Mu-Ency -- The Encyclopedia of the Mandelbrot Set at MROB A second-order embedded Julia set This is a picture from the Mandelbrot Set, one of the most well-known fractal images in the world. (Click it for a larger version). The Mandelbrot Set is one of my hobbies, and I have collected a large amount of information about it. Here are some entries from Mu-Ency: Mandelbrot Set: The mathematical definition. More Pictures: Some entries with pictures of parts of the Mandelbrot Set are: R2, Cusp, Embedded Julia set, 2-fold Embedded Julia set, 4-fold Embedded Julia set, Paramecia, R2.C(0), R2.C(1/3), R2.1/2.C(1/2), R2t series, Seahorse Valley, Delta Hausdorff Dimension, Exponential Map, Reverse Bifurcation. You can also look up specific terms in the index. Coordinates of the image above: Center: -1.769 110 375 463 767 385 + 0.009 020 388 228 023 440 i Width (and height): 0.000 000 000 000 000 160 Algorithm: distance estimator Iterations: 10000
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]
Calculating the Distance to the Horizon For Any Game Home Up Site Map Assumptions | Method 1 | Method 2 Method 1 | Method 2 This is all based on the assumption that the horizon is the point on the world's surface at which the line of sight of the viewer, whatever their height, becomes parallel (tangential) to the surface of the world, and meets the surface of the world (so that the viewer cannot see any further than it). Note that I do not mention units in any of the equations on this page. Assumptions | Method 2 For a right-angled triangle: Where: R is the longest side (the hypotenuse), x and y are the other two sides. Using this equation on the triangle in the figure above, the longest side is the radius of the planet plus the height of the observer (r + h) , and the other two sides are d and r . Or, re-arranged: Or: So the total distance to the horizon is given by: This equation will work for any size world, and any height of observer. Assumptions | Method 1 Back to My Roleplaying Page .
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
Book Recommendations - EFnetMath These are semi-official #math book recommendations for various topics. These are all personal recommendations of channel regulars. This means that given the collective experience of the channel, these are the books to read. We made an arbitrary split between the mathematics before and after calculus. General Interest These books are intended for a general audience. history/philosophy of math, 'how to solve it' The History of Calculus and Its Conceptual Development ( by Boyer A History of Mathematics ( by Boyer A Mathematician's Apology ( by Hardy Pre-College Mathematics This category is the catch-all for topics generally preceding calculus. Schaum's outlines -- I used various ones for college-level math and they were useful, and the calculus one below is well-recommended. Algebra Field and Galois Theory ( by Morandi
Panopticism Keynote address for "Earth to Avatars"26 October 1996 Mark Pescempesce@netcom.com 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]
prime numbers 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