes, surfaces, angles, contemporary geometry has many subfields, Euclidean geometry is geometry in its classical sense. The mandatory educational curriculum of the majority of nations includes the study of points, lines, planes, angles, triangles, congruence, similarity, solid figures, circles, Euclidean geometry also has applications in computer science, crystallography, and various branches of modern mathematics. Differential geometry uses techniques of calculus and linear algebra to problems in geometry. It has applications in physics, including in general relativity, topology is the field concerned with the properties of geometric objects that are unchanged by continuous mappings. In practice, this often means dealing with large-scale properties of spaces, convex geometry investigates convex shapes in the Euclidean space and its more abstract analogues, often using techniques of real analysis. It has close connections to convex analysis, optimization and functional analysis, algebraic geometry studies geometry through the use of multivariate polynomials and other algebraic techniques. It has applications in areas, including cryptography and string theory. Discrete geometry is concerned mainly with questions of relative position of simple objects, such as points. It shares many methods and principles with combinatorics, Geometry has applications to many fields, including art, architecture, physics, as well as to other branches of mathematics. The earliest recorded beginnings of geometry can be traced to ancient Mesopotamia, the earliest known texts on geometry are the Egyptian Rhind Papyrus and Moscow Papyrus, the Babylonian clay tablets such as Plimpton 322. For example, the Moscow Papyrus gives a formula for calculating the volume of a truncated pyramid, later clay tablets demonstrate that Babylonian astronomers implemented trapezoid procedures for computing Jupiters position and motion within time-velocity space
4.
Triangle
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A triangle is a polygon with three edges and three vertices. It is one of the shapes in geometry. A triangle with vertices A, B, and C is denoted △ A B C, in Euclidean geometry any three points, when non-collinear, determine a unique triangle and a unique plane. This article is about triangles in Euclidean geometry except where otherwise noted, triangles can be classified according to the lengths of their sides, An equilateral triangle has all sides the same length. An equilateral triangle is also a polygon with all angles measuring 60°. An isosceles triangle has two sides of equal length, some mathematicians define an isosceles triangle to have exactly two equal sides, whereas others define an isosceles triangle as one with at least two equal sides. The latter definition would make all equilateral triangles isosceles triangles, the 45–45–90 right triangle, which appears in the tetrakis square tiling, is isosceles. A scalene triangle has all its sides of different lengths, equivalently, it has all angles of different measure. Hatch marks, also called tick marks, are used in diagrams of triangles, a side can be marked with a pattern of ticks, short line segments in the form of tally marks, two sides have equal lengths if they are both marked with the same pattern. In a triangle, the pattern is no more than 3 ticks. Similarly, patterns of 1,2, or 3 concentric arcs inside the angles are used to indicate equal angles, triangles can also be classified according to their internal angles, measured here in degrees. A right triangle has one of its interior angles measuring 90°, the side opposite to the right angle is the hypotenuse, the longest side of the triangle. The other two sides are called the legs or catheti of the triangle, special right triangles are right triangles with additional properties that make calculations involving them easier. One of the two most famous is the 3–4–5 right triangle, where 32 +42 =52, in this situation,3,4, and 5 are a Pythagorean triple. The other one is a triangle that has 2 angles that each measure 45 degrees. Triangles that do not have an angle measuring 90° are called oblique triangles, a triangle with all interior angles measuring less than 90° is an acute triangle or acute-angled triangle. If c is the length of the longest side, then a2 + b2 > c2, a triangle with one interior angle measuring more than 90° is an obtuse triangle or obtuse-angled triangle. If c is the length of the longest side, then a2 + b2 < c2, a triangle with an interior angle of 180° is degenerate
5.
Surveying
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Surveying or land surveying is the technique, profession, and science of determining the terrestrial or three-dimensional position of points and the distances and angles between them. A land surveying professional is called a land surveyor, Surveyors work with elements of geometry, trigonometry, regression analysis, physics, engineering, metrology, programming languages and the law. Surveying has been an element in the development of the environment since the beginning of recorded history. The planning and execution of most forms of construction require it and it is also used in transport, communications, mapping, and the definition of legal boundaries for land ownership. It is an important tool for research in other scientific disciplines. Basic surveyance has occurred since humans built the first large structures, the prehistoric monument at Stonehenge was set out by prehistoric surveyors using peg and rope geometry. In ancient Egypt, a rope stretcher would use simple geometry to re-establish boundaries after the floods of the Nile River. The almost perfect squareness and north-south orientation of the Great Pyramid of Giza, built c.2700 BC, the Groma instrument originated in Mesopotamia. The mathematician Liu Hui described ways of measuring distant objects in his work Haidao Suanjing or The Sea Island Mathematical Manual, the Romans recognized land surveyors as a profession. They established the basic measurements under which the Roman Empire was divided, Roman surveyors were known as Gromatici. In medieval Europe, beating the bounds maintained the boundaries of a village or parish and this was the practice of gathering a group of residents and walking around the parish or village to establish a communal memory of the boundaries. Young boys were included to ensure the memory lasted as long as possible, in England, William the Conqueror commissioned the Domesday Book in 1086. It recorded the names of all the owners, the area of land they owned, the quality of the land. It did not include maps showing exact locations, abel Foullon described a plane table in 1551, but it is thought that the instrument was in use earlier as his description is of a developed instrument. Gunters chain was introduced in 1620 by English mathematician Edmund Gunter and it enabled plots of land to be accurately surveyed and plotted for legal and commercial purposes. Leonard Digges described a Theodolite that measured horizontal angles in his book A geometric practice named Pantometria, joshua Habermel created a theodolite with a compass and tripod in 1576. Johnathon Sission was the first to incorporate a telescope on a theodolite in 1725, in the 18th century, modern techniques and instruments for surveying began to be used. Jesse Ramsden introduced the first precision theodolite in 1787 and it was an instrument for measuring angles in the horizontal and vertical planes
6.
Triangulation (surveying)
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The point can then be fixed as the third point of a triangle with one known side and two known angles. Triangulation can also refer to the surveying of systems of very large triangles. Surveying error is minimized if a mesh of triangles at the largest appropriate scale is established first, points inside the triangles can all then be accurately located with reference to it. Such triangulation methods were used for accurate large-scale land surveying until the rise of global satellite systems in the 1980s. Triangulation may be used to find the position of the ship when the positions of A and B are known, an observer at A measures the angle α, while the observer at B measures β. The position of any vertex of a triangle can be calculated if the position of one side, the following formulae are strictly correct only for a flat surface. If the curvature of the Earth must be allowed for, then spherical trigonometry must be used, take L as the distance between A and B. It can readily be seen that d = L * / which is the result required, however, this simple rule is only useful when a manually observed result is to be manually calculated. In that case, the anomaly when α is an angle can be handled by simply saying d = L* when the case is encountered. The procedure below is perfectly general, at a higher cost, the cost is, Simple, Lookup, lookup, divide, divide. General, Lookup, lookup, multiply, add, lookup, add, lookup, divide, the well-known book by Doerr, All the Light We Cannot See, gets this wrong. On pages 245 and 335 he suggests that this calculation must be performed before transferring the angles observed to a map, triangulation today is used for many purposes, including surveying, navigation, metrology, astrometry, binocular vision, model rocketry and gun direction of weapons. Abu Rayhan Biruni also introduced triangulation techniques to measure the size of the Earth, simplified Roman techniques then seem to have co-existed with more sophisticated techniques used by professional surveyors. But it was rare for such methods to be translated into Latin and this became very influential, and the technique spread across Germany, Austria and the Netherlands. Snell underestimated the distance by 3. 5%, snell calculated how the planar formulae could be corrected to allow for the curvature of the earth. He also showed how to resection, or calculate, the position of a point inside a triangle using the angles cast between the vertices at the unknown point and these could be measured much more accurately than bearings of the vertices, which depended on a compass. This established the key idea of surveying a primary network of control points first. Thanks to improvements in instruments and accuracy, Picards is rated as the first reasonably accurate measurement of the radius of the earth, multilateration, where a point is calculated using the time-difference-of-arrival between other known points Parallax Resection SOCET SET Stellar triangulation Stereopsis Trig point Bagrow, L
7.
Angle
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In planar geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles formed by two rays lie in a plane, but this plane does not have to be a Euclidean plane, Angles are also formed by the intersection of two planes in Euclidean and other spaces. Angles formed by the intersection of two curves in a plane are defined as the angle determined by the tangent rays at the point of intersection. Similar statements hold in space, for example, the angle formed by two great circles on a sphere is the dihedral angle between the planes determined by the great circles. Angle is also used to designate the measure of an angle or of a rotation and this measure is the ratio of the length of a circular arc to its radius. In the case of an angle, the arc is centered at the vertex. In the case of a rotation, the arc is centered at the center of the rotation and delimited by any other point and its image by the rotation. The word angle comes from the Latin word angulus, meaning corner, cognate words are the Greek ἀγκύλος, meaning crooked, curved, both are connected with the Proto-Indo-European root *ank-, meaning to bend or bow. Euclid defines a plane angle as the inclination to each other, in a plane, according to Proclus an angle must be either a quality or a quantity, or a relationship. In mathematical expressions, it is common to use Greek letters to serve as variables standing for the size of some angle, lower case Roman letters are also used, as are upper case Roman letters in the context of polygons. See the figures in this article for examples, in geometric figures, angles may also be identified by the labels attached to the three points that define them. For example, the angle at vertex A enclosed by the rays AB, sometimes, where there is no risk of confusion, the angle may be referred to simply by its vertex. However, in geometrical situations it is obvious from context that the positive angle less than or equal to 180 degrees is meant. Otherwise, a convention may be adopted so that ∠BAC always refers to the angle from B to C. Angles smaller than an angle are called acute angles. An angle equal to 1/4 turn is called a right angle, two lines that form a right angle are said to be normal, orthogonal, or perpendicular. Angles larger than an angle and smaller than a straight angle are called obtuse angles. An angle equal to 1/2 turn is called a straight angle, Angles larger than a straight angle but less than 1 turn are called reflex angles
8.
