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Paul De Casteljau
Paul de Casteljau (19 November 1930 – 24 March 2022) was a French physicist and mathematician. In 1959, while working at Citroën, he developed an algorithm for evaluating calculations on a certain family of curves, which would later be formalized and popularized by engineer Pierre Bézier, leading to the curves widely known as Bézier curves. He studied at École normale supérieure (Paris), École Normale Supérieure, and worked at Citroën from 1958 until his retirement in 1992. When he arrived there, "Specialists admitted that all electrical, electronic and mechanical problems had more or less been solved. All—except for one single formality which made up for 5%, but certainly not for 20% of the problem; in other words, how to express component parts by equations." A short autobiographic sketch goes back to the early 1990s, a longer autobiography talks about his education and life at Citroën until his retirement. He continued publishing in retirement, which led to three ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brackets
A bracket is either of two tall fore- or back-facing punctuation marks commonly used to isolate a segment of text or data from its surroundings. They come in four main pairs of shapes, as given in the box to the right, which also gives their names, that vary between British English, British and American English. "Brackets", without further qualification, are in British English the ... marks and in American English the ... marks. Other symbols are repurposed as brackets in specialist contexts, such as International Phonetic Alphabet#Brackets and transcription delimiters, those used by linguists. Brackets are typically deployed in symmetric pairs, and an individual bracket may be identified as a "left" or "right" bracket or, alternatively, an "opening bracket" or "closing bracket", respectively, depending on the Writing system#Directionality, directionality of the context. In casual writing and in technical fields such as computing or linguistic analysis of grammar, brackets ne ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Regular Polygons
In Euclidean geometry, a regular polygon is a polygon that is Equiangular polygon, direct equiangular (all angles are equal in measure) and Equilateral polygon, equilateral (all sides have the same length). Regular polygons may be either ''convex polygon, convex'' or ''star polygon, star''. In the limit (mathematics), limit, a sequence of regular polygons with an increasing number of sides approximates a circle, if the perimeter or area is fixed, or a regular apeirogon (effectively a Line (geometry), straight line), if the edge length is fixed. General properties These properties apply to all regular polygons, whether convex or star polygon, star: *A regular ''n''-sided polygon has rotational symmetry of order ''n''. *All vertices of a regular polygon lie on a common circle (the circumscribed circle); i.e., they are concyclic points. That is, a regular polygon is a cyclic polygon. *Together with the property of equal-length sides, this implies that every regular polygon also h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1930 Births
Events January * January 15 – The Moon moves into its nearest point to Earth, called perigee, at the same time as its fullest phase of the Lunar Cycle. This is the closest moon distance at in recent history, and the next one will be on January 1, 2257, at . * January 26 – The Indian National Congress declares this date as Independence Day, or as the day for Purna Swaraj (Complete Independence). * January 28 – The first patent for a field-effect transistor is granted in the United States, to Julius Edgar Lilienfeld. * January 30 – Pavel Molchanov launches a radiosonde from Pavlovsk, Saint Petersburg, Slutsk in the Soviet Union. February * February 10 – The Việt Nam Quốc Dân Đảng launch the Yên Bái mutiny in the hope of ending French Indochina, French colonial rule in Vietnam. * February 18 – While studying photographs taken in January, Clyde Tombaugh confirms the existence of Pluto, a celestial body considered a planet until redefined as a dwarf planet ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
French Physicists
French may refer to: * Something of, from, or related to France ** French language, which originated in France ** French people, a nation and ethnic group ** French cuisine, cooking traditions and practices Arts and media * The French (band), a British rock band * "French" (episode), a live-action episode of ''The Super Mario Bros. Super Show!'' * ''Française'' (film), a 2008 film * French Stewart (born 1964), American actor Other uses * French (surname), a surname (including a list of people with the name) * French (tunic), a type of military jacket or tunic * French's, an American brand of mustard condiment * French (catheter scale), a unit of measurement * French Defence, a chess opening * French kiss, a type of kiss See also * France (other) * Franch, a surname * French Revolution (other) * French River (other), several rivers and other places * Frenching (other) Frenching may refer to: * Frenching (automobile), recessing or mou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
French Engineers
French may refer to: * Something of, from, or related to France ** French language, which originated in France ** French people, a nation and ethnic group ** French cuisine, cooking traditions and practices Arts and media * The French (band), a British rock band * "French" (episode), a live-action episode of ''The Super Mario Bros. Super Show!'' * ''Française'' (film), a 2008 film * French Stewart (born 1964), American actor Other uses * French (surname), a surname (including a list of people with the name) * French (tunic), a type of military jacket or tunic * French's, an American brand of mustard condiment * French (catheter scale), a unit of measurement * French Defence, a chess opening * French kiss, a type of kiss See also * France (other) * Franch, a surname * French Revolution (other) * French River (other), several rivers and other places * Frenching (other) Frenching may refer to: * Frenching (automobile), recessing or mou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
