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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, 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." He continued publishing in retirement. De Casteljau curves De Casteljau's algorithm is widely used, with some modifications, as it is the most robust and numerically stable method for evaluating polynomials. Other methods, such as Horner's me ... [...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. Typically deployed in symmetric pairs, an individual bracket may be identified as a 'left' or 'right' bracket or, alternatively, an "opening bracket" or "closing bracket", respectively, depending on the directionality of the context. Specific forms of the mark include parentheses (also called "rounded brackets"), square brackets, curly brackets (also called 'braces'), and angle brackets (also called 'chevrons'), as well as various less common pairs of symbols. As well as signifying the overall class of punctuation, the word "bracket" is commonly used to refer to a specific form of bracket, which varies from region to region. In most English-speaking countries, an unqualified word "bracket" refers to the parenthesis (round bracket); in the United States, the square bracket. Various forms of brackets are used in mathematics, with ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
École Normale Supérieure (Paris)
The ''École normale supérieure - PSL'' (; also known as ''ENS'', ''Normale sup, ''Ulm'' or ''ENS Paris'') is a ''grande école'' university in Paris, France. It is one of the constituent members of Paris Sciences et Lettres University (PSL). Originally conceived during the French Revolution, the school was founded in 1794 to provide homogeneous training of high-school teachers in France but it later closed. The school was subsequently reestablished by Napoleon I as ''pensionnat normal'' from 1808 to 1822, before being recreated in 1826 and taking the name of ''École normale'' in 1830. When institutes for primary teachers training called é''coles normales'' were created in 1845, the word ''supérieure'' (meaning upper) was added to form the current name. It has since developed into an institution which has become a platform for French students to pursue careers in government and academia. The ENS has a highly competitive selection process consisting of written and oral exami ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Citroën
Citroën () is a French automobile brand. The "Automobiles Citroën" manufacturing company was founded in March 1919 by André Citroën. Citroën is owned by Stellantis since 2021 and previously was part of the PSA Group after Peugeot acquired 89.95% share in 1976. Citroën's head office is located in the Stellantis Poissy Plant in Saint-Ouen-sur-Seine since 2021 (previously in Rueil-Malmaison) and its offices studies and research in Vélizy-Villacoublay, Poissy (CEMR), Carrières-sous-Poissy and Sochaux-Montbéliard. In 1934, the firm established its reputation for innovative technology with the Traction Avant. This was the world's first car to be mass-produced with front-wheel drive, four-wheel independent suspension, as well as unibody construction, omitting a separate chassis, and instead using the body of the car itself as its main load-bearing structure. In 1954, they produced the world's first hydropneumatic self-levelling suspension system then, in 1955, the revolutio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algorithm
In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can perform automated deductions (referred to as automated reasoning) and use mathematical and logical tests to divert the code execution through various routes (referred to as automated decision-making). Using human characteristics as descriptors of machines in metaphorical ways was already practiced by Alan Turing with terms such as "memory", "search" and "stimulus". In contrast, a heuristic is an approach to problem solving that may not be fully specified or may not guarantee correct or optimal results, especially in problem domains where there is no well-defined correct or optimal result. As an effective method, an algorithm can be expressed within a finite amount of space ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pierre Bézier
Pierre Étienne Bézier (1 September 1910 – 25 November 1999; ) was a French engineer and one of the founders of the fields of solid, geometric and physical modelling as well as in the field of representing curves, especially in computer-aided design and manufacturing systems. As an engineer at Renault, he became a leader in the transformation of design and manufacturing, through mathematics and computing tools, into computer-aided design and three-dimensional modeling. Bézier patented and popularized the Bézier curves and Bézier surfaces that are now used in most computer-aided design and computer graphics systems. Background Born in Paris, Bézier was the son and grandson of engineers. He obtained a degree in mechanical engineering from the École nationale supérieure d'arts et métiers in 1930. He earned a second degree in electrical engineering in 1931 at the École supérieure d'électricité, and a doctorate in 1977 in mathematics from the Pierre-and-Mar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bézier Curve