Navigation
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Navigation is a field of study that focuses on the process of monitoring and controlling the movement of a craft or vehicle from one place to another. The field of navigation includes four categories, land navigation, marine navigation, aeronautic navigation. It is also the term of art used for the specialized knowledge used by navigators to perform navigation tasks, all navigational techniques involve locating the navigators position compared to known locations or patterns. Navigation, in a sense, can refer to any skill or study that involves the determination of position and direction. In this sense, navigation includes orienteering and pedestrian navigation, for information about different navigation strategies that people use, visit human navigation. In the European medieval period, navigation was considered part of the set of seven mechanical arts, early Pacific Polynesians used the motion of stars, weather, the position of certain wildlife species, or the size of waves to find the path from one island to another. Maritime navigation using scientific instruments such as the mariners astrolabe first occurred in the Mediterranean during the Middle Ages, the perfecting of this navigation instrument is attributed to Portuguese navigators during early Portuguese discoveries in the Age of Discovery. Open-seas navigation using the astrolabe and the compass started during the Age of Discovery in the 15th century, the Portuguese began systematically exploring the Atlantic coast of Africa from 1418, under the sponsorship of Prince Henry. In 1488 Bartolomeu Dias reached the Indian Ocean by this route, in 1492 the Spanish monarchs funded Christopher Columbuss expedition to sail west to reach the Indies by crossing the Atlantic, which resulted in the Discovery of America. In 1498, a Portuguese expedition commanded by Vasco da Gama reached India by sailing around Africa, soon, the Portuguese sailed further eastward, to the Spice Islands in 1512, landing in China one year later. The fleet of seven ships sailed from Sanlúcar de Barrameda in Southern Spain in 1519, crossed the Atlantic Ocean, some ships were lost, but the remaining fleet continued across the Pacific making a number of discoveries including Guam and the Philippines. By then, only two galleons were left from the original seven, the Victoria led by Elcano sailed across the Indian Ocean and north along the coast of Africa, to finally arrive in Spain in 1522, three years after its departure. The Trinidad sailed east from the Philippines, trying to find a path back to the Americas. He arrived in Acapulco on October 8,1565, the term stems from 1530s, from Latin navigationem, from navigatus, pp. of navigare to sail, sail over, go by sea, steer a ship, from navis ship and the root of agere to drive. Roughly, the latitude of a place on Earth is its angular distance north or south of the equator, latitude is usually expressed in degrees ranging from 0° at the Equator to 90° at the North and South poles. The height of Polaris in degrees above the horizon is the latitude of the observer, similar to latitude, the longitude of a place on Earth is the angular distance east or west of the prime meridian or Greenwich meridian. Longitude is usually expressed in degrees ranging from 0° at the Greenwich meridian to 180° east and west, sydney, for example, has a longitude of about 151° east. New York City has a longitude of 74° west, for most of history, mariners struggled to determine longitude
9.
Metrology
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The field of metrology is important for establishing a common understanding of units, which is crucial in linking human activities. This led to the creation of the decimal based metric system in 1795 to establish a set of standards for types of measurements. This has since evolved into the International System of Units as a result of a made in the 11th Conference Generale des Poids et Mesures in 1960. The NMS greatly effects how measurements are undertaken in the country and this has wide reaching impacts in a variety of different regions of society. It has implications in the area of economies, energy, environment, health, manufacturing, industry, consumer confidence, the effects of metrology on trade and the economy are some of the easiest observed societal impacts. The field of metrology is important for establishing a common understanding of units and these base concepts of metrology are propagated by the three main fields of metrology, which are, scientific or fundamental metrology, applied, technical or industrial metrology, and legal metrology. While there is no definition of fundamental metrology it is considered to be the top level of scientific metrology that strives for the highest level of accuracy. The BIPM maintains a database of the calibration and measurement capabilities of various institutes around the world. These institutes, whose activities are peer-reviewed, provide the reference points for metrological traceability. In the area of measurement, the BIPM has identified nine metrology areas, including length, mass, although the emphasis in this area of metrology is on the measurements themselves, traceability of the calibration of the measurement devices is necessary to ensure confidence in the measurements. Industrial metrology is important to the economical and industrial development of a country, such statutory requirements might arise from, amongst others, the needs for protection of health, public safety, the environment, enabling taxation, protection of consumers and fair trade. The International Organization for Legal Metrology was established to assist in harmonising such regulations across national boundaries to ensure that legal requirements do not inhibit trade. In Europe WELMEC was established in 1990 to promote cooperation on the field of metrology in the European Union. Throughout history the ability to make measurements has been instrumental in the progress of mankind, the ability to measure alone is not sufficient, rather the ability to compare separate measurements and have agreeability is crucial for the measurements to be meaningful. The first record of a permanent standard is from 2900 BC, the cubit was decreed to be the length of the Pharaohs forearm plus the width of his hand and replica standards were given out to builders. The success of standardized length during the building of the pyramids is evidenced by the lengths of the pyramid bases differing by no more than 0. 05%, other civilizations produced their own measurement standards that were accepted throughout their nations. The architecture of the Roman and Greek empires were based on their own systems of measurement. Nonetheless, the fall of great empires and the rise of the Dark Ages caused much of measurement knowledge
10.
Astrometry
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Astrometry is the branch of astronomy that involves precise measurements of the positions and movements of stars and other celestial bodies. The information obtained by astrometric measurements provides information on the kinematics and physical origin of the Solar System and our galaxy, the history of astrometry is linked to the history of star catalogues, which gave astronomers reference points for objects in the sky so they could track their movements. This can be dated back to Hipparchus, who around 190 BC used the catalogue of his predecessors Timocharis, in doing so, he also developed the brightness scale still in use today. Hipparchus compiled a catalogue with at least 850 stars and their positions, hipparchuss successor, Ptolemy, included a catalogue of 1,022 stars in his work the Almagest, giving their location, coordinates, and brightness. Ibn Yunus observed more than 10,000 entries for the Suns position for years using a large astrolabe with a diameter of nearly 1.4 metres. In the 15th century, the Timurid astronomer Ulugh Beg compiled the Zij-i-Sultani, like the earlier catalogs of Hipparchus and Ptolemy, Ulugh Begs catalogue is estimated to have been precise to within approximately 20 minutes of arc. In the 16th century, Tycho Brahe used improved instruments, including large mural instruments, to measure star positions more accurately than previously, Taqi al-Din measured the right ascension of the stars at the Istanbul observatory of Taqi al-Din using the observational clock he invented. When telescopes became commonplace, setting circles sped measurements James Bradley first tried to measure stellar parallaxes in 1729, the stellar movement proved too insignificant for his telescope, but he instead discovered the aberration of light and the nutation of the Earths axis. His cataloguing of 3222 stars was refined in 1807 by Friedrich Bessel and he made the first measurement of stellar parallax,0.3 arcsec for the binary star 61 Cygni. Being very difficult to measure, only about 60 stellar parallaxes had been obtained by the end of the 19th century, astrographs using astronomical photographic plates sped the process in the early 20th century. Automated plate-measuring machines and more sophisticated technology of the 1960s allowed more efficient compilation of star catalogues. In the 1980s, charge-coupled devices replaced photographic plates and reduced optical uncertainties to one milliarcsecond and this technology made astrometry less expensive, opening the field to an amateur audience. In 1989, the European Space Agencys Hipparcos satellite took astrometry into orbit, operated from 1989 to 1993, Hipparcos measured large and small angles on the sky with much greater precision than any previous optical telescopes. During its 4-year run, the positions, parallaxes, and proper motions of 118,218 stars were determined with a degree of accuracy. A new Tycho catalog drew together a database of 1,058,332 to within 20-30 mas, additional catalogues were compiled for the 23,882 double/multiple stars and 11,597 variable stars also analyzed during the Hipparcos mission. Today, the catalogue most often used is USNO-B1.0, during the past 50 years,7,435 Schmidt camera plates were used to complete several sky surveys that make the data in USNO-B1.0 accurate to within 0.2 arcsec. In observational astronomy, astrometric techniques help identify stellar objects by their unique motions and it is instrumental for keeping time, in that UTC is basically the atomic time synchronized to Earths rotation by means of exact observations. Astrometry is an important step in the distance ladder because it establishes parallax distance estimates for stars in the Milky Way
11.
Binocular vision
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Binocular vision is vision in which creatures having two eyes use them together. The word binocular comes from two Latin roots, bini for double, and oculus for eye, according to Fahle, having two eyes confers six advantages over having one. It gives a creature a spare eye in one is damaged. It gives a wider field of view and it can give stereopsis in which binocular disparity provided by the two eyes different positions on the head gives precise depth perception. This also allows a creature to break the camouflage of another creature and it allows the angles of the eyes lines of sight, relative to each other, and those lines relative to a particular object to be determined from the images in the two eyes. These properties are necessary for the third advantage and it allows a creature to see more of, or all of, an object behind an obstacle. It gives binocular summation in which the ability to detect faint objects is enhanced, other phenomena of binocular vision include utrocular discrimination, eye dominance, allelotropia, binocular fusion or singleness of vision, and binocular rivalry. Binocular vision helps with performance skills such as catching, grasping and it also allows humans to walk over and around obstacles at greater speed and with more assurance. Optometrists and/or Orthoptists are eyecare professionals who fix binocular vision problems, some animals, usually, but not always, prey animals, have their two eyes positioned on opposite sides of their heads to give the widest possible field of view. Examples include rabbits, buffaloes, and antelopes, in such animals, the eyes often move independently to increase the field of view. Even without moving their eyes, some birds have a 360-degree field of view, other animals that are not necessarily predators, such as fruit bats and a number of primates also have forward-facing eyes. These are usually animals that need fine depth discrimination/perception, for instance, binocular vision improves the ability to pick a chosen fruit or to find, the direction of a point relative to the head is called visual direction, or version. The angle between the line of sight of the two eyes when fixating a point is called the disparity, binocular parallax, or vergence demand. The relation between the position of the two eyes, version and vergence is described by Herings law of visual direction, in animals with forward-facing eyes, the eyes usually move together. Eye movements are either conjunctive, version eye movements, usually described by their type, or they are disjunctive, vergence eye movements. The relation between version and vergence eye movements in humans is described by Herings law of equal innervation, some animals use both of the above strategies. A starling, for example, has laterally placed eyes to cover a wide field of view, a remarkable example is the chameleon, whose eyes appear as if mounted on turrets, each moving independently of the other, up or down, left or right. Nevertheless, the chameleon can bring both of its eyes to bear on an object when it is hunting, showing vergence
12.
