Epicycles de Ptolémée Epicycles de Ptolémée Pour les grecs depuis Aristote (−385, −322) la Terre était le centre du Monde. Seul Aristarque de Samos (−310, −230) avait envisagé un système héliocentrique. La Terre est le centre du Monde et seuls sont possibles les mouvements rectilignes et circulaires uniformes étaient deux dogmes. Mais ces dogmes posaient aux observateurs du ciel un problème majeur : Comment expliquer les boucles des planètes ? Utilisation : La partie gauche du schéma représente dans le système héliocentrique le mouvement de la Terre (en bleu) et d'une planète hypothétique (en jaune) qui mettrait exactement trois années terrestre pour parcourir son orbite. Le slider rouge permet de modifier le rapport des vitesses de rotation entre l'épicycle et le déférent. Le slider vert permet de modifier le rayon de l'épicycle. Le bouton [Départ] permet de lancer l'animation la pause et la reprise de l'animation..
Pascal - 17th Century Mathematics - The Story of Mathematics The Frenchman Blaise Pascal was a prominent 17th Century scientist, philosopher and mathematician. Like so many great mathematicians, he was a child prodigy and pursued many different avenues of intellectual endeavour throughout his life. Much of his early work was in the area of natural and applied sciences, and he has a physical law named after him (that “pressure exerted anywhere in a confined liquid is transmitted equally and undiminished in all directions throughout the liquid”), as well as the international unit for the meaurement of pressure. But Pascal was also a mathematician of the first order. He is best known, however, for Pascal’s Triangle, a convenient tabular presentation of binomial co-efficients, where each number is the sum of the two numbers directly above it. Pascal was far from the first to study this triangle. Pascal also made the conceptual leap to use the Triangle to help solve problems in probability theory.
The Spooky Nature of Electromagnetic Radiation Our story begins a little over one hundred years ago in Bern, Switzerland, where a young man employed as a patent clerk went off to work. He took the electric trolley in each day, and each day he would pass an unassuming clock tower. But today was different, it was special. For today he would pose to himself a question – a question whose answer would set forth a fascinating dilemma. The hands of the clock appeared to move the same no matter if his trolley was stopped or was speeding away from the clock tower. He knew that the electromagnetic radiation which enabled him to see the clock traveled at a finite speed. There was no way for him to know that it would take three years to answer this question. Now it might have taken Einstein a few years to develop the answer we now know as the Special Theory of Relativity, but it most certainly took him no longer than a few days to realize that Issac Newton… must be wrong. T = 2h/c c²t² = v²t² + w² then, t²(c² – v²) = w² t²(1 – v²/c²) = w²/c²
La beauté de la multiplication Question : faut-il être fou pour parler d'arithmétique modulaire à un collégien ?Réponse : non ! On l'utilise même tous les jours en regardant l'heure... L'idée de base de l'arithmétique modulaire est de travailler non sur les nombres eux-mêmes, mais sur les restes de leur division par quelque chose.Par exemple, s’il est 16h52 et que j’attends 15 minutes, il sera 17h07, autrement dit 52+15=7 dans l’arithmétique (des minutes) de l’horloge. Ce que nous en écrivons, en mathématiques : 52 + 15 ≡ 7 (mod. 60) et que nous lisons : « 52 plus 15 est congru à 7 modulo 60 ». Pourquoi congru ? Pour lire la sublime biographie de Gauss, c'est dans un autre article : cliquer ici. Vous comprenez maintenant, je l’espère, les congruences suivantes : 5 ≡ 2 (mod. 3) ; 1985 ≡ 5 (mod. 10) ; 20 ≡ 8 (mod. 12). L’arithmétique modulaire est enseignée en Terminale Scientifique, pour ceux qui choisissent la spécialité mathématiques.Autant dire à des années de ce que pourrait comprendre un élève de collège…
Top 10 Secrets of Pascal’s Triangle – Math Memoirs The beauty of Pascal’s Triangle is that it’s so simple, yet so mathematically rich. It’s one of those novelties in math that highlight just how extraordinary this logical system we’ve devised truly is. So let’s do this! Top 10 things you probably didn’t know were hiding in Pascal’s Triangle!! But First…How to Build Pascal’s Triangle At the top center of your paper write the number “1.”On the next row write two 1’s, forming a triangle.On each subsequent row start and end with 1’s and compute each interior term by summing the two numbers above it. Secret #1: Hidden Sequences Note: I’ve left-justified the triangle to help us see these hidden sequences. The first two columns aren’t too interesting, they’re just the ones and the natural numbers. The next column is the triangular numbers. Similarly the fourth column is the tetrahedral numbers, or triangular pyramidal numbers. Secret #2: Powers of Two If we sum each row, we obtain powers of base 2, beginning with 2⁰=1. Secret #3: Powers of Eleven
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Pascal's Triangle A really interesting Number Patterns is Pascal's Triangle (named after Blaise Pascal, a famous French Mathematician and Philosopher). To build the triangle, start with "1" at the top, then continue placing numbers below it in a triangular pattern. Each number is the numbers directly above it added together. (Here I have highlighted that 1+3 = 4) Patterns Within the Triangle Diagonals The first diagonal is, of course, just "1"s The next diagonal has the Counting Numbers (1,2,3, etc). The third diagonal has the triangular numbers (The fourth diagonal, not highlighted, has the tetrahedral numbers.) Symmetrical The triangle is also symmetrical. Horizontal Sums What do you notice about the horizontal sums? Is there a pattern? They double each time (powers of 2). (Why? Exponents of 11 Each line is also the powers (exponents) of 11: 110=1 (the first line is just a "1") 111=11 (the second line is "1" and "1") 112=121 (the third line is "1", "2", "1") etc! But what happens with 115 ? Squares Examples: Paths
