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Werner Formulas
Prosthaphaeresis (from the Greek ''προσθαφαίρεσις'') was an algorithm used in the late 16th century and early 17th century for approximate multiplication and division using formulas from trigonometry. For the 25 years preceding the invention of the logarithm in 1614, it was the only known generally applicable way of approximating products quickly. Its name comes from the Greek ''prosthesis'' (πρόσθεσις) and ''aphaeresis'' (ἀφαίρεσις), meaning addition and subtraction, two steps in the process. by Brian Borchers History and motivation In 16th-century Europe, of ships on long voyages relied heavily on ...[...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 Computational problem, 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 (computer science), 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 ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Joost Bürgi
Joost () was an Internet TV service, created by Niklas Zennström and Janus Friis (founders of Skype and Kazaa). During 2007–2008 Joost used peer-to-peer TV (P2PTV) technology to distribute content to their Mozilla-based desktop player; in late 2008 this was migrated to use a Flash-based Web player instead. Joost began development in 2006. Working under the code name "The Venice Project", Zennström and Friis assembled teams of some 150 software developers in about six cities around the world, including New York City, London, Leiden and Toulouse. According to Zennström at a 25 July 2007 press conference about Skype held in Tallinn, Estonia, Joost had signed up more than a million beta testers, and its launch was scheduled for the end of 2007. The team signed up with Warner Music, Indianapolis Motor Speedway Productions (Indianapolis 500, IndyCar Series) and production company Endemol for the beta.Orlowski, Andrew (17 January 2007)Joost – the new, new TV thing.''The Registe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nearest-neighbor Interpolation
Nearest-neighbor interpolation (also known as proximal interpolation or, in some contexts, point sampling) is a simple method of multivariate interpolation in one or more dimensions. Interpolation is the problem of approximating the value of a function for a non-given point in some space when given the value of that function in points around (neighboring) that point. The nearest neighbor algorithm selects the value of the nearest point and does not consider the values of neighboring points at all, yielding a piecewise-constant interpolant. The algorithm is very simple to implement and is commonly used (usually along with mipmapping) in real-time 3D rendering to select color values for a textured surface. Connection to Voronoi diagram For a given set of points in space, a Voronoi diagram is a decomposition of space into cells, one for each given point, so that anywhere in space, the closest given point is inside the cell. This is equivalent to nearest neighbour interpolation, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euler's Formula
Euler's formula, named after Leonhard Euler, is a mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric functions and the complex exponential function. Euler's formula states that for any real number : e^ = \cos x + i\sin x, where is the base of the natural logarithm, is the imaginary unit, and and are the trigonometric functions cosine and sine respectively. This complex exponential function is sometimes denoted ("cosine plus i sine"). The formula is still valid if is a complex number, and so some authors refer to the more general complex version as Euler's formula. Euler's formula is ubiquitous in mathematics, physics, and engineering. The physicist Richard Feynman called the equation "our jewel" and "the most remarkable formula in mathematics". When , Euler's formula may be rewritten as , which is known as Euler's identity. History In 1714, the English mathematician Roger Cotes presented a geometrical ar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trigonometric Function
In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others. They are among the simplest periodic functions, and as such are also widely used for studying periodic phenomena through Fourier analysis. The trigonometric functions most widely used in modern mathematics are the sine, the cosine, and the tangent. Their reciprocals are respectively the cosecant, the secant, and the cotangent, which are less used. Each of these six trigonometric functions has a corresponding inverse function, and an analog among the hyperbolic functions. The oldest definitions of trigonometric functions, related to right-angle triangles, define them only for acute angles. To extend the sine and co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Percent Error
In any quantitative science, the terms relative change and relative difference are used to compare two quantities while taking into account the "sizes" of the things being compared, i.e. dividing by a ''standard'' or ''reference'' or ''starting'' value. The comparison is expressed as a ratio and is a unitless number. By multiplying these ratios by 100 they can be expressed as percentages so the terms percentage change, percent(age) difference, or relative percentage difference are also commonly used. The terms "change" and "difference" are used interchangeably. Relative change is often used as a quantitative indicator of quality assurance and quality control for repeated measurements where the outcomes are expected to be the same. A special case of percent change (relative change expressed as a percentage) called ''percent error'' occurs in measuring situations where the reference value is the accepted or actual value (perhaps theoretically determined) and the value being compared to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jost Bürgi
