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Vector Notation
In mathematics and physics, vector notation is a commonly used notation for representing vectors, which may be Euclidean vectors, or more generally, members of a vector space. For representing a vector, the common typographic convention is lower case, upright boldface type, as in . The International Organization for Standardization (ISO) recommends either bold italic serif, as in , or non-bold italic serif accented by a right arrow, as in \vec. In advanced mathematics, vectors are often represented in a simple italic type, like any variable. History In 1835 Giusto Bellavitis introduced the idea of equipollent directed line segments AB \bumpeq CD which resulted in the concept of a vector as an equivalence class of such segments. The term ''vector'' was coined by W. R. Hamilton around 1843, as he revealed quaternions, a system which uses vectors and scalars to span a four-dimensional space. For a quaternion ''q'' = ''a'' + ''b''i + ''c''j + ''d''k, Hamilton used two pro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vector Component
In mathematics, physics, and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector or spatial vector) is a geometric object that has magnitude (or length) and direction. Vectors can be added to other vectors according to vector algebra. A Euclidean vector is frequently represented by a '' directed line segment'', or graphically as an arrow connecting an ''initial point'' ''A'' with a ''terminal point'' ''B'', and denoted by \overrightarrow . A vector is what is needed to "carry" the point ''A'' to the point ''B''; the Latin word ''vector'' means "carrier". It was first used by 18th century astronomers investigating planetary revolution around the Sun. The magnitude of the vector is the distance between the two points, and the direction refers to the direction of displacement from ''A'' to ''B''. Many algebraic operations on real numbers such as addition, subtraction, multiplication, and negation have close analogues for vectors, operations w ... [...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. Hamilton defined a quaternion as the quotient of two '' directed lines'' in a three-dimensional space, or, equivalently, as the quotient of two vectors. Multiplication of quaternions is noncommutative. Quaternions are generally represented in the form :a + b\ \mathbf i + c\ \mathbf j +d\ \mathbf k where , and are real numbers; and , and are the ''basic quaternions''. 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, and crystallographic texture analysis. They can be used alongside other methods of rotation, such as Euler angles and rotation matrices, or as an alternative to th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
James Clerk Maxwell
James Clerk Maxwell (13 June 1831 – 5 November 1879) was a Scottish mathematician and scientist responsible for the classical theory of electromagnetic radiation, which was the first theory to describe electricity, magnetism and light as different manifestations of the same phenomenon. Maxwell's equations for electromagnetism have been called the " second great unification in physics" where the first one had been realised by Isaac Newton. With the publication of " A Dynamical Theory of the Electromagnetic Field" in 1865, Maxwell demonstrated that electric and magnetic fields travel through space as waves moving at the speed of light. He proposed that light is an undulation in the same medium that is the cause of electric and magnetic phenomena. (This article accompanied an 8 December 1864 presentation by Maxwell to the Royal Society. His statement that "light and magnetism are affections of the same substance" is at page 499.) The unification of light and elec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fraktur
Fraktur () is a calligraphic hand of the Latin alphabet and any of several blackletter typefaces derived from this hand. The blackletter lines are broken up; that is, their forms contain many angles when compared to the curves of the Antiqua (common) typefaces modeled after antique Roman square capitals and Carolingian minuscule. From this, Fraktur is sometimes contrasted with the "Latin alphabet" in northern European texts, which is sometimes called the "German alphabet", simply being a typeface of the Latin alphabet. Similarly, the term "Fraktur" or "Gothic" is sometimes applied to ''all'' of the blackletter typefaces (known in German as , "Broken Script"). The word derives from Latin ("a break"), built from , passive participle of ("to break"), the same root as the English word "fracture". Characteristics Besides the 26 letters of the ISO basic Latin alphabet, Fraktur includes the ( ), vowels with umlauts, and the ('' long s''). Some Fraktur typefaces also incl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Greek Letters
The Greek alphabet has been used to write the Greek language since the late 9th or early 8th century BCE. It is derived from the earlier Phoenician alphabet, and was the earliest known alphabetic script to have distinct letters for vowels as well as consonants. In Archaic and early Classical times, the Greek alphabet existed in many local variants, but, by the end of the 4th century BCE, the Euclidean alphabet, with 24 letters, ordered from alpha to omega, had become standard and it is this version that is still used for Greek writing today. The uppercase and lowercase forms of the 24 letters are: : , , , , , , , , , , , , , , , , , /ς, , , , , , . The Greek alphabet is the ancestor of the Latin and Cyrillic scripts. Like Latin and Cyrillic, Greek originally had only a single form of each letter; it developed the letter case distinction between uppercase and lowercase in parallel with Latin during the modern era. Sound values and conventional transcriptions for some of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Clarendon (typeface)
Clarendon is the name of a slab-serif typeface that was released in 1845 by Thorowgood and Co. (or Thorowgood and Besley) of London, a letter foundry often known as the Fann Street Foundry. The original Clarendon design is credited to Robert Besley, a partner in the foundry, and was originally engraved by punchcutter Benjamin Fox, who may also have contributed to its design. Many copies, adaptations and revivals have been released, becoming almost an entire genre of type design. Clarendons have a bold, solid structure, similar in letter structure to the "modern" serif typefaces popular in the nineteenth century for body text (for instance showing an 'R' with a curled leg and ball terminals on the 'a' and 'c'), but bolder and with less contrast in stroke weight. Clarendon designs generally have a structure with bracketed serifs, which become larger as they reach the main stroke of the letter. Mitja Miklavčič describes the basic features of Clarendon designs (and ones labelled Io ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oliver Heaviside