Model rocket
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A model rocket is a small rocket designed to reach low altitudes and recovered by a variety of means. According to the United States National Association of Rocketry Safety Code, model rockets are constructed of paper, wood, plastic, the code also provides guidelines for motor use, launch site selection, launch methods, launcher placement, recovery system design and deployment and more. Since the early 1960s, a copy of the Model Rocket Safety Code has been provided with most model rocket kits, in the early thirteenth century the Chinese turned black-powder–propelled objects, formerly only used for entertainment, into weapons of war. The Chinese ‘arrows of fire’ were fired from a sort of catapult launcher, the black powder was packed in a closed tube that had a hole in one end for escaping hot gases, and a long stick as an elementary stability and guidance system. Refinements in rocket design were made over the few hundred years. In 1591 a Belgian, Jean Beavie, described and sketched the important idea of multistage rockets, multistaging, placing two or more pockets of fuel in line and firing them in step fashion, is the practical answer to the problem of escaping earths gravitational attraction. They originally designed the motor and rocket for Robert to use in lectures on the principles of rocket-powered flight, but then Orville read articles written in Popular Mechanics by G. Harry Stine about the safety problems associated with young people trying to make their own rocket engines. With the launch of Sputnik, many people were trying to build their own rocket motors. Some of these attempts were dramatized in the fact-based movie October Sky, the Carlisles realized their motor design could be marketed and provide a safe outlet for a new hobby. They sent samples to Mr. Stine in January 1957, Stine, a range safety officer at White Sands Missile Range, built and flew the models, and then devised a safety handbook for the activity based on his experience at the range. The first American model rocket company was Model Missiles Incorporated, in Denver, Colorado, opened by Stine, Stine had model rocket engines made by a local fireworks company recommended by Carlisle, but reliability and delivery problems forced Stine to approach others. Stine eventually approached Vernon Estes, the son of a fireworks maker. Estes founded Estes Industries in 1958 in Denver, Colorado and developed an automated machine for manufacturing solid model rocket motors for MMI. The machine, nicknamed Mabel, made low-cost motors with great reliability, stines business faltered and this enabled Estes to market the motors separately. Subsequently, he began marketing model rocket kits in 1960, and eventually, Estes moved his company to Penrose, Colorado in 1961. Estes Industries was acquired by Damon Industries in 1970 and it continues to operate in Penrose today. Estes produces and sells Black Powder Rocket Motors, companies like Aerotech, Vulcan, and Kosdon were widely popular at launches during this time as high-power rockets routinely broke Mach 1 and reached heights over 3,000 m. High-power motor reliability was a significant issue in the late 1980s and early 1990s, at costs exceeding $300 per motor, the need to find a cheaper and more reliable alternative was apparent
13.
Weapon
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A weapon, arm, or armament is any device used with intent to inflict damage or harm to living beings, structures, or systems. Weapons are used to increase the efficacy and efficiency of such as hunting, crime, law enforcement, self-defense. In a broader context, weapons may be construed to include anything used to gain a strategic, something that has been re-purposed, converted, or enhanced to become a weapon of war is termed weaponized, such as a weaponized virus or weaponized lasers. The use of objects as weapons has been observed among chimpanzees, however, this can not be confirmed using physical evidence because wooden clubs, spears, and unshaped stones would not have left an unambiguous record. The earliest unambiguous weapons to be found are the Schöninger Speere, the first defensive structures and fortifications appeared in the Bronze Age, indicating an increased need for security. Weapons designed to breach fortifications followed soon after, for example the battering ram was in use by 2500 BC, although early Iron Age swords were not superior to their bronze predecessors, once iron-working developed, around 1300 BC in Greece Alex Webb, Metalworking in Ancient Greece. Domestication of the horse and widespread use of spoked wheels by ca.2000 BC, led to the light, the mobility provided by chariots were important during this era. Spoke-wheeled chariot usage peaked around 1300 BC and then declined, ceasing to be militarily relevant by the 4th century BC. Cavalry developed once horses were bred to support the weight of a man, the horse extended the range and increased the speed of attacks. Ships built as weapons or warships such as the trireme were in use by the 7th century BC and these ships were eventually replaced by larger ships by the 4th century BC. European warfare during the Post-classical history was dominated by groups of knights supported by massed infantry. They were involved in combat and sieges which involved various siege weapons. Knights on horseback developed tactics for charging with lances providing an impact on the enemy formations, whereas infantry, in the age before structured formations, relied on cheap, sturdy weapons such as spears and billhooks in close combat and bows from a distance. As armies became more professional, their equipment was standardized and infantry transitioned to pikes, pikes are normally seven to eight feet in length, in conjunction with smaller side-arms. In Eastern and Middle Eastern warfare, similar tactics were developed independent of European influences, the introduction of gunpowder from the Far East at the end of this period revolutionized warfare. Formations of musketeers, protected by pikemen came to dominate open battles, the European Renaissance marked the beginning of the implementation of firearms in western warfare. Guns and rockets were introduced to the battlefield, firearms are qualitatively different from earlier weapons because they release energy from combustible propellants such as gunpowder, rather than from a counter-weight or spring. This energy is released very rapidly and can be replicated without much effort by the user, therefore even early firearms such as the arquebus were much more powerful than human-powered weapons. During the U. S. Civil War various technologies including the gun and ironclad warship emerged that would be recognizable and useful military weapons today
14.
Ptolemaic dynasty
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Their rule lasted for 275 years, from 305 to 30 BC. They were the last dynasty of ancient Egypt, Ptolemy, one of the seven somatophylakes who served as Alexander the Greats generals and deputies, was appointed satrap of Egypt after Alexanders death in 323 BC. In 305 BC, he declared himself Ptolemy I, later known as Sōter Saviour, the Egyptians soon accepted the Ptolemies as the successors to the pharaohs of independent Egypt. Ptolemys family ruled Egypt until the Roman conquest of 30 BC, all the male rulers of the dynasty took the name Ptolemy. Ptolemaic queens regnant, some of whom were the sisters of their husbands, were usually called Cleopatra, Arsinoe or Berenice. The most famous member of the line was the last queen, Cleopatra VII and her apparent suicide at the conquest by Rome marked the end of Ptolemaic rule in Egypt. Dates in brackets represent the dates of the Ptolemaic pharaohs. They frequently ruled jointly with their wives, who were also their sisters. Of these, one of the last and most famous was Cleopatra, several systems exist for numbering the later rulers, the one used here is the one most widely used by modern scholars. Arsinoe IV, in opposition to Cleopatra Ptolemy Keraunos - eldest son of Ptolemy I Soter, Ptolemy Apion - son of Ptolemy VIII Physcon. Ptolemy Philadelphus - son of Mark Antony and Cleopatra VII, Ptolemy of Mauretania - son of King Juba II of Numidia and Mauretania and Cleopatra Selene II, daughter of Cleopatra VII and Mark Antony. Contemporaries describe a number of the Ptolemaic dynasty members as extremely obese, whilst sculptures and coins reveal prominent eyes, familial Graves disease could explain the swollen necks and eye prominence, although this is unlikely to occur in the presence of morbid obesity. A. Lampela, Rome and the Ptolemies of Egypt, the development of their political relations 273-80 B. C. J. G. Manning, The Last Pharaohs, Egypt Under the Ptolemies, 305-30 BC. Livius. org, Ptolemies — by Jona Lendering
15.
Thales of Miletus
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Thales of Miletus was a pre-Socratic Greek/Phoenician philosopher, mathematician and astronomer from Miletus in Asia Minor. He was one of the Seven Sages of Greece, Thales is recognized for breaking from the use of mythology to explain the world and the universe, and instead explaining natural objects and phenomena by theories and hypothesis, i. e. science. Aristotle reported Thales hypothesis that the principle of nature and the nature of matter was a single material substance. In mathematics, Thales used geometry to calculate the heights of pyramids and he is the first known individual to use deductive reasoning applied to geometry, by deriving four corollaries to Thales theorem. He is the first known individual to whom a mathematical discovery has been attributed, the ancient source, Apollodorus of Athens, writing during the 2nd century BCE, thought Thales was born about the year 625 BCE. The dates of Thales life are not exactly known, but are roughly established by a few events mentioned in the sources. According to Herodotus Thales predicted the eclipse of May 28,585 BC. Diogenes Laërtius quotes the chronicle of Apollodorus of Athens as saying that Thales died at the age of 78 during the 58th Olympiad and attributes his death to heat stroke while watching the games. Plutarch had earlier told this version, Solon visited Thales and asked him why he remained single, nevertheless, several years later, anxious for family, he adopted his nephew Cybisthus. Thales involved himself in many activities, taking the role of an innovator, some say that he left no writings, others say that he wrote On the Solstice and On the Equinox. Diogenes Laërtius quotes two letters from Thales, one to Pherecydes of Syros, offering to review his book on religion, Thales identifies the Milesians as Athenian colonists. He was aware of the existence of the lodestone, and was the first to be connected to knowledge of this in history, according to Aristotle, Thales thought lodestones had souls, because iron is attracted to them. According to Hieronymus, historically quoted by Diogenes Laertius, Thales found the height of pyramids by comparison between the lengths of the shadows cast by a person and by the pyramids, several anecdotes suggest Thales was not just a philosopher, but also a businessman. A story, with different versions, recounts how Thales achieved riches from an olive harvest by prediction of the weather, in one version, he bought all the olive presses in Miletus after predicting the weather and a good harvest for a particular year. Thales’ political life had mainly to do with the involvement of the Ionians in the defense of Anatolia against the power of the Persians. In neighbouring Lydia, a king had come to power, Croesus and he had conquered most of the states of coastal Anatolia, including the cities of the Ionians. The story is told in Herodotus, the war endured for five years, but in the sixth an eclipse of the Sun spontaneously halted a battle in progress. It seems that Thales had predicted this solar eclipse, the Seven Sages were most likely already in existence, as Croesus was also heavily influenced by Solon of Athens, another sage
16.
