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History Of Quaternions
In mathematics, quaternions are a non-commutative number system that extends the complex numbers. Quaternions and their applications to rotations were first described in print by Olinde Rodrigues in all but name in 1840, but independently discovered by Irish mathematician Sir William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space. They find uses in both theoretical and applied mathematics, in particular for calculations involving three-dimensional rotations. Hamilton's discovery In 1843, Hamilton knew that the complex numbers could be viewed as points in a plane and that they could be added and multiplied together using certain geometric operations. Hamilton sought to find a way to do the same for points in space. Points in space can be represented by their coordinates, which are triples of numbers and have an obvious addition, but Hamilton had difficulty defining the appropriate multiplication. According to a letter Hamilton wrote later to his son ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inscription On Broom Bridge (Dublin) Regarding The Discovery Of Quaternions Multiplication By Sir William Rowan Hamilton
Epigraphy () is the study of inscriptions, or epigraphs, as writing; it is the science of identifying graphemes, clarifying their meanings, classifying their uses according to dates and cultural contexts, and drawing conclusions about the writing and the writers. Specifically excluded from epigraphy are the historical significance of an epigraph as a document and the artistic value of a literary composition. A person using the methods of epigraphy is called an ''epigrapher'' or ''epigraphist''. For example, the Behistun inscription is an official document of the Achaemenid Empire engraved on native rock at a location in Iran. Epigraphists are responsible for reconstructing, translating, and dating the trilingual inscription and finding any relevant circumstances. It is the work of historians, however, to determine and interpret the events recorded by the inscription as document. Often, epigraphy and history are competences practised by the same person. Epigraphy is a primar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Biquaternion
In abstract algebra, the biquaternions are the numbers , where , and are complex numbers, or variants thereof, and the elements of multiply as in the quaternion group and commute with their coefficients. There are three types of biquaternions corresponding to complex numbers and the variations thereof: * Biquaternions when the coefficients are complex numbers. * Split-biquaternions when the coefficients are split-complex numbers. * Dual quaternions when the coefficients are dual numbers. This article is about the ''ordinary biquaternions'' named by William Rowan Hamilton in 1844 (see ''Proceedings of the Royal Irish Academy'' 1844 & 1850 page 388). Some of the more prominent proponents of these biquaternions include Alexander Macfarlane, Arthur W. Conway, Ludwik Silberstein, and Cornelius Lanczos. As developed below, the unit quasi-sphere of the biquaternions provides a representation of the Lorentz group, which is the foundation of special relativity. The algebra of biquatern ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jules Hoüel
Guillaume-Jules Hoüel (7 April 1823 – 14 June 1886) was a French people, French mathematician. He entered the École Normale Supérieure in 1843 and received his doctoral degree in 1855 from the University of Paris, Sorbonne. He was sought by Urbain Le Verrier at the Paris Observatory, but chose instead to return to Thaon to study there. In 1859 he began to teach at Bordeaux. In 1863 Hoüel expressed his doubts about the verifiability of the parallel postulate of Euclid. In 1867 Hoüel produced French translations of two key publications of non-Euclidean geometry: Lobachevski's ''Geometrical Studies on the Theory of Parallels'' and Bolyai's ''Science of Absolute Space''. Hoüel published a four volume work titled ''Théorie Élémentaire des Quantités Complexes''. Volume four, published in 1874, began with an discussion of properties of algebraic operations (commutativity, associativity, distribution, and inverses) and used the algebra of quaternions and versors to describe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equipollence (geometry)
In Euclidean geometry, equipollence is a binary relation between directed line segments. Two parallel line segments are equipollent when they have the same length and direction. Parallelogram property A definitive feature of Euclidean space is the parallelogram property of vectors: If two segments are equipollent, then they form two sides of a parallelogram: History The concept of equipollent line segments was advanced by Giusto Bellavitis in 1835. Subsequently the term vector was adopted for a class of equipollent line segments. Bellavitis's use of the idea of a relation to compare different but similar objects has become a common mathematical technique, particularly in the use of equivalence relations. Bellavitis used a special notation for the equipollence of segments ''AB'' and ''CD'': :AB \bumpeq CD . The following passages, translated by Michael J. Crowe, show the anticipation that Bellavitis had of vector concepts: :Equipollences continue to hold when one substitute ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Giusto Bellavitis
Giusto Bellavitis (22 November 1803 – 6 November 1880) was an Italian mathematician, senator, and municipal councilor. Charles Laisant (1880) "Giusto Bellavitis. Nécrologie", ''Bulletin des sciences mathématiques et astronomiques'', 2nd série, 4(1): 343–8 According to Charles Laisant, :His principle achievement, which marks his place, in the future and the present, among the names of geometers that will endure, is the invention of the method of equipollences, a new method of analytic geometry that is both philosophical and fruitful. Born in Bassano del Grappa in 1803 to Ernesto Bellavitis and Giovanna Navarini, Giusto studied largely alone. In 1840 he entered Institut Venitian and in 1842 began instructing at Lycee de Vicence. In 1845 he became professor of descriptive geometry at University of Padua. With the unification of Italy he took the opportunity to revise the curriculum to include complementary algebra and analytic geometry. Bellavitis married in 1842 and had ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coquaternion