Oliver Heaviside FRS (; 18 May 1850 – 3 February 1925) was an English self-taught mathematician and physicist who invented a new technique for solving differential equations (equivalent to the Laplace transform), independently developed vector calculus, and rewrote Maxwell's equations in the form commonly used today. He significantly shaped the way Maxwell's equations are understood and applied in the decades following Maxwell's death. His formulation of the telegrapher's equations became commercially important during his own lifetime, after their significance went unremarked for a long while, as few others were versed at the time in his novel methodology. Although at odds with the scientific establishment for most of his life, Heaviside changed the face of telecommunications, mathematics, and science. Biography Early life Heaviside was born in Camden Town, London, at 55 Kings Street (now Plender Street), the youngest of three children of Thomas, a draughtsman and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Internet Archive
The Internet Archive is an American digital library with the stated mission of "universal access to all knowledge". It provides free public access to collections of digitized materials, including websites, software applications/games, music, movies/videos, moving images, and millions of books. In addition to its archiving function, the Archive is an activist organization, advocating a free and open Internet. , the Internet Archive holds over 35 million books and texts, 8.5 million movies, videos and TV shows, 894 thousand software programs, 14 million audio files, 4.4 million images, 2.4 million TV clips, 241 thousand concerts, and over 734 billion web pages in the Wayback Machine. The Internet Archive allows the public to upload and download digital material to its data cluster, but the bulk of its data is collected automatically by its web crawlers, which work to preserve as much of the public web as possible. Its web archive, the Wayback Machine, contains hundreds of bi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Edwin Bidwell Wilson
Edwin Bidwell Wilson (April 25, 1879 – December 28, 1964) was an American mathematician, statistician, physicist and general polymath. He was the sole protégé of Yale University physicist Josiah Willard Gibbs and was mentor to MIT economist Paul Samuelson. Wilson had a distinguished academic career at Yale and MIT, followed by a long and distinguished period of service as a civilian employee of the US Navy in the Office of Naval Research. In his latter role, he was awarded the Distinguished Civilian Service Award, the highest honorary award available to a civilian employee of the US Navy. Wilson made broad contributions to mathematics, statistics and aeronautics, and is well-known for producing a number of widely used textbooks. He is perhaps best known for his derivation of the eponymously named Wilson score interval, which is a confidence interval used widely in statistics. Life Edwin Bidwell Wilson was born in Hartford, Connecticut to Edwin Horace Wilson (a teacher ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vector Analysis (Gibbs/Wilson)
Vector calculus, or vector analysis, is concerned with differentiation and integration of vector fields, primarily in 3-dimensional Euclidean space \mathbb^3. The term "vector calculus" is sometimes used as a synonym for the broader subject of multivariable calculus, which spans vector calculus as well as partial differentiation and multiple integration. Vector calculus plays an important role in differential geometry and in the study of partial differential equations. It is used extensively in physics and engineering, especially in the description of electromagnetic fields, gravitational fields, and fluid flow. Vector calculus was developed from quaternion analysis by J. Willard Gibbs and Oliver Heaviside near the end of the 19th century, and most of the notation and terminology was established by Gibbs and Edwin Bidwell Wilson in their 1901 book, ''Vector Analysis''. In the conventional form using cross products, vector calculus does not generalize to higher dimension ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vector Product
In mathematics, the cross product or vector product (occasionally directed area product, to emphasize its geometric significance) is a binary operation on two vectors in a three-dimensional oriented Euclidean vector space (named here E), and is denoted by the symbol \times. Given two linearly independent vectors and , the cross product, (read "a cross b"), is a vector that is perpendicular to both and , and thus normal to the plane containing them. It has many applications in mathematics, physics, engineering, and computer programming. It should not be confused with the dot product (projection product). If two vectors have the same direction or have the exact opposite direction from each other (that is, they are ''not'' linearly independent), or if either one has zero length, then their cross product is zero. More generally, the magnitude of the product equals the area of a parallelogram with the vectors for sides; in particular, the magnitude of the product of two perpendicul ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scalar Product
In mathematics, the dot product or scalar productThe term ''scalar product'' means literally "product with a scalar as a result". It is also used sometimes for other symmetric bilinear forms, for example in a pseudo-Euclidean space. is an algebraic operation that takes two equal-length sequences of numbers (usually coordinate vectors), and returns a single number. In Euclidean geometry, the dot product of the Cartesian coordinates of two vectors is widely used. It is often called the inner product (or rarely projection product) of Euclidean space, even though it is not the only inner product that can be defined on Euclidean space (see Inner product space for more). Algebraically, the dot product is the sum of the products of the corresponding entries of the two sequences of numbers. Geometrically, it is the product of the Euclidean magnitudes of the two vectors and the cosine of the angle between them. These definitions are equivalent when using Cartesian coordinates. In ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