Similarity (geometry)
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Two geometrical objects are called similar if they both have the same shape, or one has the same shape as the mirror image of the other. More precisely, one can be obtained from the other by uniformly scaling and this means that either object can be rescaled, repositioned, and reflected, so as to coincide precisely with the other object. If two objects are similar, each is congruent to the result of a uniform scaling of the other. A modern and novel perspective of similarity is to consider geometrical objects similar if one appears congruent to the other zoomed in or out at some level. For example, all circles are similar to other, all squares are similar to each other. On the other hand, ellipses are not all similar to other, rectangles are not all similar to each other. If two angles of a triangle have measures equal to the measures of two angles of triangle, then the triangles are similar. Corresponding sides of similar polygons are in proportion, and corresponding angles of similar polygons have the same measure and it can be shown that two triangles having congruent angles are similar, that is, the corresponding sides can be proved to be proportional. This is known as the AAA similarity theorem, due to this theorem, several authors simplify the definition of similar triangles to only require that the corresponding three angles are congruent. There are several statements each of which is necessary and sufficient for two triangles to be similar,1, the triangles have two congruent angles, which in Euclidean geometry implies that all their angles are congruent. That is, If ∠BAC is equal in measure to ∠B′A′C′, and ∠ABC is equal in measure to ∠A′B′C′, then this implies that ∠ACB is equal in measure to ∠A′C′B′, all the corresponding sides have lengths in the same ratio, AB/A′B′ = BC/B′C′ = AC/A′C′. This is equivalent to saying that one triangle is an enlargement of the other, two sides have lengths in the same ratio, and the angles included between these sides have the same measure. For instance, AB/A′B′ = BC/B′C′ and ∠ABC is equal in measure to ∠A′B′C′ and this is known as the SAS Similarity Criterion. When two triangles △ABC and △A′B′C′ are similar, one writes △ABC ∼ △A′B′C′, there are several elementary results concerning similar triangles in Euclidean geometry, Any two equilateral triangles are similar. Two triangles, both similar to a triangle, are similar to each other. Corresponding altitudes of similar triangles have the ratio as the corresponding sides. Two right triangles are similar if the hypotenuse and one side have lengths in the same ratio. Given a triangle △ABC and a line segment DE one can, with ruler and compass, the statement that the point F satisfying this condition exists is Walliss Postulate and is logically equivalent to Euclids Parallel Postulate
17.
Pyramid
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A pyramid is a structure whose outer surfaces are triangular and converge to a single point at the top, making the shape roughly a pyramid in the geometric sense. The base of a pyramid can be trilateral, quadrilateral, or any polygon shape, as such, a pyramid has at least three outer triangular surfaces. The square pyramid, with base and four triangular outer surfaces, is a common version. A pyramids design, with the majority of the closer to the ground. This distribution of weight allowed early civilizations to create stable monumental structures and it has been demonstrated that the common shape of the pyramids of antiquity, from Egypt to Central America, represents the dry-stone construction that requires minimum human work. Pyramids have been built by civilizations in many parts of the world, khufus Pyramid is built mainly of limestone, and is considered an architectural masterpiece. It contains over 2,000,000 blocks ranging in weight from 2.5 tonnes to 15 tonnes and is built on a base with sides measuring about 230 m. Its four sides face the four cardinal points precisely and it has an angle of 52 degrees and it is still the tallest pyramid. The largest pyramid by volume is the Great Pyramid of Cholula, the Mesopotamians built the earliest pyramidal structures, called ziggurats. In ancient times, these were painted in gold/bronze. Since they were constructed of sun-dried mud-brick, little remains of them, ziggurats were built by the Sumerians, Babylonians, Elamites, Akkadians, and Assyrians for local religions. Each ziggurat was part of a complex which included other buildings. The precursors of the ziggurat were raised platforms that date from the Ubaid period during the fourth millennium BC, the earliest ziggurats began near the end of the Early Dynastic Period. The latest Mesopotamian ziggurats date from the 6th century BC, built in receding tiers upon a rectangular, oval, or square platform, the ziggurat was a pyramidal structure with a flat top. Sun-baked bricks made up the core of the ziggurat with facings of fired bricks on the outside, the facings were often glazed in different colors and may have had astrological significance. Kings sometimes had their names engraved on these glazed bricks, the number of tiers ranged from two to seven. It is assumed that they had shrines at the top, but there is no evidence for this. Access to the shrine would have been by a series of ramps on one side of the ziggurat or by a ramp from base to summit
18.
Ancient Egypt
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Ancient Egypt was a civilization of ancient Northeastern Africa, concentrated along the lower reaches of the Nile River in what is now the modern country of Egypt. It is one of six civilizations to arise independently, Egyptian civilization followed prehistoric Egypt and coalesced around 3150 BC with the political unification of Upper and Lower Egypt under the first pharaoh Narmer. In the aftermath of Alexander the Greats death, one of his generals, Ptolemy Soter and this Greek Ptolemaic Kingdom ruled Egypt until 30 BC, when, under Cleopatra, it fell to the Roman Empire and became a Roman province. The success of ancient Egyptian civilization came partly from its ability to adapt to the conditions of the Nile River valley for agriculture, the predictable flooding and controlled irrigation of the fertile valley produced surplus crops, which supported a more dense population, and social development and culture. Its art and architecture were widely copied, and its antiquities carried off to far corners of the world and its monumental ruins have inspired the imaginations of travelers and writers for centuries. The Nile has been the lifeline of its region for much of human history, nomadic modern human hunter-gatherers began living in the Nile valley through the end of the Middle Pleistocene some 120,000 years ago. By the late Paleolithic period, the climate of Northern Africa became increasingly hot and dry. In Predynastic and Early Dynastic times, the Egyptian climate was less arid than it is today. Large regions of Egypt were covered in treed savanna and traversed by herds of grazing ungulates, foliage and fauna were far more prolific in all environs and the Nile region supported large populations of waterfowl. Hunting would have been common for Egyptians, and this is also the period when many animals were first domesticated. The largest of these cultures in upper Egypt was the Badari, which probably originated in the Western Desert, it was known for its high quality ceramics, stone tools. The Badari was followed by the Amratian and Gerzeh cultures, which brought a number of technological improvements, as early as the Naqada I Period, predynastic Egyptians imported obsidian from Ethiopia, used to shape blades and other objects from flakes. In Naqada II times, early evidence exists of contact with the Near East, particularly Canaan, establishing a power center at Hierakonpolis, and later at Abydos, Naqada III leaders expanded their control of Egypt northwards along the Nile. They also traded with Nubia to the south, the oases of the desert to the west. Royal Nubian burials at Qustul produced artifacts bearing the oldest-known examples of Egyptian dynastic symbols, such as the crown of Egypt. They also developed a ceramic glaze known as faience, which was used well into the Roman Period to decorate cups, amulets, and figurines. During the last predynastic phase, the Naqada culture began using written symbols that eventually were developed into a system of hieroglyphs for writing the ancient Egyptian language. The Early Dynastic Period was approximately contemporary to the early Sumerian-Akkadian civilisation of Mesopotamia, the third-century BC Egyptian priest Manetho grouped the long line of pharaohs from Menes to his own time into 30 dynasties, a system still used today
19.
Rhind Mathematical Papyrus
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The Rhind Mathematical Papyrus is one of the best known examples of Egyptian mathematics. It is named after Alexander Henry Rhind, a Scottish antiquarian and it dates to around 1550 BC. 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 than the former. The Rhind Mathematical Papyrus dates to the Second Intermediate Period of Egypt and it was copied by the scribe Ahmes, from a now-lost text from the reign of king Amenemhat III. Written in the script, this Egyptian manuscript is 33 cm tall. The papyrus began to be transliterated and mathematically translated in the late 19th century, the mathematical translation aspect remains incomplete in several respects. The document is dated to Year 33 of the Hyksos king Apophis and also contains a separate later historical note on its verso likely dating from the period of his successor, Khamudi. In the opening paragraphs of the papyrus, Ahmes presents the papyrus as giving Accurate reckoning for inquiring into things, the scribe Ahmose writes this copy. Several books and articles about the Rhind Mathematical Papyrus have been published, a more recent overview of the Rhind Papyrus was published in 1987 by Robins and Shute. The first part of the Rhind papyrus consists of reference tables, the problems start out with simple fractional expressions, followed by completion problems and more involved linear equations. The first part of the papyrus is taken up by the 2/n table, the fractions 2/n for odd n ranging from 3 to 101 are expressed as sums of unit fractions. For example,2 /15 =1 /10 +1 /30. The decomposition of 2/n into unit fractions is never more than 4 terms long as in for example 2 /101 =1 /101 +1 /202 +1 /303 +1 /606. This table is followed by a smaller, tiny table of fractional expressions for the numbers 1 through 9 divided by 10. Problems 1-7, 7B and 8-40 are concerned with arithmetic and elementary algebra, problems 1–6 compute divisions of a certain number of loaves of bread by 10 men and record the outcome in unit fractions. Problems 7–20 show how to multiply the expressions 1 + 1/2 + 1/4 = 7/4 and 1 + 2/3 + 1/3 =2 by different fractions, problems 21–23 are problems in completion, which in modern notation are simply subtraction problems. Problems 24–34 are ‘’aha’’ problems, these are linear equations, problem 32 for instance corresponds to solving x + 1/3 x + 1/4 x =2 for x. Problems 35–38 involve divisions of the heqat, which is an ancient Egyptian unit of volume, problems 39 and 40 compute the division of loaves and use arithmetic progressions
20.
Slope
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In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line. The direction of a line is increasing, decreasing, horizontal or vertical. A line is increasing if it goes up from left to right, the slope is positive, i. e. m >0. A line is decreasing if it goes down from left to right, the slope is negative, i. e. m <0. If a line is horizontal the slope is zero, if a line is vertical the slope is undefined. The steepness, incline, or grade of a line is measured by the value of the slope. A slope with an absolute value indicates a steeper line Slope is calculated by finding the ratio of the vertical change to the horizontal change between two distinct points on a line. Sometimes the ratio is expressed as a quotient, giving the 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 rise of a road between two points is the difference between the altitude of the road at two points, say y1 and y2, or in other words, the rise is = Δy. Here the slope of the road between the two points is described as the ratio of the altitude change to the horizontal distance between any two points on the line. In mathematical language, the m of the line is m = y 2 − y 1 x 2 − x 1. The concept of slope applies directly to grades or gradients in geography, as a generalization of this practical description, the mathematics of differential calculus defines the slope of a curve at a point as the slope of the tangent line at that point. When the curve given by a series of points in a diagram or in a list of the coordinates of points, thereby, the simple idea of slope becomes one of the main basis of the modern world in terms of both technology and the built environment. This is described by the equation, m = Δ y Δ x = vertical change horizontal change = rise run. Given two points and, the change in x from one to the other is x2 − x1, substituting both quantities into the above equation generates the formula, m = y 2 − y 1 x 2 − x 1. The formula fails for a line, parallel to the y axis. Suppose a line runs through two points, P = and Q =, since the slope is positive, the direction of the line is increasing
21.