French National Centre For Scientific Research
The French National Centre for Scientific Research (, , CNRS) is the French state research organisation and is the largest fundamental science agency in Europe. In 2016, it employed 31,637 staff, including 11,137 tenured researchers, 13,415 engineers and technical staff, and 7,085 contractual workers. It is headquartered in Paris and has administrative offices in Brussels, Beijing, Tokyo, Singapore, Washington, D.C., Bonn, Moscow, Tunis, Johannesburg, Santiago de Chile, Israel, and New Delhi. Organization The CNRS operates on the basis of research units, which are of two kinds: "proper units" (UPRs) are operated solely by the CNRS, and Joint Research Unit, Joint Research Units (UMRs – ) are run in association with other institutions, such as List of colleges and universities in France, universities or INSERM. Members of Joint Research Units may be either CNRS researchers or university employees (Academic ranks in France, ''maîtres de conférences'' or ''professeurs''). Each ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abbe Sine Condition
In optics, the Abbe sine condition is a condition that must be fulfilled by a lens or other optical system in order for it to produce sharp images of off-axis as well as on-axis objects. It was formulated by Ernst Abbe in the context of microscopes. The Abbe sine condition says that the sine of the object-space angle \alpha_\mathrm should be proportional to the sine of the image space angle \alpha_\mathrm Furthermore, the ratio equals the magnification of the system multiplied by the ratio of refractive indices. In mathematical terms this is: \frac = \frac = \frac, M, where the variables (\alpha_\mathrm, \beta_\mathrm) are the angles (relative to the optic axis) of any two rays as they leave the object, and (\alpha_\mathrm, \beta_\mathrm) are the angles of the same rays where they reach the image plane (say, the film plane of a camera). For example, (\alpha_\mathrm, \alpha_\mathrm) might represent a paraxial ray (i.e., a ray nearly parallel with the optic axis), and (\beta_\m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometric Optics
Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician who works in the field of geometry is called a '' geometer''. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point, line, plane, distance, angle, surface, and curve, as fundamental concepts. Originally developed to model the physical world, geometry has applications in almost all sciences, and also in art, architecture, and other activities that are related to graphics. Geometry also has applications in areas of mathematics that are apparently unrelated. For example, methods of algebraic geometry are fundamental in Wiles's proof of Fermat's Last Theorem, a problem that was stated in terms of elementary arithmetic, and remained unsolved for several centuries. Duri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quaternion
In mathematics, the quaternion number system extends the complex numbers. Quaternions were first described by the Irish mathematician William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space. The algebra of quaternions is often denoted by (for ''Hamilton''), or in blackboard bold by \mathbb H. Quaternions are not a field, because multiplication of quaternions is not, in general, commutative. Quaternions provide a definition of the quotient of two vectors in a three-dimensional space. Quaternions are generally represented in the form a + b\,\mathbf i + c\,\mathbf j +d\,\mathbf k, where the coefficients , , , are real numbers, and , are the ''basis vectors'' or ''basis elements''. Quaternions are used in pure mathematics, but also have practical uses in applied mathematics, particularly for calculations involving three-dimensional rotations, such as in three-dimensional computer graphics, computer vision, robotics, magnetic resonance i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lorentz Transformation
In physics, the Lorentz transformations are a six-parameter family of Linear transformation, linear coordinate transformation, transformations from a Frame of Reference, coordinate frame in spacetime to another frame that moves at a constant velocity relative to the former. The respective inverse transformation is then parameterized by the negative of this velocity. The transformations are named after the Dutch physicist Hendrik Lorentz. The most common form of the transformation, parametrized by the real constant v, representing a velocity confined to the -direction, is expressed as \begin t' &= \gamma \left( t - \frac \right) \\ x' &= \gamma \left( x - v t \right)\\ y' &= y \\ z' &= z \end where and are the coordinates of an event in two frames with the spatial origins coinciding at , where the primed frame is seen from the unprimed frame as moving with speed along the -axis, where is the speed of light, and \gamma = \frac is the Lorentz factor. When speed is much smal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Strophoid
In geometry, a strophoid is a curve generated from a given curve and points (the fixed point) and (the pole) as follows: Let be a variable line passing through and intersecting at . Now let and be the two points on whose distance from is the same as the distance from to (i.e. ). The locus of such points and is then the strophoid of with respect to the pole and fixed point . Note that and are at right angles in this construction. In the special case where is a line, lies on , and is not on , then the curve is called an oblique strophoid. If, in addition, is perpendicular to then the curve is called a right strophoid, or simply ''strophoid'' by some authors. The right strophoid is also called the logocyclic curve or foliate. Equations Polar coordinates Let the curve be given by r = f(\theta), where the origin is taken to be . Let be the point . If K = (r \cos\theta,\ r \sin\theta) is a point on the curve the distance from to is :d = \sqrt = \sqrt. Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
