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Sagitta (geometry)
In geometry, the sagitta (sometimes abbreviated as sag) of a circular arc is the distance from the center of the arc to the center of its base. 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. Formulae In the following equations, denotes the sagitta (the depth or height of the arc), equals the radius of the circle, and the length of the chord spanning the base of the arc. As and are two sides of a right triangle with as the hypotenuse, the Pythagorean theorem gives us : r^2 = \left(\frac\right)^2 + \left(r-s\right)^2. This may be rearranged to give any of the other three: : \begin s &= r - \sqrt, \\ pxl &= 2\sqrt, \\ pxr &= \frac = \frac+\frac. \end The sagitta may also be calculated from the versine function, for an arc that spans an angle of , and coincides wi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Circular Segment
In geometry, a circular segment (symbol: ), also known as a disk segment, is a region of a disk which is "cut off" from the rest of the disk by a secant or a chord. More formally, a circular segment is a region of two-dimensional space that is bounded by a circular arc (of less than π radians by convention) and by the circular chord connecting the endpoints of the arc. 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 and central angle are usually calcula ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sagitta
Sagitta is a dim but distinctive constellation in the northern sky. Its name is Latin for 'arrow', not to be confused with the significantly larger constellation Sagittarius 'the archer'. It was included among the 48 constellations listed by the 2nd-century astronomer Ptolemy, and it remains one of the 88 modern constellations defined by the International Astronomical Union. Although it dates to antiquity, Sagitta has no star brighter than 3rd magnitude and has the third-smallest area of any constellation. Gamma Sagittae is the constellation's brightest star, with an apparent magnitude of 3.47. It is an aging red giant star 90% as massive as the Sun that has cooled and expanded to a diameter 54 times greater than it. Delta, Epsilon, Zeta, and Theta Sagittae are each multiple stars whose components can be seen in small telescopes. V Sagittae is a cataclysmic variable—a binary star system composed of a white dwarf accreting mass of a donor star that is expected to go nova and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Research & Education Association
Research & Education Association (REA) publishes test preparation materials and study guides, both in print and electronic form. History REA was founded by Max Fogiel in 1959 as an educational publisher, concentrating on problems and solutions, or what's known as test preparation today. The company produced the iconic "Problem Solver" series of comprehensive solution guides. The Problem Solver series eventually encompassed over 30 topics with more than 28,000 problem/solution sets, covering differential equations, electric circuits, electronic circuits, precalculus, calculus, advanced calculus, algebra and trigonometry, physics, linear algebra, statistics, organic chemistry, mechanics, thermodynamics, electromagnetics, geometry, chemistry, probability, materials strength, heat transfer, economics, robotics, discrete math, fluid mechanics and dynamics, numerical analysis, optics, topology, electronic communications, operations research, and several others. Recently REA has foc ... [...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 Āryabhaṭa's sine table , ''Aryabhatia'', Section I) trigonometric tables. The versine of an angle is 1 minus its cosine. 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 or versed sine is a trigonometric function already appearing in some of ...[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Philosophiæ Naturalis Principia Mathematica
(English: ''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 first published on 5 July 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." A more recent assessment has been that while acceptance of Newton's laws was not immediate, by the end of the century after publication in 1687, "no one could deny that" (out of the ) "a science had emerged that, at least in ce ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Isaac Newton
Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, physicist, astronomer, alchemist, theologian, and author (described in his time as a "natural philosopher"), widely recognised as one of the greatest mathematicians and physicists and among the most influential scientists of all time. He was a key figure in the philosophical revolution known as the Enlightenment. His book (''Mathematical Principles of Natural Philosophy''), first published in 1687, established classical mechanics. Newton also made seminal contributions to optics, and shares credit with German mathematician Gottfried Wilhelm Leibniz for developing infinitesimal calculus. In the , Newton formulated the laws of motion and universal gravitation that formed the dominant scientific viewpoint for centuries until it was superseded by the theory of relativity. Newton used his mathematical description of gravity to derive Kepler's laws of planetary motion, account for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Momentum
In Newtonian mechanics, momentum (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 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 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 it is a ''conserved'' quantity, meaning that if a closed system is not affected by external forces, its total linear momentum does not change. Momentum is also conserved in special relativity (with a modified formula) and, in a modified form, in electrodynamics, quantum mechanics, quan ... [...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 its boilin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cambridge University Press
Cambridge University Press is the university press of the University of Cambridge. Granted letters patent by Henry VIII of England, King Henry VIII in 1534, it is the oldest university press A university press is an academic publishing house specializing in monographs and scholarly journals. Most are nonprofit organizations and an integral component of a large research university. They publish work that has been reviewed by schola ... in the world. It is also the King's Printer. Cambridge University Press is a department of the University of Cambridge and is both an academic and educational publisher. It became part of Cambridge University Press & Assessment, following a merger with Cambridge Assessment in 2021. With a global sales presence, publishing hubs, and offices in more than 40 Country, countries, it publishes over 50,000 titles by authors from over 100 countries. Its publishing includes more than 380 academic journals, monographs, reference works, school and uni ... [...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 w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shen Kuo
Shen Kuo (; 1031–1095) or Shen Gua, courtesy name Cunzhong (存中) and pseudonym Mengqi (now usually given as Mengxi) Weng (夢溪翁),Yao (2003), 544. was a Chinese polymathic scientist and statesman of the Song dynasty (960–1279). Shen was a master in many fields of study including mathematics, optics, and horology. In his career as a civil servant, he became a finance minister, governmental state inspector, head official for the Bureau of Astronomy in the Song court, Assistant Minister of Imperial Hospitality, and also served as an academic chancellor.Needham (1986), Volume 4, Part 2, 33. At court his political allegiance was to the Reformist faction known as the New Policies Group, headed by Chancellor Wang Anshi (1021–1085). In his ''Dream Pool Essays'' or ''Dream Torrent Essays'' (; ''Mengxi Bitan'') of 1088, Shen was the first to describe the magnetic needle compass, which would be used for navigation (first described in Europe by Alexander Neckam in 1187).Bowma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
