Strang's Strange Figures Strang's strange figures are the figures produced by plotting a periodic function as a function of an integer argument for , 2, .... Unexpected patterns and periodicities result from near-commensurabilities of certain rational numbers with the period (Richert 1992). Strang figures are shown above for a number of common functions. Chiliogone Un article de Wikipédia, l'encyclopédie libre. Un chiliogone régulier. Un chiliogone [kilijɔgɔn] ou chiliagone ou chiligone (du grec χίλιοι (khílioi) : « mille » et γωνία (gônía) : « angle ») est un polygone à 1 000 côtés possédant 498 500 diagonales. Caractéristiques d'un chiliogone régulier[modifier | modifier le code] Si est la longueur d'une arête. Périmètre[modifier | modifier le code] Apothème[modifier | modifier le code] Rayon[modifier | modifier le code] Valeurs remarquables d'un chiliogone régulier[modifier | modifier le code] Pour les angles au centre[modifier | modifier le code] Pour les angles internes[modifier | modifier le code] Angle interne : 179,64°Somme des angles internes : 179 640° Pour les angles externes[modifier | modifier le code] Angle externe : 180,36°Somme des angles externes : 180 360° Symbolique[modifier | modifier le code] Ce terme est utilisé à plusieurs reprises par René Descartes dans ses méditations métaphysiques (Méditation Sixième).
Ulam spiral Do you see any pattern in this graph? You will not believe at first glance that it is generated using prime numbers. In order to generate it, the numbers are arranged in a spiral, as follows: Then the prime numbers are marked. Note the abundance of diagonals. In the applet above you can see the spiral made up to 1014. Move the graph by clicking in the arrows or using the arrow keys. You can also see the position (x, y) in the spiral and the number n of any point of the graph by moving the cursor to that point. Move the center by typing a new number (up to 14 digits) in the left input box and press the return key. Change the starting number in the center of the spiral by typing a new number (up to 14 digits) in the right input box and press the return key. The formula that gives the numbers in the diagonal lines can be expressed using quadratic polynomials. When the quadratic polynomial cannot be factorized, then its diagonal will contain primes.
The Collection of Computer Science Bibliographies About the Collection This is a collection of bibliographies of scientific literature in computer science from various sources, covering most aspects of computer science. The bibliographies are updated weekly from their original locations such that you'll always find the most recent versions here. The collection currently contains more than 3 millions of references (mostly to journal articles, conference papers and technical reports), clustered in about 1500 bibliographies, and consists of more than 2.3 GBytes (530MB gzipped) of BibTeX entries. More than 600 000 references contain crossreferences to citing or cited publications. More than 1 million of references contain URLs to an online version of the paper. For more information on the contents of this collection have a look at the bibliographic statistics. Search for publications in the bibliography collection Since the bibliographies are not just referenced by links, but actually mirrored and present as a local copy, they are searchable.
Justin Mullins JavaView Homepage Sound Braid (inspired by Vi Hart) Primal Chaos The image shows a random multiple of 6 at "6k". In order to have twin primes we cannot have any circle intersecting adjacently to 6k (obviously). Let's see how this happens: Please note that the reason I'm only using prime numbers for this is because we only need prime numbers. -Multiples of 3 can only fall on 6k. -Multiples of 5 can fall on 6k, 6k-2, 6k-3. -Multiples of 7 can fall on 6k, 6k-2, 6k-3, 6k-4, 6k-5. -Similarly Multiples of 11 can fall on 6k, 6k-2, 6k-3, 6k-4, 6k-5, 6k-6, 6k-7, 6k-8, 6k-9. Let's put this in a chart of sorts. Chladni Theory Page To understand the modal patterns of the circular and rectangular plates, we must first investigate the solutions to wave equation in two dimensions: Solution for Rectangular Plates: By assuming a product solution u(x,y,t) = X(x)Y(y)T(t), we separate variables and obtain three distinct equations: where Thus These are equations for a simple harmonic oscillator. Note: We can also write the real part of the equation as: This equation essentially describes two wavefronts. So, There will be (n-1) nodes running in the y-direction and (m-1) running in the x-direction. From the relationship , we see that the modal frequencies will be Notice that the modal frequencies are not integral multiples of each other, as is the case with a vibrating string. If we graph on a log-log scale the modal frequencies w versus we should get a straight line of slope 1/2. Theory for Circular Plates: For the circular plate, the wave equation in polar coordinates solves out to be: Here is So, Notice that for values of n*theta; =
Mathematics breathes new life into Escher’s art Posted by Anonymous on June 23, 2011 M. C. Escher, who died in 1972, is famous for using mathematical ideas in his art, drawing on concepts from symmetry and hyperbolic geometry to create complex tessellated images. Now an artist is continuing his work using mathematics that Escher never had the chance to explore. Like this: Like Loading...
