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Sagitta (geometry)
In geometry, the sagitta (sometimes abbreviated as sag) of a circular arc is the distance from the midpoint of the arc to the midpoint of its chord. It is used extensively in architecture when calculating the arc necessary to span a certain height and distance and also in optics where it is used to find the depth of a spherical mirror or lens. The name comes directly from Latin ''sagitta'', meaning an "arrow". Formulas In the following equations, s denotes the sagitta (the depth or height of the arc), r equals the radius of the circle, and l the length of the chord spanning the base of the arc. As \tfrac12l and r - s are two sides of a right triangle with r as the hypotenuse, the Pythagorean theorem gives us : r^2 = \left(\tfrac12l\right)^2 + \left(r-s\right)^2. This may be rearranged to give any of the other three: : \begin s &= r - \sqrt, \\ 0mul &= 2\sqrt, \\ pxr &= \frac = \frac+\frac. \end The sagitta may also be calculated from the versine function, for an arc that spa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Circular Segment
In geometry, a circular segment or disk segment (symbol: ) is a region of a disk which is "cut off" from the rest of the disk by a straight line. The complete line is known as a '' secant'', and the section inside the disk as a '' chord''. More formally, a circular segment is a plane region bounded by a circular arc (of less than π radians by convention) and the circular chord connecting its endpoints. Formulae Let ''R'' be the radius of the arc which forms part of the perimeter of the segment, ''θ'' the central angle subtending the arc in radians, ''c'' the chord length, ''s'' the arc length, ''h'' the sagitta (height) of the segment, ''d'' the apothem of the segment, and ''a'' the area of the segment. Usually, chord length and height are given or measured, and sometimes the arc length as part of the perimeter, and the unknowns are area and sometimes arc length. These can't be calculated simply from chord length and height, so two intermediate quantities, the radius ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Visualization Of The Sagitta With Pythagorean Theorem Relationship
Visualization or visualisation may refer to: *Visualization (graphics), the physical or imagining creation of images, diagrams, or animations to communicate a message * Data and information visualization, the practice of creating visual representations of complex data and information * Music visualization, animated imagery based on a piece of music * Mental image, the experience of images without the relevant external stimuli * "Visualization", a song by Blank Banshee on the 2012 album ''Blank Banshee 0'' See also * Creative visualization (other) * Visualizer (other) * * * * Graphics * List of graphical methods, various forms of visualization * Guided imagery, a mind-body intervention by a trained practitioner * Illustration, a decoration, interpretation or visual explanation of a text, concept or process * Image, an artifact that depicts visual perception, such as a photograph or other picture * Infographics Infographics (a clipped compound of "informatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Llewellyn Woodward
Sir Ernest Llewellyn Woodward, FBA (1890–1971) was a British historian. He was educated at Merchant Taylors' School and Corpus Christi College, Oxford, and after the First World War became a lecturer in Modern History and fellow of All Souls College from 1919 to 1944 and a fellow at New College from 1922 to 1939. Later he was Montague Burton Professor of International Relations (1944–1947) and then Professor of Modern History at Oxford. He later taught at Princeton University in the United States (1951–1962). His scope was impressively wide, his first publication being on the late Roman Empire whilst on sick leave from service in the First World War but his most famous works being on the First World War. He wrote ''The Age of Reform'' in the ''Oxford History of England''. Woodward was a Member of the American Philosophical Society The American Philosophical Society (APS) is an American scholarly organization and learned society founded in 1743 in Philadelphia that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jyā, Koti-jyā And Utkrama-jyā
Jyā, koṭi-jyā and utkrama-jyā are three trigonometric functions introduced by Indian mathematics, Indian mathematicians and astronomers. The earliest known Indian treatise containing references to these functions is Surya Siddhanta. These are functions of arcs of circles and not functions of angles. Jyā and koti-jyā are closely related to the modern trigonometric functions of sine and cosine. In fact, the origins of the modern terms of "sine" and "cosine" have been traced back to the Sanskrit words jyā and koti-jyā. Definition Let 'arc AB' denote an Arc (geometry), arc whose two extremities are A and B of a circle with center 'O'. If a perpendicular BM is dropped from B to OA, then: * ''jyā'' of arc AB = BM * ''koti-jyā'' of arc AB = OM * ''utkrama-jyā'' of arc AB = MA If the radius of the circle is ''R'' and the length of arc AB is ''s'', the angle subtended by arc AB at O measured in radians is θ = ''s'' / ''R''. The three Indian functions are related to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Versine
The versine or versed sine is a trigonometric function found in some of the earliest (Sanskrit ''Aryabhatia'', Section I) trigonometric tables. The versine of an angle is 1 minus its . There are several related functions, most notably the coversine and haversine. The latter, half a versine, is of particular importance in the haversine formula of navigation. Overview The versine[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Philosophiæ Naturalis Principia Mathematica
(English: ''The Mathematical Principles of Natural Philosophy''), often referred to as simply the (), is a book by Isaac Newton that expounds Newton's laws of motion and his law of universal gravitation. The ''Principia'' is written in Latin and comprises three volumes, and was authorized, imprimatur, by Samuel Pepys, then-President of the Royal Society on 5 July 1686 and first published in 1687. The is considered one of the most important works in the history of science. The French mathematical physicist Alexis Clairaut assessed it in 1747: "The famous book of ''Mathematical Principles of Natural Philosophy'' marked the epoch of a great revolution in physics. The method followed by its illustrious author Sir Newton ... spread the light of mathematics on a science which up to then had remained in the darkness of conjectures and hypotheses." The French scientist Joseph-Louis Lagrange described it as "the greatest production of the human mind". French polymath Pierre-Simon ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Isaac Newton