Jost Bürgi (also ''Joost, Jobst''; Latinisation of names, Latinized surname ''Burgius'' or ''Byrgius''; 28 February 1552 – 31 January 1632), active primarily at the courts in Kassel and Prague, was a Swiss clockmaker, a maker of astronomical instruments and a mathematician. Life Bürgi was born in 1552 Lichtensteig, Toggenburg, at the time a subject territory of the Abbey of St. Gall (now part of the canton of St. Gallen, Switzerland). Not much is known about his life or education before his employment as astronomer and clockmaker at the court of William IV in Kassel in 1579; it has been theorized that he acquired his mathematical knowledge at Strasbourg, among others from Swiss mathematician Conrad Dasypodius, but there are no facts to support this. Although an autodidact, he was already during his lifetime considered as one of the most excellent mechanical engineers of his generation. His employer, William IV, Landgrave of Hesse-Kassel, in a letter to Tycho Brahe praise ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trigonometric Function
In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others. They are among the simplest periodic functions, and as such are also widely used for studying periodic phenomena through Fourier analysis. The trigonometric functions most widely used in modern mathematics are the sine, the cosine, and the tangent. Their reciprocals are respectively the cosecant, the secant, and the cotangent, which are less used. Each of these six trigonometric functions has a corresponding inverse function, and an analog among the hyperbolic functions. The oldest definitions of trigonometric functions, related to right-angle triangles, define them only for acute angles. To extend the sine and co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trigonometric Identity
In trigonometry, trigonometric identities are Equality (mathematics), equalities that involve trigonometric functions and are true for every value of the occurring Variable (mathematics), variables for which both sides of the equality are defined. Geometrically, these are identity (mathematics), identities involving certain functions of one or more angles. They are distinct from Trigonometry#Triangle identities, triangle identities, which are identities potentially involving angles but also involving side lengths or other lengths of a triangle. These identities are useful whenever expressions involving trigonometric functions need to be simplified. An important application is the integral, integration of non-trigonometric functions: a common technique involves first using the Trigonometric substitution, substitution rule with a trigonometric function, and then simplifying the resulting integral with a trigonometric identity. Pythagorean identities The basic relationship betwe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
De Revolutionibus Orbium Coelestium
''De revolutionibus orbium coelestium'' (English translation: ''On the Revolutions of the Heavenly Spheres'') is the seminal work on the heliocentric theory of the astronomer Nicolaus Copernicus (1473–1543) of the Polish Renaissance. The book, first printed in 1543 in Nuremberg, Holy Roman Empire, offered an alternative model of the universe to Ptolemy's geocentric system, which had been widely accepted since ancient times. History Copernicus initially outlined his system in a short, untitled, anonymous manuscript that he distributed to several friends, referred to as the ''Commentariolus''. A physician's library list dating to 1514 includes a manuscript whose description matches the ''Commentariolus'', so Copernicus must have begun work on his new system by that time. Most historians believe that he wrote the ''Commentariolus'' after his return from Italy, possibly only after 1510. At this time, Copernicus anticipated that he could reconcile the motion of the Earth with the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nicholas Copernicus
Nicolaus Copernicus (; pl, Mikołaj Kopernik; gml, Niklas Koppernigk, german: Nikolaus Kopernikus; 19 February 1473 – 24 May 1543) was a Renaissance polymath, active as a mathematician, astronomer, and Catholic canon, who formulated a model of the universe that placed the Sun rather than Earth at its center. In all likelihood, Copernicus developed his model independently of Aristarchus of Samos, an ancient Greek astronomer who had formulated such a model some eighteen centuries earlier. The publication of Copernicus's model in his book ' (''On the Revolutions of the Celestial Spheres''), just before his death in 1543, was a major event in the history of science, triggering the Copernican Revolution and making a pioneering contribution to the Scientific Revolution. Copernicus was born and died in Royal Prussia, a region that had been part of the Kingdom of Poland since 1466. A polyglot and polymath, he obtained a doctorate in canon law and was a mathematician, astro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Napier
John Napier of Merchiston (; 1 February 1550 – 4 April 1617), nicknamed Marvellous Merchiston, was a Scottish landowner known as a mathematician, physicist, and astronomer. He was the 8th Laird of Merchiston. His Latinized name was Ioannes Neper. John Napier is best known as the discoverer of logarithms. He also invented the so-called "Napier's bones" and made common the use of the decimal point in arithmetic and mathematics. Napier's birthplace, Merchiston Tower in Edinburgh, is now part of the facilities of Edinburgh Napier University. There is a memorial to him at St Cuthbert's at the west side of Edinburgh. Life Napier's father was Sir Archibald Napier of Merchiston Castle, and his mother was Janet Bothwell, daughter of the politician and judge Francis Bothwell, and a sister of Adam Bothwell who became the Bishop of Orkney. Archibald Napier was 16 years old when John Napier was born. There are no records of Napier's early education, but many believe that he was ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