C’est quoi un chakra ? | Pour Un Monde Meilleur... Un chakra, c’est quoi ? Vous avez tous, un jour ou l’autre, entendu parler des chakras. Beaucoup de personnes associent ce terme à la « zénitude » ou à la méditation. On entend souvent ce mot en soin énergétique lorsqu’il s’agit de rééquilibrer ses corps subtils. Dans la culture indienne, le mot chakra vient du sanskrit qui veut dire « roue ». C’est un cercle qui désigne le disque solaire, attribut du dieu hindouiste Vishnu, que l’on surnomme « l’Agissant ». Le sanskrit est la langue mère des peuples de l’Inde, qui fut utilisée pour rédiger les plus anciens textes de leur littérature (le sanskrit est un peu ce qu’est le latin à la langue française). Selon cet ancien système de médecine, il y a sept chakras dans le corps qui commencent au bas de la colonne vertébrale pour aller jusqu’au dessus de la tête. Soumis aux aléas de santé de la personne, les chakras pourraient présenter des symptômes de rigidité ou d’affaissement, d’encombrement ou de perte de vitalité. Les chakras plus en détail…
Ulam's primes spiral _ wikipedia Ulam spiral of size 200×200. Black dots represent prime numbers. Diagonal, vertical, and horizontal lines with a high density of prime numbers are clearly visible. The Ulam spiral, or prime spiral (in other languages also called the Ulam Cloth) is a simple method of visualizing the prime numbers that reveals the apparent tendency of certain quadratic polynomials to generate unusually large numbers of primes. It was discovered by the mathematician Stanislaw Ulam in 1963, while he was doodling during the presentation of a "long and very boring paper" at a scientific meeting. Shortly afterwards, in an early application of computer graphics, Ulam with collaborators Myron Stein and Mark Wells used MANIAC II at Los Alamos Scientific Laboratory to produce pictures of the spiral for numbers up to 65,000. In an addendum to the Scientific American column, Gardner mentions work of the herpetologist Laurence M. Construction[edit] All prime numbers, except for the number 2, are odd numbers.
The MPFR Library Sculpture - News January 30 A new multi-part, multi-material thing: And the pieces are like this: Like the Tetrabox piece last month, which went well and is now in stock, this one is held together with rare-earth magnets and improved with glow-in-the-dark glass. December 24 Thanks again for a great holiday season! And since I just realized I didn't announce it here, for completeness: Behold the Glow Cuttlefish Bottle Opener. December 10 This year's factory seconds sale is on. Update: Well, that lasted about two days. December 2 Why so serious? WhaleSnail In other news, I set up gift certificates through Paypal: December 2 Christmas Shipping When to order to be reasonably sure your package will arrive on time. Our last shipping day before Christmas is Monday the 23rd (cutoff at noon Eastern time!) Best wishes for a great holiday season! October 22 I made a sculpture that comes in four pieces and assembles to make sort of a box. I don't have stock of this yet – just my proof – but I've ordered parts for more. August 26