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Graphical representation of quaternion units product as 90°-rotation in 4D-space, ij = k, ji = −k, ij = −ji History[edit] Quaternion plaque on Brougham (Broom) Bridge, Dublin, which says: Here as he walked by on the 16th of October 1843 Sir William Rowan Hamilton in a flash of genius discovered the fundamental formula for quaternion multiplicationi2 = j2 = k2 = ijk = −1 & cut it on a stone of this bridge Quaternion algebra was introduced by Hamilton in 1843.[7] Important precursors to this work included Euler's four-square identity (1748) and Olinde Rodrigues' parameterization of general rotations by four parameters (1840), but neither of these writers treated the four-parameter rotations as an algebra.[8][9] Carl Friedrich Gauss had also discovered quaternions in 1819, but this work was not published until 1900.[10][11] i2 = j2 = k2 = ijk = −1, into the stone of Brougham Bridge as he paused on it. On the following day, Hamilton wrote a letter to his friend and fellow mathematician, John T. Related:  .caisson.caisson

PicoVico. Creer des videos a partir de vos photos PicoVico est un outil multimédia en ligne qui permet de créer une magnifique vidéo à partir d’une série de photos. PicoVico est particulièrement facile à utiliser et permet aux enseignants comme aux élèves de réaliser des vidéos mixant textes et vidéos en quelques minutes. Le résultat particulièrement réussi mettra en valeur simplement le travail réalisé. Une fois inscrit sur le service, vous allez pouvoir commencer à créer votre première vidéo.Il suffit pour cela de lui donner un titre. L’étape suivante est d’uploader les images. C’est pratiquement terminé. Dans la classe. On aime la simplicité d’utilisation de PicoVico qui permet de le mettre à disposition des élèves même jeunes tant la prise en main est intuitive même si le site est anglais. PicoVico est entièrement en ligne et fonctionne sur tous les navigateurs modernes. Lien : PicoVico Sur le même thème

Convex regular polychoron The tesseract is one of 6 convex regular polychora In mathematics, a convex regular polychoron is a polychoron (4-polytope) that is both regular and convex. These are the four-dimensional analogs of the Platonic solids (in three dimensions) and the regular polygons (in two dimensions). These polychora were first described by the Swiss mathematician Ludwig Schläfli in the mid-19th century. Schläfli discovered that there are precisely six such figures. Properties[edit] Since the boundaries of each of these figures is topologically equivalent to a 3-sphere, whose Euler characteristic is zero, we have the 4-dimensional analog of Euler's polyhedral formula: where Nk denotes the number of k-faces in the polytope (a vertex is a 0-face, an edge is a 1-face, etc.). Visualizations[edit] The following table shows some 2-dimensional projections of these polychora. See also[edit] References[edit] External links[edit]

Researchers make magnetic graphene -- ScienceDaily Graphene, a one-atom thick sheet of carbon atoms arranged in a hexagonal lattice, has many desirable properties. Magnetism alas is not one of them. Magnetism can be induced in graphene by doping it with magnetic impurities, but this doping tends to disrupt graphene's electronic properties. Now a team of physicists at the University of California, Riverside has found an ingenious way to induce magnetism in graphene while also preserving graphene's electronic properties. They have accomplished this by bringing a graphene sheet very close to a magnetic insulator -- an electrical insulator with magnetic properties. "This is the first time that graphene has been made magnetic this way," said Jing Shi, a professor of physics and astronomy, whose lab led the research. The finding has the potential to increase graphene's use in computers, as in computer chips that use electronic spin to store data. Study results appeared online earlier this month in Physical Review Letters.

Spacetime In non-relativistic classical mechanics, the use of Euclidean space instead of spacetime is appropriate, as time is treated as universal and constant, being independent of the state of motion of an observer.[disambiguation needed] In relativistic contexts, time cannot be separated from the three dimensions of space, because the observed rate at which time passes for an object depends on the object's velocity relative to the observer and also on the strength of gravitational fields, which can slow the passage of time for an object as seen by an observer outside the field. Until the beginning of the 20th century, time was believed to be independent of motion, progressing at a fixed rate in all reference frames; however, later experiments revealed that time slows at higher speeds of the reference frame relative to another reference frame. Such slowing, called time dilation, is explained in special relativity theory. Spacetime in literature[edit] Mathematical concept[edit] is that

Panopticism Keynote address for "Earth to Avatars"26 October 1996 Mark Part One: A Brief History of the Virtual Word What is interesting is that we’ve never envisioned cyberspace as anything but a social space. Gibson’s Matrix was filled with users - legal and illegal - AI’s and, when it changed, the Loa of Voudon. Gibson dreams his tech but Stephenson has it down cold; so everything in the Matrix is perfect, while The Street, populated with barbies and low-rez avatars gave us a real direction, a real vision. The success of The Palace and Alphaworld - which must be admitted as immature technologies - proves the existence of a powerful drive to connect. Because connection is the only thing in that space is real, the only thing that persists after the servers go down and the networks jam up. An avatar, then, serves one purpose above all - as a vehicle of communication. Part Two: Self in Cyberspace What does this digital incarnation of the self communicate? Cyberspace: First Steps.