In abstract algebra, the split-quaternions or coquaternions form an algebraic structure introduced by James Cockle in 1849 under the latter name. They form an associative algebra of dimension four over the real numbers. After introduction in the 20th century of coordinate-free definitions of rings and algebras, it has been proved that the algebra of split-quaternions is isomorphic to the ring of the real matrices. So the study of split-quaternions can be reduced to the study of real matrices, and this may explain why there are few mentions of split-quaternions in the mathematical literature of the 20th and 21st centuries. Definition The ''split-quaternions'' are the linear combinations (with real coefficients) of four basis elements that satisfy the following product rules: :, :, :, :. By associativity, these relations imply :, :, and also . So, the split-quaternions form a real vector space of dimension four with as a basis. They form also a noncommutative ring, by ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tessarine
In abstract algebra, a bicomplex number is a pair of complex numbers constructed by the Cayley–Dickson process that defines the bicomplex conjugate (w,z)^* = (w, -z), and the product of two bicomplex numbers as :(u,v)(w,z) = (u w - v z, u z + v w). Then the bicomplex norm is given by :(w,z)^* (w,z) = (w, -z)(w,z) = (w^2 + z^2, 0), a quadratic form in the first component. The bicomplex numbers form a commutative algebra over C of dimension two, which is isomorphic to the direct sum of algebras . The product of two bicomplex numbers yields a quadratic form value that is the product of the individual quadratic forms of the numbers: a verification of this property of the quadratic form of a product refers to the Brahmagupta–Fibonacci identity. This property of the quadratic form of a bicomplex number indicates that these numbers form a composition algebra. In fact, bicomplex numbers arise at the binarion level of the Cayley–Dickson construction based on \mathbb with no ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
James Cockle
Sir James Cockle FRS FRAS FCPS (14 January 1819 – 27 January 1895) was an English lawyer and mathematician. Cockle was born on 14 January 1819. He was the second son of James Cockle, a surgeon, of Great Oakley, Essex. Educated at Charterhouse and Trinity College, Cambridge, he entered the Middle Temple in 1838, practising as a special pleader in 1845 and being called in 1846. Joining the midland circuit, he acquired a good practice, and on the recommendation of Chief Justice Sir William Erle he was appointed as the first Chief Justice of the Supreme Court of Queensland in Queensland, Australia on 21 February 1863; he served until his retirement on 24 June 1879. Cockle was made a Fellow of the Royal Society (FRS) on 1 June 1865. He received the honour of knighthood on 29 July 1869. He returned to England in 1878. Personal life Sir James married Adelaide, who became Lady Cockle when he was knighted in 1869. His residence Oakwal in Windsor, Queensland, Brisbane is listed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Four-dimensional Space
A four-dimensional space (4D) is a mathematical extension of the concept of three-dimensional or 3D space. Three-dimensional space is the simplest possible abstraction of the observation that one only needs three numbers, called ''dimensions'', to describe the sizes or locations of objects in the everyday world. For example, the volume of a rectangular box is found by measuring and multiplying its length, width, and height (often labeled ''x'', ''y'', and ''z''). The idea of adding a fourth dimension began with Jean le Rond d'Alembert's "Dimensions" being published in 1754, was followed by Joseph-Louis Lagrange in the mid-1700s, and culminated in a precise formalization of the concept in 1854 by Bernhard Riemann. In 1880, Charles Howard Hinton popularized these insights in an essay titled "What is the Fourth Dimension?", which explained the concept of a " four-dimensional cube" with a step-by-step generalization of the properties of lines, squares, and cubes. The simplest form ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
A K Peters
A K Peters, Ltd. was a publisher of scientific and technical books, specializing in mathematics and in computer graphics, robotics, and other fields of computer science. They published the journals ''Experimental Mathematics'' and the '' Journal of Graphics Tools'', as well as mathematics books geared to children. Background Klaus Peters wrote a doctoral dissertation on complex manifolds at the University of Erlangen in 1962, supervised by Reinhold Remmert. He then joined Springer Verlag, becoming their first specialist mathematics editor. As a Springer director from 1971, he hired Alice Merker for Springer New York: they were married that year, and moved to Heidelberg. Leaving Springer, they founded Birkhäuser Boston in 1979; Birkhäuser ran into financial difficulties, and was taken over by Springer. Klaus and Alice then spent a period running a Boston office for Harcourt Brace Jovanovich and their imprint Academic Press. With the takeover of Harcourt Brace Jovanovich by Gener ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John H
John is a common English name and surname: * John (given name) * John (surname) John may also refer to: New Testament Works * Gospel of John, a title often shortened to John * First Epistle of John, often shortened to 1 John * Second Epistle of John, often shortened to 2 John * Third Epistle of John, often shortened to 3 John People * John the Baptist (died c. AD 30), regarded as a prophet and the forerunner of Jesus Christ * John the Apostle (lived c. AD 30), one of the twelve apostles of Jesus * John the Evangelist, assigned author of the Fourth Gospel, once identified with the Apostle * John of Patmos, also known as John the Divine or John the Revelator, the author of the Book of Revelation, once identified with the Apostle * John the Presbyter, a figure either identified with or distinguished from the Apostle, the Evangelist and John of Patmos Other people with the given name Religious figures * John, father of Andrew the Apostle and Saint Peter * Pope Jo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leonhard Euler
Leonhard Euler ( , ; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, geographer, logician and engineer who founded the studies of graph theory and topology and made pioneering and influential discoveries in many other branches of mathematics such as analytic number theory, complex analysis, and infinitesimal calculus. He introduced much of modern mathematical terminology and notation, including the notion of a mathematical function. He is also known for his work in mechanics, fluid dynamics, optics, astronomy and music theory. Euler is held to be one of the greatest mathematicians in history and the greatest of the 18th century. A statement attributed to Pierre-Simon Laplace expresses Euler's influence on mathematics: "Read Euler, read Euler, he is the master of us all." Carl Friedrich Gauss remarked: "The study of Euler's works will remain the best school for the different fields of mathematics, and nothing else can replace it." Euler is a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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