Dioptra
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A dioptra is a classical astronomical and surveying instrument, dating from the 3rd century BCE. The dioptra was a 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, greek astronomers used the dioptra to measure the positions of stars, both Euclid and Geminus refer to the dioptra in their astronomical works. By the time of Ptolemy, it was obsolete as an astronomical instrument and it continued in use as an effective surveying tool. Adapted to surveying, the dioptra is similar to the theodolite, or surveyors transit and it is a more accurate version of the groma. The dioptra may have been sophisticated enough, for example, to construct a tunnel through two points in a mountain. There is some speculation that it may have used to build the Eupalinian aqueduct. Scholars disagree whether the dioptra was available that early, an entire book about the construction and surveying usage of the dioptra is credited to Hero of Alexandria. Hero was one of history’s most ingenious engineers and applied mathematicians, the dioptra was used extensively on aqueduct building projects. Screw turns on different parts of the instrument made it easy to calibrate for very precise measurements The dioptra was replaced as a surveying instrument by the theodolite. Alidade Isaac Moreno Gallo The Dioptra Tesis and reconstructon of the Dioptra, the History and Practice of Ancient Astronomy, pages 34-35. Oxford University Press. net Tom M. Apostol, The Tunnel of Samos, Engineering and Science,64, 30-40
22.
Alidade
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An alidade 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 draw a line on a table in the direction of the object or to measure the angle to the object from some reference point. Angles measured can be horizontal, vertical or in any chosen plane, the alidade was originally a part of many types of scientific and astronomical instrument. At one time, some alidades, particularly used on graduated circles as on astrolabes, were also called diopters. With modern technology, the name is applied to instruments such as the plane table alidade. The word in Arabic, signifies the same device, in Greek and Latin, it is respectively called διοπτρα, dioptra, and linea fiduciae, fiducial line. The earliest alidades consisted of a bar, rod or similar component with a vane on each end, each vane has a hole, slot or other indicator through which one can view a distant object. There may also be a pointer or pointers on the alidade to indicate a position on a scale, alidades have been made of wood, ivory, brass and other materials. The figure on the left displays drawings that attempt to show the general forms of various alidades that can be found on many antique instruments, real alidades of these types could be much more decorative, revealing the makers artistic talents as well as his technical skills. In the terminology of the time, the edge of an alidade at which one reads a scale or draws a line is called a fiducial edge, alidade B in the diagram shows a straight, flat bar with a vane at either end. The vanes are not centred on the bar but offset so that the line coincides with the edge of the bar. The vanes have a hole in each with a fine wire held vertically in the opening. To use the alidade, the user sights an object and lines it up with the wires in each vane and this type of alidade could be found on a plane table, graphometer or similar instrument. Alidades A and C are similar to B but have a slit or circular hole without a wire, in the diagram, the openings are exaggerated in size to show the shape, they would be smaller in a real alidade, perhaps 2 mm or so in width. One can look through the openings and line the openings up with the object of interest in the distance, with a small opening, the error in sighting the object is small. However, if a dim object such as a star is observed through a small hole and this form is shown in the diagram as having pointers. These can be used to read off an angle on a scale that is engraved around the edge of the instrument. Alidades of this form are found on astrolabes, mariners astrolabes, alidade D has vanes without any openings
23.
Hero of Alexandria
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Hero of Alexandria was a Greek mathematician and engineer who was active in his native city of Alexandria, Roman Egypt. He is considered the greatest experimenter of antiquity and his work is representative of the Hellenistic scientific tradition, Hero published a well recognized description of a steam-powered device called an aeolipile. Among his most famous inventions was a windwheel, constituting the earliest instance of wind harnessing on land and he is said to have been a follower of the atomists. Some of his ideas were derived from the works of Ctesibius, much of Heros original writings and designs have been lost, but some of his works were preserved in Arabic manuscripts. Hero described the construction of the aeolipile which was a reaction engine. It was created almost two millennia before the industrial revolution, another engine used air from a closed chamber heated by an altar fire to displace water from a sealed vessel, the water was collected and its weight, pulling on a rope, opened temple doors. Some historians have conflated the two inventions to assert that the aeolipile was capable of useful work. The first vending machine was one of his constructions, when a coin was introduced via a slot on the top of the machine. This was included in his list of inventions in his book Mechanics and Optics, when the coin was deposited, it fell upon a pan attached to a lever. The lever opened up a valve which let some water flow out, the pan continued to tilt with the weight of the coin until it fell off, at which point a counter-weight would snap the lever back up and turn off the valve. A windwheel operating an organ, marking the first instance of wind powering a machine in history, the sound of thunder was produced by the mechanically-timed dropping of metal balls onto a hidden drum. The force pump was used in the Roman world. A syringe-like device was described by Hero to control the delivery of air or liquids. In optics, Hero formulated the principle of the shortest path of light, If a ray of light propagates from point A to point B within the same medium, a standalone fountain that operates under self-contained hydrostatic energy A programmable cart that was powered by a falling weight. The program consisted of strings wrapped around the drive axle, Hero described a method for iteratively computing the square root of a number. Today, however, his name is most closely associated with Heros formula for finding the area of a triangle from its side lengths, the most comprehensive edition of Heros works was published in five volumes in Leipzig by the publishing house Teubner in 1903. The Mechanical Technology of Greek and Roman Antiquity, A Study of the Literary Sources, madison, WI, University of Wisconsin Press. Greek and Roman Artillery, Technical Treatises, Schellenberg, H. M. Anmerkungen zu Hero von Alexandria und seinem Werk über den Geschützbau, in, Schellenberg, H. M. / Hirschmann, V. E. / Krieckhaus, A
24.
Pei Xiu
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Pei Xiu, courtesy name Jiyan, was a minister, geographer, and cartographer of the state of Cao Wei during the Three Kingdoms period of Chinese history, as well as the subsequent Jin Dynasty. Pei Xiu was very trusted by Sima Zhao, and participated in the suppression of Zhuge Dans coup. Following Sima Yan taking the throne of the newly established Jin Dynasty, he, in the year 267, Pei was appointed as the Minister of Works for the Jin Dynasty. Pei Xiu outlined and analyzed the advancements of cartography, surveying, there is also evidence that Zhang Heng was the first to establish the grid reference system in Chinese cartography. Pei is best known for his work in cartography, the preface to Pei Xius written work was preserved in the 35th chapter of the Book of Jin, which is the official history for the Jin Dynasty and one of the Twenty-four Histories. It was written in the Book of Jin that Pei made a study of ancient texts in order to update the naming conventions of geographic locations described in old texts. His maps —drawn upon rolls of silk — were presented to the Jin emperor, Pei Xius maps have since been lost, decayed, or destroyed. Yet the oldest existing terrain maps from China date to the 4th century BC, Han Dynasty era maps from the 2nd century BC were found earlier in the 1973 excavation of Mawangdui. In 1697, Qing Dynasty cartographer Hu Wei reconstructed Peis maps in his Yugong Zhuizhui, modern scholars have also used Peis writing to reproduce his works, and historians such as Herrmann have compared Pei to other great ancient cartographers such as the Greek cartographer Ptolemy. Pei Xiu wrote a preface to his maps with essential background information regarding older maps in China, Pei Xiu also provided a great deal of criticism about the existing maps from the Han Dynasty in his time. Later Chinese ideas about the quality of made during the Han Dynasty and before stem from the assessment given by Pei Xiu. Pei Xiu noted that the extant Han maps at his disposal were of use since they featured too many inaccuracies. However, the Qin State maps and Mawangdui maps of the Han Dynasty discovered by archeologists were far superior in quality than those examined and criticized by Pei Xiu. It was not until the 20th century that Pei Xius 3rd century assessment of earlier maps dismal quality would be overturned, the makers of the Han maps were familiar with the use of scale, while the Qin map makers had pinpointed the course of rivers with some accuracy. What these earlier maps did not feature was topographical elevation, which Pei Xiu would outline with his six principles of cartography, Pei also referred to the officer Xiao He, who assembled the maps made during the recently fallen Qin Dynasty. This was done after the founder of the Han Dynasty, Liu Bang had sacked the city of Xianyang, Pei Xiu states, The origin of maps and geographical treatises goes back into former ages. Under the three there were special officials for this. Then, when the Han people sacked Xianyang, Xiao He collected all the maps, now it is no longer possible to find the old maps in the secret archives, and even those Xiao He found are missing
25.
Liu Hui
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Liu Hui was an Ancient Chinese mathematician. He lived in the state of Cao Wei during the Three Kingdoms period of Chinese history, in 263, he edited and published a book with solutions to mathematical problems presented in the famous Chinese book of mathematics known as The Nine Chapters on the Mathematical Art. He was a descendant of the Marquis of Zixiang of the Han dynasty and he completed his commentary to the Nine Chapters in the year 263. He probably visited Luoyang, and measured the suns shadow, along with Zu Chongzhi, Liu Hui was known as one of the greatest mathematicians of ancient China. Liu Hui expressed all of his results in the form of decimal fractions. Liu provided commentary on a proof of a theorem identical to the Pythagorean theorem. In the field of plane areas and solid figures, Liu Hui was one of the greatest contributors to empirical solid geometry, for example, he found that a wedge with rectangular base and both sides sloping could be broken down into a pyramid and a tetrahedral wedge. He also found that a wedge with trapezoid base and both sides sloping could be made to give two tetrahedral wedges separated by a pyramid, in his commentaries on the Nine Chapters, he presented, An algorithm for calculation of pi in the comments to chapter 1. He calculated pi to 3.141024 < π <3.142074 with a 192 sided polygon, Archimedes used a circumscribed 96-polygon to obtain the inequality π <227, and then used an inscribed 96-gon to obtain the inequality 22371 < π. Liu Hui used only one inscribed 96-gon to obtain his π inequality, but he commented that 3.142074 was too large, and picked the first three digits of π =3.141024 ~3.14 and put it in fraction form π =15750. He later invented a method and obtained π =3.1416. Nine Chapters had used the value 3 for π, but Zhang Heng had previously estimated pi to the root of 10. Cavalieris principle to find the volume of a cylinder and the intersection of two perpendicular cylinders although this work was finished by Zu Chongzhi and Zu Gengzhi. Lius commentaries often include explanations why some methods work and why others do not, although his commentary was a great contribution, some answers had slight errors which was later corrected by the Tang mathematician and Taoist believer Li Chunfeng. Liu Hui also presented, in an appendix of 263 AD called Haidao Suanjing or The Sea Island Mathematical Manual, several problems related to surveying. This book contained many practical problems of geometry, including the measurement of the heights of Chinese pagoda towers and this smaller work outlined instructions on how to measure distances and heights with tall surveyors poles and horizontal bars fixed at right angles to them. Liu Huis information about surveying was known to his contemporaries as well, the cartographer and state minister Pei Xiu outlined the advancements of cartography, surveying, and mathematics up until his time. This included the first use of a grid and graduated scale for accurate measurement of distances on representative terrain maps
26.