4-manifold In mathematics, 4-manifold is a 4-dimensional topological manifold. A smooth 4-manifold is a 4-manifold with a smooth structure. In dimension four, in marked contrast with lower dimensions, topological and smooth manifolds are quite different. There exist some topological 4-manifolds which admit no smooth structure and even if there exists a smooth structure it need not be unique (i.e. there are smooth 4-manifolds which are homeomorphic but not diffeomorphic). 4-manifolds are of importance in physics because, in General Relativity, spacetime is modeled as a pseudo-Riemannian 4-manifold. Topological 4-manifolds[edit] Examples: Freedman's classification can be extended to some cases when the fundamental group is not too complicated; for example, when it is Z there is a classification similar to the one above using Hermitian forms over the group ring of Z. For any finitely presented group it is easy to construct a (smooth) compact 4-manifold with it as its fundamental group. See also[edit]

Réalité augmentée au British Museum - ARC/blog « le Centre a su se montrer innovant en mobilisant le meilleur des technologies numériques dans le cadre de ses ateliers à destination du jeune pubic. Nous avons d’ores et déjà fait appel aux codes QR, à la capture de mouvement, à l’animation, à la modélisation en 3D, aux interfaces de mouvement avec Kinect et des sites Web mobiles. » Il y a dix-huit mois, l’équipe des programmes d’apprentissage numérique du British Museum a pris un nouveau cap stratégique. Objectif : explorer le champ des possibilités offertes par la réalité augmentée. Nous avions pleinement conscience de la popularité grandissante des techniques de réalité augmentée dans un certain nombre d’activités de type commercial ; il s’agissait pour nous de comprendre quels bénéfices pouvait présenter cette option technologique pour les visiteurs des musées. Après deux autres coups d’essai à petite échelle, nous avons entrepris un projet plus ambitieux, en partenariat avec quatre lycées londoniens. Shelley Mannion

Four-dimensional space In modern physics, space and time are unified in a four-dimensional Minkowski continuum called spacetime, whose metric treats the time dimension differently from the three spatial dimensions (see below for the definition of the Minkowski metric/pairing). Spacetime is not a Euclidean space. History[edit] An arithmetic of four dimensions called quaternions was defined by William Rowan Hamilton in 1843. This associative algebra was the source of the science of vector analysis in three dimensions as recounted in A History of Vector Analysis. Soon after tessarines and coquaternions were introduced as other four-dimensional algebras over R. One of the first major expositors of the fourth dimension was Charles Howard Hinton, starting in 1880 with his essay What is the Fourth Dimension? Little, if anything, is gained by representing the fourth Euclidean dimension as time. Vectors[edit] This can be written in terms of the four standard basis vectors (e1, e2, e3, e4), given by Geometry[edit]

StereoPhoto Maker (French) English , German , Japanese StereoPhoto Maker (SPM) est un éditeur d'images stéréo très souple et performant mais aussi un outil pour visionner les images stéréo. Il permet aussi aux utilisateurs ayant quelques notions de HTML de créer des pages Web utilisant la 'StereoPhotoViewer Applet'. Téléchargement :StereoPhoto Maker Ver5.06 1310 Ko 30/Sep/2014StereoPhoto Maker 64bit Ver5.06 1974 Ko 30/Sep/2014 Ver. 4.43->4.50See here Ver. 4.41->4.43See here English Online Help Great thanks to Pierre MEINDRE for the French-language documentation. Exemples :Exemples d'images stéréo 1Exemples d'images stéréo 2Exemple d'anaglyphe en jaillissement La plupart des modes de visualisation stéréoscopiques sont supportés ainsi qu'un mode monoscopique : Winx3D n'est plus disponible sur le site web original. Alternativement, le logiciel RivaTuner peut être utilisé pour "patcher" une carte nVidia GeForce en "Quadro" rendant ainsi disponibles le mode stéréo OpenGL et les autres fonctionnalités "professionnelles".

The Brane multiverse String theory landscape The string theory landscape refers to the huge number of possible false vacua in string theory.[1] The large number of theoretically allowed configurations has prompted suggestions that certain physical mysteries, particularly relating to the fine-tuning of constants like the cosmological constant or the Higgs boson mass, may be explained not by a physical mechanism but by assuming that many different vacua are physically realized.[2] The anthropic landscape thus refers to the collection of those portions of the landscape that are suitable for supporting intelligent life, an application of the anthropic principle that selects a subset of the otherwise possible configurations. Anthropic principle[edit] Bayesian probability[edit] Some physicists, starting with Weinberg, have proposed that Bayesian probability can be used to compute probability distributions for fundamental physical parameters, where the probability of observing some fundamental parameters is given by, where and . Criticism[edit]