Sir Isaac Newton () was an English polymath active as a mathematician, physicist, astronomer, alchemist, theologian, and author. Newton was a key figure in the Scientific Revolution and the Age of Enlightenment, Enlightenment that followed. His book (''Mathematical Principles of Natural Philosophy''), first published in 1687, achieved the Unification of theories in physics#Unification of gravity and astronomy, first great unification in physics and established classical mechanics. Newton also made seminal contributions to optics, and Leibniz–Newton calculus controversy, shares credit with German mathematician Gottfried Wilhelm Leibniz for formulating calculus, infinitesimal calculus, though he developed calculus years before Leibniz. Newton contributed to and refined the scientific method, and his work is considered the most influential in bringing forth modern science. In the , Newton formulated the Newton's laws of motion, laws of motion and Newton's law of universal g ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Momentum
In Newtonian mechanics, momentum (: momenta or momentums; more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If is an object's mass and is its velocity (also a vector quantity), then the object's momentum (from Latin '' pellere'' "push, drive") is: \mathbf = m \mathbf. In the International System of Units (SI), the unit of measurement of momentum is the kilogram metre per second (kg⋅m/s), which is dimensionally equivalent to the newton-second. Newton's second law of motion states that the rate of change of a body's momentum is equal to the net force acting on it. Momentum depends on the frame of reference, but in any inertial frame of reference, it is a ''conserved'' quantity, meaning that if a closed system is not affected by external forces, its total momentum does not change. Momentum is also conserved in special relativity (with a mo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bubble Chamber
A bubble chamber is a vessel filled with a superheated transparent liquid (most often liquid hydrogen) used to detect electrically charged particles moving through it. It was invented in 1952 by Donald A. Glaser, for which he was awarded the 1960 Nobel Prize in Physics. Supposedly, Glaser was inspired by the bubbles in a glass of beer; however, in a 2006 talk, he refuted this story, although saying that while beer was not the inspiration for the bubble chamber, he did experiments using beer to fill early prototypes. While bubble chambers were extensively used in the past, they have now mostly been supplanted by wire chambers, spark chambers, drift chambers, and silicon detectors. Notable bubble chambers include the Big European Bubble Chamber (BEBC) and Gargamelle. __TOC__ Function and use The bubble chamber is similar to a cloud chamber, both in application and in basic principle. It is normally made by filling a large cylinder with a liquid heated to just below ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cambridge University Press
Cambridge University Press was the university press of the University of Cambridge. Granted a letters patent by King Henry VIII in 1534, it was the oldest university press in the world. Cambridge University Press merged with Cambridge Assessment to form Cambridge University Press and Assessment under Queen Elizabeth II's approval in August 2021. With a global sales presence, publishing hubs, and offices in more than 40 countries, it published over 50,000 titles by authors from over 100 countries. Its publications include more than 420 academic journals, monographs, reference works, school and university textbooks, and English language teaching and learning publications. It also published Bibles, runs a bookshop in Cambridge, sells through Amazon, and has a conference venues business in Cambridge at the Pitt Building and the Sir Geoffrey Cass Sports and Social Centre. It also served as the King's Printer. Cambridge University Press, as part of the University of Cambridge, was a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Guo Shoujing
Guo Shoujing (, 1231–1316), courtesy name Ruosi (), was a Chinese astronomer, hydraulic engineer, mathematician, and politician of the Yuan dynasty. The later Johann Adam Schall von Bell (1591–1666) was so impressed with the preserved astronomical instruments of Guo that he called him "the Tycho Brahe of China." Jamal ad-Din cooperated with him. Early life In 1231, in Xingtai, Hebei province, China, Guo Shoujing was born into a poor family.O'Connor. He was raised primarily by his paternal grandfather, Guo Yong, who was famous throughout China for his expertise in a wide variety of topics, ranging from the study of the Five Classics to astronomy, mathematics, and hydraulics. Guo Shoujing was a child prodigy, showing exceptional intellectual promise. By his teens, he obtained a blueprint for a water clock which his grandfather was working on, and realized its principles of operation. He improved the design of a type of water clock called a lotus clepsydra, a water clock wi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shen Kuo
Shen Kuo (; 1031–1095) or Shen Gua, courtesy name Cunzhong (存中) and Art name#China, pseudonym Mengqi (now usually given as Mengxi) Weng (夢溪翁),Yao (2003), 544. was a Chinese polymath, scientist, and statesman of the Song dynasty (960–1279). Shen was a master in many fields of study including Chinese mathematics, mathematics, history of optics, optics, and horology. In his career as a civil servant, he became a finance minister, governmental state inspector, head official for the Chinese astronomy, Bureau of Astronomy in the Song court, Assistant Minister of Imperial Hospitality, and also served as an Chancellor (education), academic chancellor.Needham (1986), Volume 4, Part 2, 33. At court his political allegiance was to the Reformist faction known as the History of the Song dynasty#Partisans and factions, reformers and conservatives, New Policies Group, headed by Chancellor of China, Chancellor Wang Anshi (1021–1085). In his ''Dream Pool Essays'' or ''Dream Torren ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