Multilateration
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Multilateration is a surveillance technique based on the measurement of the difference in distance to two stations at known locations by broadcast signals at known times. Unlike measurements of distance or angle, measuring the difference in distance between two stations results in an infinite number of locations that satisfy the measurement. When these possible locations are plotted, they form a hyperbolic curve, when the two curves are compared, a small number of possible locations are revealed, producing a fix. Multilateration is a technique in radio navigation systems, where it is known as hyperbolic navigation. These systems are easy to construct as there is no need for a common clock. This formed the basis of a number of widely used navigation systems starting in World War II with the British Gee system, the introduction of the microprocessor greatly simplified operation, greatly increasing popularity during the 1980s. The most popular navigation system was LORAN-C, which was used around the world until the system was shut down in 2010. Other systems continue to be used, but the use of satellite navigation systems like GPS have made these systems largely redundant. Both of these systems are commonly used with radio navigation systems. In fact, for locations of the two receivers, a whole set of emitter locations would give the same measurement of TDOA. Given two receiver locations and a known TDOA, the locus of possible emitter locations is one half of a two-sheeted hyperboloid, in simple terms, with two receivers at known locations, an emitter can be located onto a hyperboloid. Note that the receivers do not need to know the time at which the pulse was transmitted – only the time difference is needed. Consider now a third receiver at a third location and this would provide one extra independent TDOA measurement and the emitter is located on the curve determined by the two intersecting hyperboloids. With four receivers there are 3 independent TDOA, three independent parameters are needed for a point in three dimensional space, with additional receivers enhanced accuracy can be obtained. For an overdetermined constellation a least squares can be used for reducing the errors, extended Kalman filters are used for improving the individual signal timings. Averaging over longer times, can improve accuracy. The accuracy also improves if the receivers are placed in a configuration that minimizes the error of the estimate of the position, the emitting platform may, or may not, cooperate in the multilateration surveillance processes. Multilateration can also be used by a receiver to locate itself
27.
Parallax
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The term is derived from the Greek word παράλλαξις, meaning alternation. Due to foreshortening, nearby objects have a larger parallax than more distant objects when observed from different positions, astronomers use the principle of parallax to measure distances to the closer stars. Here, the parallax is the semi-angle of inclination between two sight-lines to the star, as observed when the Earth is on opposite sides of the Sun in its orbit. Parallax also affects optical instruments such as rifle scopes, binoculars, microscopes, many animals, including humans, have two eyes with overlapping visual fields that use parallax to gain depth perception, this process is known as stereopsis. In computer vision the effect is used for stereo vision, and there is a device called a parallax rangefinder that uses it to find range. A simple everyday example of parallax can be seen in the dashboard of motor vehicles that use a needle-style speedometer gauge. When viewed from directly in front, the speed may show exactly 60, as the eyes of humans and other animals are in different positions on the head, they present different views simultaneously. This is the basis of stereopsis, the process by which the brain exploits the parallax due to the different views from the eye to gain depth perception, animals also use motion parallax, in which the animals move to gain different viewpoints. For example, pigeons bob their heads up and down to see depth, the motion parallax is exploited also in wiggle stereoscopy, computer graphics which provide depth cues through viewpoint-shifting animation rather than through binocular vision. Parallax arises due to change in viewpoint occurring due to motion of the observer, of the observed, what is essential is relative motion. By observing parallax, measuring angles, and using geometry, one can determine distance, astronomers also use the word parallax as a synonym for distance measurent by other methods, see parallax #Astronomy. In a geostatic model, the movement of the star would have to be taken as real with the star oscillating across the sky with respect to the background stars, the parsec is defined as the distance for which the annual parallax is 1 arcsecond. Annual parallax is measured by observing the position of a star at different times of the year as the Earth moves through its orbit. Measurement of annual parallax was the first reliable way to determine the distances to the closest stars, the first successful measurements of stellar parallax were made by Friedrich Bessel in 1838 for the star 61 Cygni using a heliometer. Stellar parallax remains the standard for calibrating other measurement methods, accurate calculations of distance based on stellar parallax require a measurement of the distance from the Earth to the Sun, now based on radar reflection off the surfaces of planets. The angles involved in these calculations are very small and thus difficult to measure, the nearest star to the Sun, Proxima Centauri, has a parallax of 0.7687 ±0.0003 arcsec. This angle is approximately that subtended by an object 2 centimeters in diameter located 5.3 kilometers away, the fact that stellar parallax was so small that it was unobservable at the time was used as the main scientific argument against heliocentrism during the early modern age. In 1989, the satellite Hipparcos was launched primarily for obtaining improved parallaxes and proper motions for over 100,000 nearby stars, increasing the reach of the method tenfold
28.
Stereopsis
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Because the eyes of humans, and many animals, are located at different lateral positions on the head, binocular vision results in two slightly different images projected to the retinas of the eyes. The differences are mainly in the horizontal position of objects in the two images. These positional differences are referred to as horizontal disparities or, more generally, disparities are processed in the visual cortex of the brain to yield depth perception. The perception of depth in such cases is referred to as stereoscopic depth. Therefore, the term stereopsis can also specifically to the unique impression of depth associated with binocular vision. There are two aspects to stereopsis, coarse stereopsis and fine stereopsis, and provide depth information of different degree of spatial and temporal precision. Coarse stereopsis appears to be used to judge stereoscopic motion in the periphery and it provides the sense of being immersed in ones surroundings and is therefore sometimes also referred to as qualitative stereopsis. Coarse stereopsis is important for orientation in space while moving, for example when descending a flight of stairs, fine stereopsis is mainly based on static differences. It allows the individual to determine the depth of objects in the visual area and is therefore also called quantitative stereopsis. Fine stereopsis is important for fine-motorical tasks such as threading a needle, the stereopsis which an individual can achieve is limited by the level of visual acuity of the poorer eye. In particular, patients who have comparatively lower visual acuity tend to need relatively larger spatial frequencies to be present in the input images, else they cannot achieve stereopsis. Fine stereopsis requires both eyes to have a visual acuity in order to detect small spatial differences, and is easily disrupted by early visual deprivation. Furthermore, there are indications that coarse stereopsis is the mechanism that keeps the two eyes aligned after strabismus surgery and it has also been suggested to distinguish between two different types of stereoscopic depth perception, static depth perception and motion-in-depth perception. Some individuals who have strabismus and show no depth perception using static stereotests do perceive motion in depth when tested using dynamic random dot stereograms, one study found the combination of motion stereopsis and no static stereopsis to be present only in exotropes, not in esotropes. There are strong indications that the stereoscopic mechanism consists of at least two mechanisms, possibly three. The coarse stereoscopic system seems to be able to provide residual binocular depth information in some individuals who lack fine stereopsis, individuals have been found to integrate the various stimuli, for example stereoscopic cues and motion occlusion, in different ways. Not everyone has the ability to see using stereopsis. Stereopsis has an impact on exercising practical tasks such as needle-threading, ball-catching, pouring liquids
29.
Tessellation
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A tessellation of a flat surface is the tiling of a plane using one or more geometric shapes, called tiles, with no overlaps and no gaps. In mathematics, tessellations can be generalized to higher dimensions and a variety of geometries, a periodic tiling has a repeating pattern. The patterns formed by periodic tilings can be categorized into 17 wallpaper groups, a tiling that lacks a repeating pattern is called non-periodic. An aperiodic tiling uses a set of tile shapes that cannot form a repeating pattern. In the geometry of higher dimensions, a space-filling or honeycomb is called a tessellation of space. A real physical tessellation is a made of materials such as cemented ceramic squares or hexagons. Such tilings may be decorative patterns, or may have such as providing durable and water-resistant pavement. Historically, tessellations were used in Ancient Rome and in Islamic art such as in the decorative geometric tiling of the Alhambra palace, in the twentieth century, the work of M. C. Escher often made use of tessellations, both in ordinary Euclidean geometry and in geometry, for artistic effect. Tessellations are sometimes employed for decorative effect in quilting, Tessellations form a class of patterns in nature, for example in the arrays of hexagonal cells found in honeycombs. Tessellations were used by the Sumerians in building wall decorations formed by patterns of clay tiles, decorative mosaic tilings made of small squared blocks called tesserae were widely employed in classical antiquity, sometimes displaying geometric patterns. In 1619 Johannes Kepler made a documented study of tessellations. He wrote about regular and semiregular tessellations in his Harmonices Mundi, he was possibly the first to explore and to explain the structures of honeycomb. Some two hundred years later in 1891, the Russian crystallographer Yevgraf Fyodorov proved that every periodic tiling of the features one of seventeen different groups of isometries. Fyodorovs work marked the beginning of the mathematical study of tessellations. Other prominent contributors include Shubnikov and Belov, and Heinrich Heesch, in Latin, tessella is a small cubical piece of clay, stone or glass used to make mosaics. The word tessella means small square and it corresponds to the everyday term tiling, which refers to applications of tessellations, often made of glazed clay. Tessellation or tiling in two dimensions is a topic in geometry that studies how shapes, known as tiles, can be arranged to fill a plane without any gaps, according to a given set of rules
30.