The International Date Line, Explained Dan Heim taught physics and mathematics for 30 years — more if you count his grade-school science club. Since 1999, he's been a freelance writer and creates educational computer graphics and animations. Dan is President of the Desert Foothills Astronomy Club in New River, Ariz. His weekly blog Sky Lights covers topics including astronomy, meteorology, and earth science, and questions from readers are encouraged. We all heard about the International Date Line (IDL) in geography class — it was this special line on the globe where the day and date change. That's probably why I keep getting questions like these on my blog: What is the IDL, why do we need it, and who invented it? Frequent international travelers are comfortable with the IDL. So here's a definitive explanation of the IDL. There are no equations, but you might encounter a few new terms. Before there were clocks Back in the days before mechanical clocks, time was measured mostly using sundials. Latitude and longitude Time zones
Stock footage of Newsreel story: In Selma, Alabama, General James W Moore, of the Confederate Army dies at 99. DVArchive Clip ID 000-5383. Royalty free stock footage, video, and movie clips - 000-5383.jpg About Public Domain Clip Prices Some commercial libraries charge license fees for clips in the Public Domain. DVArchive believes it is more in keeping with the spirit and intent of PD to offer these clips for free to the public with only a modest handling fee to cover our expenses in preparing, resizing, transferring or improving the clips for download and making them available to you. Our handling fees are as follows: $35 for clips under 30 seconds $45 for clips from :30 to 1:00 $55 for clips 1-2 minutes $65 for clips over 2 minutes About the Public Domain Copyright DVarchive has taken reasonable steps to verify the copyright status of this work or clip and has determined that it is most likely in the public domain, and can be freely used and re-used in projects at your discretion. Any Trademarks used in this item listing are used for strictly descriptive purposes only.
Free books: 100 legal sites to download literature | Just English The Classics Browse works by Mark Twain, Joseph Conrad and other famous authors here. Classic Bookshelf: This site has put classic novels online, from Charles Dickens to Charlotte Bronte.The Online Books Page: The University of Pennsylvania hosts this book search and database.Project Gutenberg: This famous site has over 27,000 free books online.Page by Page Books: Find books by Sir Arthur Conan Doyle and H.G. Wells, as well as speeches from George W. Textbooks If you don’t absolutely need to pay for your textbooks, save yourself a few hundred dollars by reviewing these sites. Math and Science Turn to this list to find books about math, science, engineering and technology. Children’s Books Even children’s books are now available online. Philosophy and Religion For books about philosophy and religion, check out these websites. Plays From Shakespeare to George Bernard Shaw to more contemporary playwrights, visit these sites. Modern Fiction, Fantasy and Romance Foreign Language History and Culture
instaGrok | A new way to learn roots Typesetting math: 8% John Baez December 15, 2011 Around 2006, my friend Dan Christensen created a fascinating picture of all the roots of all polynomials of degree ≤ 5 with integer coefficients ranging from -4 to 4: Click on the picture for bigger view. You can see lots of fascinating patterns here, like how the roots of polynomials with integer coefficients tend to avoid integers and roots of unity - except when they land right on these points! Now you see beautiful feathers surrounding the blank area around the point 1 on the real axis, a hexagonal star around \exp(i \pi/ 3), a strange red curve from this point to 1, smaller stars around other points, and more.... People should study this sort of thing! Inspired by the pictures above, Sam Derbyshire decided to to make a high resolution plot of some roots of polynomials. The coloring shows the density of roots, from black to dark red to yellow to white. Here's a closeup of the hole at 1: Note the white line along the real axis. For example:
Top 6 Open Source Back-to-School Apps: A SourceForge Downloader’s Guide | SourceForge Community Blog The Hardest Thing To Find In The Universe? : Krulwich Wonders... What is rarer than a shooting star? Rarer than a diamond? Rarer than any metal, any mineral, so rare that if you scan the entire earth, all six million billion billion kilos or 13,000,000,000,000,000,000,000,000 pounds of our planet, you would find only one ounce of it? What is so rare it has never been seen directly, because if you could get enough of it together, it would self-vaporize from its own radioactive heat? What is this stuff that can't be seen or found? iStockphoto.com "At" stands for astatine. The problem is, there's something about 85 protons in a tight space that nature doesn't enjoy. This element has a half life of roughly 8 hours, meaning if you could get a clump of it to stay on a table (you can't), half of it would disintegrate in 8 hours, and then every 8 hours another half would go until in a few days, there'd be no astatine on the table. By comparison, a clump of bismuth (atomic number 83) loses half its atoms in 20 billion billion years. How Do You Know It's There?