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Ulam spiral

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. In an addendum to the Scientific American column, Gardner mentions work of the herpetologist Laurence M. Construction[edit] Ulam constructed the spiral by writing down a regular rectangular grid of numbers, starting with 1 at the center, and spiraling out: He then circled all of the prime numbers and he got the following picture: To his surprise, the circled numbers tended to line up along diagonal lines. Variants[edit]

3 awesome free Math programs Posted by Antonio Cangiano in Software on June 2nd, 2007 | 109 responses Mathematical software can be very expensive. Programs like Mathematica, Maple and Matlab are incredibly powerful, flexible and usually well documented and supported. Their price tags however are a big let down for many people, even if there are cheap (in some cases crippled) versions available for educational purposes (if you are a student or a teacher). 1. A general purpose CAS (Computer Algebra System) is a program that’s able to perform symbolic manipulation for the resolution of common problems. Valuable mentions are: 2. Matlab is the standard for numerical computing, but there are a few clones and valid alternatives that are entirely free. Valid alternatives are: For statistical computing and analysis in the Open Source world, it doesn’t get any better than R. As usual, please feel free to share your experiences and add your suggestions to enrich the discussion.

Annals of Mathematics: Manifold Destiny On the evening of June 20th, several hundred physicists, including a Nobel laureate, assembled in an auditorium at the Friendship Hotel in Beijing for a lecture by the Chinese mathematician Shing-Tung Yau. In the late nineteen-seventies, when Yau was in his twenties, he had made a series of breakthroughs that helped launch the string-theory revolution in physics and earned him, in addition to a Fields Medal—the most coveted award in mathematics—a reputation in both disciplines as a thinker of unrivalled technical power. Yau had since become a professor of mathematics at Harvard and the director of mathematics institutes in Beijing and Hong Kong, dividing his time between the United States and China. His lecture at the Friendship Hotel was part of an international conference on string theory, which he had organized with the support of the Chinese government, in part to promote the country’s recent advances in theoretical physics. Grigory Perelman is indeed reclusive. E.

Spirale di Sacks Da Wikipedia, l'enciclopedia libera. La spirale di Sacks è una rappresentazione grafica della disposizione dei numeri primi in una spirale, disegnata per la prima volta da Robert Sacks nel 1994, su esempio della più ben nota spirale di Ulam. In particolare, Sacks disegnò la curva: Ponendo il numero zero al centro del grafico;Disponendo gli altri numeri interi positivi secondo la spirale di Archimede compiendo una rotazione completa per ogni numero che sia un quadrato perfetto.Evidenziando i numeri primi. La texture che appare, estremamente regolare e ripetitiva, è ancora misteriosa. , scoperto da Leonardo Eulero nel 1774. A 10 minute tutorial for solving Math problems with Maxima Posted by Antonio Cangiano in Essential Math, Software on June 4th, 2007 | 132 responses About 50,000 people read my article 3 awesome free Math programs. Chances are that at least some of them downloaded and installed Maxima. Maxima as a calculator You can use Maxima as a fast and reliable calculator whose precision is arbitrary within the limits of your PC’s hardware. (%i1) 9+7; (%o1) (%i2) -17*19; (%o2) (%i3) 10/2; (%o3) Maxima allows you to refer to the latest result through the % character, and to any previous input or output by its respective prompted %i (input) or %o (output). (%i4) % - 10; (%o4) (%i5) %o1 * 3; (%o5) For the sake of simplicity, from now on we will omit the numbered input and output prompts produced by Maxima’s console, and indicate the output with a => sign. float(1/3); => float(26/4); => As mentioned above, big numbers are not an issue: float((7/3)^35); => Constants and common functions Here is a list of common constants in Maxima, which you should be aware of: log(%e); =>

mimeTeX quickstart Announcement: If latex is installed on your server then see mathTeX , the successor to mimeTeX. It's based on real LaTeX and renders higher quality images than mimeTeX. If latex is not available on your server, continue using mimeTeX. Copyright © 2002-2011, John Forkosh Associates, Inc. email: john@forkosh.com —— Important Notice —— This page contains more information than you'll probably need to read. " Computers are like Old Testament gods : lots of rules and no mercy –– Joseph Campbell, The Power of Myth (Doubleday 1988, page 18) (a) Introduction "Where are we going? MimeTeX, licensed under the gpl , lets you easily embed LaTeX math in your html pages. \normalsize f(x)=\int\limits_{-\infty}^xe^{-t^2}dt wherever you put that tag. "Foxes have holes and birds have nests, but the Son of man hath not where to lay his head." –– Jesus Christ, Sermon on the Mount (Matthew 8:20) There's no inherent need to repeatedly write the cumbersome tag illustrated above. image illustrated above ', "\n"; } ?