Triangulation station
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The station is usually set up by a government with known coordinate and elevation published. Many stations are located on hilltops for the purposes of visibility, a graven metal plate on the top of a pillar may provide a mounting point for a theodolite or reflector. Trigonometrical stations are grouped together to form a network of triangulation, positions of all land boundaries, roads, railways, bridges and other infrastructure can be accurately located by the network, a task that is essential to the construction of modern infrastructure. Apart from the known stations set up by government, some temporary trigonometrical stations are set up near construction sites for monitoring the precision, some trigonometrical stations use the Global Positioning System for convenience, however, the accuracy depends on factors such as ionospheric and tropospheric propagation delay errors. Although stations are no longer required for many surveying purposes, they remain useful to hikers as navigational aids and these trig stations are clearly visible for many kilometres and useful for hikers. In Japan, there are five classes of triangulation stations, Class 1 They are installed approximately every 40 kilometres, There are about 1000 throughout Japan. The pillars are 18 centimetres on a side, and each pillar is anchored with two large perpendicular rocks buried underground. Class 2 They are installed approximately every 8 kilometres, There are about 5000 throughout Japan, and the pillars are 15 centimetres on a side. Each pillar is anchored with a large perpendicular rock buried underground. Class 3 There are about 32,000 installed throughout Japan, the pillars are 15 centimetres on a side, and each pillar is anchored with a large perpendicular rock buried underground. Class 4 They are installed approximately every 2 kilometres, and there are about 69,000 throughout Japan, the pillars are 12 centimetres on a side, and each pillar is anchored with a large perpendicular rock buried underground. Class 5 These markers were installed in 1899 and are the predecessors to the modern triangulation stations used in Japan today and they are generally not used anymore since the installation of the Class 1-4 stations. Some of them still exist at various locations throughout Japan, in Spain there are 11,000 triangulation stations, concrete buildings which typically consist of a cylinder 120 cm high and 30 cm diameter over a concrete cubic base. They were erected by the Instituto Geográfico Nacional, usually painted in white, in the United Kingdom, trig points are typically concrete pillars, and were erected by the Ordnance Survey. The process of placing trig points on top of prominent hills, the Ordnance Surveys first trig point was erected on 18 April 1936 near Cold Ashby, Northamptonshire. In low-lying or flat areas some trig points are only a few metres above sea level, in most of the UK, trig points are truncated square concrete pyramids or obelisks tapering towards the top. On the top a brass plate with three arms and a depression is fixed, it is used to mount and centre a theodolite used to take angular measurements to neighbouring trig points. A benchmark is set on the side, marked with the letters O S B M
31.
Joseph Needham
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Noel Joseph Terence Montgomery Needham CH FRS FBA was a British scientist, historian and sinologist known for his scientific research and writing on the history of Chinese science. He was elected a fellow of the Royal Society in 1941, in 1992, the Queen conferred on him the Companionship of Honour, and the Royal Society noted he was the only living person to hold these three titles. Needham was the child of a London family. His father was a doctor, and his mother, Alicia Adelaïde, née Montgomery, was a composer from Oldcastle. Needham was educated at Oundle School before attending Gonville and Caius College, Cambridge, where he received a BA in 1921, an Oxbridge MA in January 1925 and he had intended to study medicine but came under the influence of Frederick Hopkins, resulting in his switch to biochemistry. His three-volume work Chemical Embryology, published in 1931, includes a history of embryology from Egyptian times up to the early 19th century and his Terry Lecture of 1936 was published by Cambridge University Press in association with Yale University Press under the title of Order and Life. In 1939 he produced a work on morphogenesis that a Harvard reviewer claimed will go down in the history of science as Joseph Needhams magnum opus. Although his career as biochemist and an academic was well established, his career developed in unanticipated directions during, three Chinese scientists came to Cambridge for graduate study in 1937, Lu Gwei-djen, Wang Ying-lai and Shen Shih-Chang. Lu, daughter of a Nanjingese pharmacist, taught Needham Chinese, igniting his interest in Chinas ancient technological and he then pursued, and mastered, the study of Classical Chinese privately with Gustav Haloun. Under the Royal Societys direction, Needham was the director of the Sino-British Science Co-operation Office in Chongqing from 1942 to 1946, during this time he made several long journeys through war-torn China and many smaller ones, visiting scientific and educational establishments and obtaining for them much needed supplies. His longest trip in late 1943 ended in far west in Gansu at the caves in Dunhuang at the end of the Great Wall where the earliest dated printed book - a copy of the Diamond Sutra - was found. The other long trip reached Fuzhou on the east coast, returning across the Xiang River just two days before the Japanese blew up the bridge at Hengyang and cut off part of China. In 1944 he visited Yunnan in an attempt to reach the Burmese border, everywhere he went he purchased and was given old historical and scientific books which he shipped back to Britain through diplomatic channels. They were to form the foundation of his later research, on his return to Europe, he was asked by Julian Huxley to become the first head of the Natural Sciences Section of UNESCO in Paris, France. In fact it was Needham who insisted that science should be included in the organisations mandate at a planning meeting. He devoted his energy to the history of Chinese science until his retirement in 1990, in 1948, Needham proposed a project to the Cambridge University Press for a book on Science and Civilisation in China. Within weeks of being accepted, the project had grown to seven volumes and his initial collaborator was the historian Wang Ling, whom he had met in Lizhuang and obtained a position for at Trinity. The first years were devoted to compiling a list of every mechanical invention and abstract idea that had been made and conceived in China
32.
Haidao Suanjing
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Haidao Suanjing was written by the Chinese mathematician Liu Hui of the Three Kingdoms era as an extension of chapter 9 of The Nine Chapters on the Mathematical Art. During the Tang Dynasty, this appendix was taken out from The Nine Chapters on the Mathematical Art as a book, titled Haidao suanjing. In the time of the early Tang dynasty, Haidao Suanjing was selected one of The Ten Computational Canons as the official mathematical texts for imperial examinations in mathematics. This book contained many practical problems of surveying using geometry and this work provided detailed instructions on how to measure distances and heights with tall surveyors poles and horizontal bars fixed at right angles to them. The unit of measurement was 1 li =180 zhang= 1800chi,1 zhang =10 chi,1 chi =10 cun,1 step =6 chi, calculation was carried out with place value decimal Rod calculus. Liu Hui used his rectangle in right angle triangle theorem as the basis for survey. Step back from the front post 123 steps, with eye on ground level, step back 127 steps from the rear pole, eye on ground level also aligns with the tip of pole and tip of island. What is the height of the island, and what is the distance to the pole, a, The height of the island is four li and 55 steps, and it is 120 li and 50 steps from the pole. As the distance of front pole to the island could not be measured directly, a pine of unknown height on a hill. Set up two poles of two each, one at front and one at the rear 50 steps in between. Let the rear pole aligns with the front pole, step back 7 steps and 4 chi, view the tip of pine tree from the ground till it aligns in a straight line with the tip of the pole. Then view the tree trunk, the line of sight intersects the poles at 2 chi and 8 cun from its tip, step back 8 steps and 5 chi from the rear pole, the view from ground also aligns with tree top and pole top. What is the height of the tree, and what is its distance from the pole. Answer, the height of the pine is 11 zhang 2 chi 8 cun, algorithm, let the numerator be the product of separation of the poles and intersection from tip of pole, let the denominator be the difference of offsets. Add the height of pole to the quotient to obtain the height of pine tree, Q, View a square city at the south of unknown size. Set up a east gnome and a west pole, six zhang apart, let the east pole aligned with the NE and SE corners. Step back 5 steps from the gnome, watch the NW corner of the city. Step back northward 13 steps and 2 chi, watch the NW corner of the city, what is the length of the square city, and what is its distance to the pole
33.
International Standard Book Number
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The International Standard Book Number is a unique numeric commercial book identifier. An ISBN is assigned to each edition and variation of a book, for example, an e-book, a paperback and a hardcover edition of the same book would each have a different ISBN. The ISBN is 13 digits long if assigned on or after 1 January 2007, the method of assigning an ISBN is nation-based and varies from country to country, often depending on how large the publishing industry is within a country. The initial ISBN configuration of recognition was generated in 1967 based upon the 9-digit Standard Book Numbering created in 1966, the 10-digit ISBN format was developed by the International Organization for Standardization and was published in 1970 as international standard ISO2108. Occasionally, a book may appear without a printed ISBN if it is printed privately or the author does not follow the usual ISBN procedure, however, this can be rectified later. Another identifier, the International Standard Serial Number, identifies periodical publications such as magazines, the ISBN configuration of recognition was generated in 1967 in the United Kingdom by David Whitaker and in 1968 in the US by Emery Koltay. The 10-digit ISBN format was developed by the International Organization for Standardization and was published in 1970 as international standard ISO2108, the United Kingdom continued to use the 9-digit SBN code until 1974. The ISO on-line facility only refers back to 1978, an SBN may be converted to an ISBN by prefixing the digit 0. For example, the edition of Mr. J. G. Reeder Returns, published by Hodder in 1965, has SBN340013818 -340 indicating the publisher,01381 their serial number. This can be converted to ISBN 0-340-01381-8, the check digit does not need to be re-calculated, since 1 January 2007, ISBNs have contained 13 digits, a format that is compatible with Bookland European Article Number EAN-13s. An ISBN is assigned to each edition and variation of a book, for example, an ebook, a paperback, and a hardcover edition of the same book would each have a different ISBN. The ISBN is 13 digits long if assigned on or after 1 January 2007, a 13-digit ISBN can be separated into its parts, and when this is done it is customary to separate the parts with hyphens or spaces. Separating the parts of a 10-digit ISBN is also done with either hyphens or spaces, figuring out how to correctly separate a given ISBN number is complicated, because most of the parts do not use a fixed number of digits. ISBN issuance is country-specific, in that ISBNs are issued by the ISBN registration agency that is responsible for country or territory regardless of the publication language. Some ISBN registration agencies are based in national libraries or within ministries of culture, in other cases, the ISBN registration service is provided by organisations such as bibliographic data providers that are not government funded. In Canada, ISBNs are issued at no cost with the purpose of encouraging Canadian culture. In the United Kingdom, United States, and some countries, where the service is provided by non-government-funded organisations. Australia, ISBNs are issued by the library services agency Thorpe-Bowker
34.