A Bézier curve ( ) is a parametric curve used in computer graphics and related fields. A set of discrete "control points" defines a smooth, continuous curve by means of a formula. Usually the curve is intended to approximate a real-world shape that otherwise has no mathematical representation or whose representation is unknown or too complicated. The Bézier curve is named after French engineer Pierre Bézier (1910–1999), who used it in the 1960s for designing curves for the bodywork of Renault cars. Other uses include the design of computer fonts and animation. Bézier curves can be combined to form a Bézier spline, or generalized to higher dimensions to form Bézier surfaces. The Bézier triangle is a special case of the latter. In vector graphics, Bézier curves are used to model smooth curves that can be scaled indefinitely. "Paths", as they are commonly referred to in image manipulation programs, are combinations of linked Bézier curves. Paths are not bound by the lim ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Horner's Method
In mathematics and computer science, Horner's method (or Horner's scheme) is an algorithm for polynomial evaluation. Although named after William George Horner, this method is much older, as it has been attributed to Joseph-Louis Lagrange by Horner himself, and can be traced back many hundreds of years to Chinese and Persian mathematicians. After the introduction of computers, this algorithm became fundamental for computing efficiently with polynomials. The algorithm is based on Horner's rule: :\begin a_0 &+ a_1x + a_2x^2 + a_3x^3 + \cdots + a_nx^n \\ &= a_0 + x \bigg(a_1 + x \Big(a_2 + x \big(a_3 + \cdots + x(a_ + x \, a_n) \cdots \big) \Big) \bigg). \end This allows the evaluation of a polynomial of degree with only n multiplications and n additions. This is optimal, since there are polynomials of degree that cannot be evaluated with fewer arithmetic operations. Alternatively, Horner's method also refers to a method for approximating the roots of polynomials, described by Ho ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Forward Difference
A finite difference is a mathematical expression of the form . If a finite difference is divided by , one gets a difference quotient. The approximation of derivatives by finite differences plays a central role in finite difference methods for the numerical solution of differential equations, especially boundary value problems. The difference operator, commonly denoted \Delta is the operator that maps a function to the function \Delta /math> defined by :\Delta x)= f(x+1)-f(x). A difference equation is a functional equation that involves the finite difference operator in the same way as a differential equation involves derivatives. There are many similarities between difference equations and differential equations, specially in the solving methods. Certain recurrence relations can be written as difference equations by replacing iteration notation with finite differences. In numerical analysis, finite differences are widely used for approximating derivatives, and the term "fini ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
French National Centre For Scientific Research
The French National Centre for Scientific Research (french: link=no, Centre national de la recherche scientifique, 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. From 2009 to 2016, the CNRS was ranked No. 1 worldwide by the SCImago Institutions Rankings (SIR), an international ranking of research-focused institutions, including universities, national research centers, and companies such as Facebook or Google. The CNRS ranked No. 2 between 2017 and 2021, then No. 3 in 2022 in the same SIR, after the Chinese Academy of Sciences and before universities such as Harvard University, MIT, or Stanfo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
French Engineers
French (french: français(e), link=no) may refer to: * Something of, from, or related to France ** French language, which originated in France, and its various dialects and accents ** French people, a nation and ethnic group identified with France ** French cuisine, cooking traditions and practices Fortnite French places 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), 2008 * French Stewart (born 1964), American actor Other uses * French (surname), a surname (including a list of people with the name) * French (tunic), a particular type of military jacket or tunic used in the Russian Empire and Soviet Union * French's, an American brand of mustard condiment * French catheter scale, a unit of measurement of diameter * French Defence, a chess opening * French kiss, a type of kiss involving the tongue See also * France (other) * Franch, a surname * Frenc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
French Physicists
French (french: français(e), link=no) may refer to: * Something of, from, or related to France ** French language, which originated in France, and its various dialects and accents ** French people, a nation and ethnic group identified with France ** French cuisine, cooking traditions and practices Fortnite French places 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), 2008 * French Stewart (born 1964), American actor Other uses * French (surname), a surname (including a list of people with the name) * French (tunic), a particular type of military jacket or tunic used in the Russian Empire and Soviet Union * French's, an American brand of mustard condiment * French catheter scale, a unit of measurement of diameter * French Defence, a chess opening * French kiss, a type of kiss involving the tongue See also * France (other) * Franch, a surname * Fren ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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