Spirale di Ulam Da Wikipedia, l'enciclopedia libera. Dopo segnò tutti i numeri primi ed ottenne: Spirale di Ulam di dimensioni 200 x 200 Sorpreso, notò che i numeri primi tendevano ad allinearsi lungo le diagonali, come si può chiaramente vedere dall'immagine qui a destra, dove è rappresentata una spirale di 200 x 200, i numeri primi segnati in nero. Il fatto interessante non è la presenza in sé dei numeri primi lungo le diagonali: infatti, è noto che tutti i numeri primi eccetto il due sono dispari. Dato che nella spirale di Ulam le diagonali sono alternativamente composte da numeri pari e da dispari, è normale che i numeri primi giacciano solo su una diagonale si ed una no. Test più rigorosi dimostrarono che effettivamente su alcune diagonali la concentrazione di numeri primi è maggiore rispetto ad altre. Questo implica che esistano molte costanti e genera, sostituendo con una serie di numeri consecutivi, una grande quantità di numeri primi. Ad esempio, nel XVIII secolo Eulero osservò che con E sostituendo a

Introduction Many of the articles on this Web site are versions of the Fermi Problem described in the first section. Others are essays - some short, some long. Some are merely attempts to come to terms with basic concepts, such as the 'size' of the speed of light or the number 'one trillion'. Others discuss more advanced concepts. The energy density article was written to fill a gap, which I noted in books on Special Relativity. The earlier pieces are nowhere near so involved, and require only a little number skill and, possibly, some high school algebra. There are many cases in science, and even in everyday life, when we encounter seemingly insolvable problems such as this. And most of all, remember to have fun!

Annals of Mathematics: Manifold Destiny On the evening of June 20th, several hundred physicists, including a Nobel laureate, assembled in an auditorium at the Friendship Hotel in Beijing for a lecture by the Chinese mathematician Shing-Tung Yau. In the late nineteen-seventies, when Yau was in his twenties, he had made a series of breakthroughs that helped launch the string-theory revolution in physics and earned him, in addition to a Fields Medal—the most coveted award in mathematics—a reputation in both disciplines as a thinker of unrivalled technical power. Yau had since become a professor of mathematics at Harvard and the director of mathematics institutes in Beijing and Hong Kong, dividing his time between the United States and China. His lecture at the Friendship Hotel was part of an international conference on string theory, which he had organized with the support of the Chinese government, in part to promote the country’s recent advances in theoretical physics. Grigory Perelman is indeed reclusive.

Spirală Ulam Spirala Ulam. Punctele negre reprezintă numerele prime. Spirala Ulam sau spirala numerelor prime este o metodă simplă de vizualizare a numerelor prime. A fost descoperită de matematicianul Stanislaw Ulam în anul 1963 și sugerează o ordonare în mulțimea haotică a numerelor prime. Simpla tabelare a mulțimii numerelor naturale cu evidențierea numerelor prime prezintă, de regulă, o distribuție haotică, apărând coloane întregi lipsite de numere prime. Exemplificativă poate fi tabelarea pe 2 coloane în care se separă numerele pare de cele impare. În vizualizarea prezentată în figura alăturată, numerele prime par ordonate fiind ușor de observat coloane înclinate la cca. 45 grade. O observație elementară arată că un tabel cu 2 coloane separă numerele naturale pare de cele impare. Similar, vizualizarea numerelor prime într-un tabel cu W coloane, unde W este produsul primelor numere prime, are aspectul principial al spiralei Ulam, dar mult mai evident, deoarece coloanele sunt verticale.

Handy Mathematics Facts for Graphics email scd@cs.brown.edu with suggested additions or corrections Eric Weisstein's world of Mathematics (which used to be called Eric's Treasure Trove of Mathematics) is an extremely comprehensive collection of math facts and definitions. Eric has other encyclopedias at www.treasure-troves.com S.O.S. Mathematics has a variety of algebra, trigonometry, calculus, and differential equations tutorial pages. Dave Eberly has a web site called Magic Software with several pages of descriptions and code that answers questions from comp.graphics.algorithms. Steve Hollasch at Microsoft has a very comprehensive page of graphics notes which he would like to turn into a graphics encyclopedia. Vector math identities and algorithms from Japan. Paul Bourke has a variety of pages with useful tidbits, many of which are linked to from Steve Hollasch's page. The graphics group at UC Davis also has notes about computer graphics. Peter H. Josh Levenberg has a page of links to yet more graphics algorithm resources. e pi

LatexRender & TeX Converter TEX Converter is for 32 bit Windows 95/98/Me/NT/2000/XP Programs that you'll need MiKTEX TeX4ht Useful book The Latex Web Companion by Michael Goosens and Sebastian Rahtz Amazon USA Amazon UK Internet Bookshop TEX Converter is freeware written by Steve Mayer © Steve Mayer 1999 LatexRender for PHP Steve's Maths Pages Introduction TEX Converter is a Windows front-end to a number of programs that convert TEX or LATEX files to another format: HEVEA converts LATEX files to HTML without using graphics TTH converts (LA)TEX files to HTML without using graphics TeX4ht converts (LA)TEX files to HTML using GIFs, PNGs or JPEGs LATEX2HTML converts LATEX files to HTML using GIFs or PNGs TeXify is part of MiKTEX and converts (LA)TEX files to DVI and PDF LATEX and pdfLATEX are part of MiKTEX and convert LATEX files to DVI and PDF respectively All these programs run in DOS and require complicated command lines. It is not necessary to install all these programs. Screen Previews Download Thanks to Philip A.

Ulam Spiral Visualization - The Pattern of Prime Numbers Quantum Random Bit Generator Service

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