Astronomy in the medieval Islamic world
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Islamic astronomy comprises the astronomical developments made in the Islamic world, particularly during the Islamic Golden Age, and mostly written in the Arabic language. These developments mostly took place in the Middle East, Central Asia, Al-Andalus, and North Africa and these included Greek, Sassanid, and Indian works in particular, which were translated and built upon. Islamic astronomy also had an influence on Chinese astronomy and Malian astronomy, a significant number of stars in the sky, such as Aldebaran, Altair and Deneb, and astronomical terms such as alidade, azimuth, and nadir, are still referred to by their Arabic names. A large corpus of literature from Islamic astronomy remains today, numbering approximately 10,000 manuscripts scattered throughout the world, even so, a reasonably accurate picture of Islamic activity in the field of astronomy can be reconstructed. These observations were based on the rising and setting of stars. Anwa continued to be developed after Islamization by the Arabs, where Islamic astronomers added mathematical methods to their empirical observations, according to David King, after the rise of Islam, the religious obligation to determine the qibla and prayer times inspired more progress in astronomy for centuries. The first astronomical texts that were translated into Arabic were of Indian and Persian origin, another text translated was the Zij al-Shah, a collection of astronomical tables compiled in Sasanid Persia over two centuries. Fragments of texts during this period indicate that Arabs adopted the function in place of the chords of arc used in Greek trigonometry. The House of Wisdom was an established in Baghdad under Abbasid caliph Al-Mamun in the early 9th century. From this time, independent investigation into the Ptolemaic system became possible, Astronomical research was greatly supported by the Abbasid caliph al-Mamun through The House of Wisdom. Baghdad and Damascus became the centers of such activity, the caliphs not only supported this work financially, but endowed the work with formal prestige. The first major Muslim work of astronomy was Zij al-Sindh by al-Khwarizmi in 830, the work contains tables for the movements of the sun, the moon and the five planets known at the time. The work is significant as it introduced Ptolemaic concepts into Islamic sciences and this work also marks the turning point in Islamic astronomy. Hitherto, Muslim astronomers had adopted a primarily research approach to the field, translating works of others, al-Khwarizmis work marked the beginning of nontraditional methods of study and calculations. In 850, al-Farghani wrote Kitab fi Jawani, the book primarily gave a summary of Ptolemic cosmography. However, it also corrected Ptolemy based on findings of earlier Arab astronomers, al-Farghani gave revised values for the obliquity of the ecliptic, the precessional movement of the apogees of the sun and the moon, and the circumference of the earth. The book was circulated through the Muslim world, and even translated into Latin. The period when a distinctive Islamic system of astronomy flourished, the period began as the Muslim astronomers began questioning the framework of the Ptolemaic system of astronomy
35.
Common Era
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Common Era or Current Era is a year-numbering system for the Julian and Gregorian calendars that refers to the years since the start of this era, i. e. since AD1. The preceding era is referred to as before the Common or Current Era, the Current Era notation system can be used as a secular alternative to the Dionysian era system, which distinguishes eras as AD and BC. The two notation systems are equivalent, thus 2017 CE corresponds to AD2017 and 400 BCE corresponds to 400 BC. The year-numbering system for the Gregorian calendar is the most widespread civil calendar used in the world today. For decades, it has been the standard, recognized by international institutions such as the United Nations. The expression has been traced back to Latin usage to 1615, as vulgaris aerae, the term Common Era can be found in English as early as 1708, and became more widely used in the mid-19th century by Jewish academics. He attempted to number years from a reference date, an event he referred to as the Incarnation of Jesus. Dionysius labeled the column of the table in which he introduced the new era as Anni Domini Nostri Jesu Christi, numbering years in this manner became more widespread in Europe with its usage by Bede in England in 731. Bede also introduced the practice of dating years before what he supposed was the year of birth of Jesus, in 1422, Portugal became the last Western European country to switch to the system begun by Dionysius. The first use of the Latin term vulgaris aerae discovered so far was in a 1615 book by Johannes Kepler, Kepler uses it again in a 1616 table of ephemerides, and again in 1617. A1635 English edition of that book has the title page in English – so far, a 1701 book edited by John LeClerc includes Before Christ according to the Vulgar Æra,6. A1716 book in English by Dean Humphrey Prideaux says, before the beginning of the vulgar æra, a 1796 book uses the term vulgar era of the nativity. The first so-far-discovered usage of Christian Era is as the Latin phrase aerae christianae on the page of a 1584 theology book. In 1649, the Latin phrase æræ Christianæ appeared in the title of an English almanac, a 1652 ephemeris is the first instance so-far-found for English usage of Christian Era. The English phrase common Era appears at least as early as 1708, a 1759 history book uses common æra in a generic sense, to refer to the common era of the Jews. The first-so-far found usage of the phrase before the era is in a 1770 work that also uses common era and vulgar era as synonyms. The 1797 edition of the Encyclopædia Britannica uses the terms vulgar era, the Catholic Encyclopedia in at least one article reports all three terms being commonly understood by the early 20th century. Thus, the era of the Jews, the common era of the Mahometans, common era of the world
36.
Anno Domini
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The terms anno Domini and before Christ are used to label or number years in the Julian and Gregorian calendars. The term anno Domini is Medieval Latin and means in the year of the Lord, There is no year zero in this scheme, so the year AD1 immediately follows the year 1 BC. This dating system was devised in 525 by Dionysius Exiguus of Scythia Minor, the Gregorian calendar is the most widely used calendar in the world today. Traditionally, English followed Latin usage by placing the AD abbreviation before the year number, however, BC is placed after the year number, which also preserves syntactic order. The abbreviation is widely used after the number of a century or millennium. Because BC is the English abbreviation for Before Christ, it is sometimes concluded that AD means After Death. However, this would mean that the approximate 33 years commonly associated with the life of Jesus would not be included in either of the BC, astronomical year numbering and ISO8601 avoid words or abbreviations related to Christianity, but use the same numbers for AD years. The Anno Domini dating system was devised in 525 by Dionysius Exiguus to enumerate the years in his Easter table. His system was to replace the Diocletian era that had used in an old Easter table because he did not wish to continue the memory of a tyrant who persecuted Christians. The last year of the old table, Diocletian 247, was followed by the first year of his table. Thus Dionysius implied that Jesus Incarnation occurred 525 years earlier, without stating the year during which his birth or conception occurred. Blackburn & Holford-Strevens briefly present arguments for 2 BC,1 BC, There were inaccuracies in the list of consuls There were confused summations of emperors regnal years It is not known how Dionysius established the year of Jesuss birth. It is convenient to initiate a calendar not from the day of an event. For example, the Islamic calendar begins not from the date of the Hegira, at the time, it was believed by some that the Resurrection and end of the world would occur 500 years after the birth of Jesus. The old Anno Mundi calendar theoretically commenced with the creation of the based on information in the Old Testament. It was believed that, based on the Anno Mundi calendar, Anno Mundi 6000 was thus equated with the resurrection and the end of the world but this date had already passed in the time of Dionysius. The Anglo-Saxon historian the Venerable Bede, who was familiar with the work of Dionysius Exiguus, used Anno Domini dating in his Ecclesiastical History of the English People, completed in 731. e. On the continent of Europe, Anno Domini was introduced as the era of choice of the Carolingian Renaissance by the English cleric and scholar Alcuin in the late eighth century
37.
Ahmad Nahavandi
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Ahmad ibn Muhammad al-Nahavandi was a Persian astronomer of the 8th and 9th centuries. His name indicates that he was from Nahavand, a city in Iran and he and Mashallah ibn Athari were among the earliest Islamic era astronomers who flourished during the reign of al-Mansur, the second Abbasid Caliph. He also compiled tables called the comprehensive, list of Iranian scientists The Golden Age of Persia. H. Suter, Die Mathematiker und Astronomen der Araber
38.
Mashallah ibn Athari
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MashaAllah ibn Atharī was an eighth-century Persian Jewish astrologer and astronomer from the city of Basra who became the leading astrologer of the late 8th century. According to Ibn al-Nadim in his Fihrist, Mashallah was a man of distinction and he served as a court astrologer for the Abbasid caliphate, and wrote a number of works on astrology in Arabic, some of which have only survived in Latin translations. Science historian Donald Hill writes that Mashallah was originally from Khorasan, the Arabic phrase ma shaa allah indicates acceptance of what God has ordained in terms of good or ill fortune that may befall a believer. Ibn al-Nadim said Mashallahs name was Mīshā, meaning Yithro, Latin translators also called him Messahala. The crater Messala on the Moon is named after him and his writings include both what would be recognized as traditional horary astrology and an earlier type of astrology which casts consultation charts to divine the clients intention. It is also known that his work was influenced by Hermes Trismegistus and Dorotheus. Only one of his writings is still extant in its original Arabic and his treatise De mercibus is the oldest extant scientific work in Arabic. One of his most popular works in the Middle Ages was a treatise which provides a comprehensive account of the whole cosmos along Aristotelian lines. In it, Mashallah covers many topics that were important in early cosmology, Mashallah had intended for his account to be aimed at laymen and therefore included diagrams with text to facilitate comprehension of his main ideas. The treatise was printed in two versions, a short version of 27 chapters known as De scientia motus orbis. The shorter version was translated by Gherardo Cremonese, both were printed in Nuremberg and in 1504 and 1549, respectively. This work is referred to as De orbe for short. Mashallah wrote the first treatise on the astrolabe in Arabic and it was later translated into Latin as De Astrolabii Compositione et Ultilitate and included in Gregor Reischs Margarita phylosophica. Its contents primarily deal with the construction and usage of an astrolabe and his On Conjunctions, Religions, and People discusses the astrology of important world events and the role Jupiter-Saturn conjunctions have in their timing. This treatise does not survive intact and is preserved only in quotations by the Christian astrologer Ibn Hibinta and his work on nativities, with the Arabic title Kitab al - Mawalid, has been partially translated into English from a Latin translation of the Arabic by James H. Holden. Other astronomical and astrological writings are quoted by Suter and Steinschneider, an Irish astronomical tract also exists based in part on a medieval Latin version. Edited with preface, translation, and glossary, by Afaula Power, the notable 12th-century scholar and astrologer Abraham ibn Ezra translated two of Mashallahs astrological treatises into Hebrew, Sheelot and Ḳadrut. Eleven of Mashallahs astrological treatises were translated out of Latin into English in 2008 and are available in The Works of Sahl, on Reception is also available in an English translation by Robert Hand from the Latin edition by Joachim Heller of Nuremberg in 1549
