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Nature by numbers. The theory behind this movie

Nature by numbers. The theory behind this movie
We can find interactive sites on the internet (like this) to draw points, move them, and check how the structure becomes updated in real time. In fact, if we have a series of random dots scattered in the plane, the best way of finding the correct Voronoi Telesación for this set is using the Delaunay triangulation. And in fact, this is precisely the idea shown on the animation: first the Delaunay Triangulation and then, subsequently, the Voronoi Tessellation. But to draw a correct Delaunay Triangulation is necessary to meet the so-called “Delaunay Condition”. This means that: a network of triangles could be considered Delaunay Triangulation if all circumcircles of all triangles of the network are “empty”. Notice that actually, given a certain number of points in the plane there is no single way to draw triangles, there are many. You see that in the graph below, extracted from Wikipedia: Podéis verlo en la siguiente gráfica, extraída de la Wikipedia:

Nerd Paradise : Divisibility Rules for Arbitrary Divisors It's rather obvious when a number is divisible by 2 or 5, and some of you probably know how to tell if a number is divisible by 3, but it is possible to figure out the division 'rule' for any number. Here are the rules for 2 through 11... The last digit is divisible by 2. The sum of all the digits in the number is divisible by 3. The last 2 digits are divisible by 4. Einstein to Weinstein: the lone genius is an exception to the rule (ScienceAlert) Albert Einstein was considered to be a ‘lone genius’ – but this was not the case, and it’s certainly not the norm, writes Katherine J Mack. Image: Catwalker/Shutterstock Developing a Theory of Everything is physics' Holy Grail. So could it have been completed in recent weeks? And by an outsider, working alone?

The Mathematics of Reddit Rankings, or, How Upvotes Are Time Travel – Built on Facts Ok, so this isn’t really physics as such, but it’s pretty fascinating. There’s a very large online community called Reddit in which users submit links which interest them. These links come with two little arrows beside them, and the users can vote the link up or down. Here’s a screenshot of how the website looks to me at the time of this writing:

The Thirty Greatest Mathematicians Click for a discussion of certain omissions. Please send me e-mail if you believe there's a major flaw in my rankings (or an error in any of the biographies). Obviously the relative ranks of, say Fibonacci and Ramanujan, will never satisfy everyone since the reasons for their "greatness" are different. I'm sure I've overlooked great mathematicians who obviously belong on this list. Long-Term Science: When Research Outlives The Researcher hide captionWilliam Beal, standing at center, started a long-term study on seed germination in 1879. He buried 20 bottles with seeds in them for later researchers to unearth and plant. Michigan State University

Common Errors in College Math I have several web pages intended for students; this seems to be the most popular one. FONTS FINALLY REPAIRED November 2009. Browser adjustments: This web page uses subscripts, superscripts, and unicode symbols. The latter may display incorrectly on your computer if you are using an old browser and/or an old operating system. Note to teachers (and anyone else who is interested): Feel free to link to this page (around 500 people have done so), tell your students about this page, or copy (with appropriate citation) parts or all of this page. You can do those things without writing to me.

Wonders of Math - The Game of Life What is the Game of Life? by Paul Callahan Rules of the Game of Life Life is played on a grid of square cells--like a chess board but extending infinitely in every direction. A cell can be live or dead. A live cell is shown by putting a marker on its square. A dead cell is shown by leaving the square empty. Policy: Twenty tips for interpreting scientific claims Science and policy have collided on contentious issues such as bee declines, nuclear power and the role of badgers in bovine tuberculosis. Calls for the closer integration of science in political decision-making have been commonplace for decades. However, there are serious problems in the application of science to policy — from energy to health and environment to education. One suggestion to improve matters is to encourage more scientists to get involved in politics. Although laudable, it is unrealistic to expect substantially increased political involvement from scientists. Another proposal is to expand the role of chief scientific advisers1, increasing their number, availability and participation in political processes.

Happy e Day. What is e? Pi gets all the attention but really, e is just as cool. I will tell you why. Write down the letter π and show it to someone. Just about everyone would recognize this at the super awesome irrational number that represents the ratio of the circumference to diameter for a circle. In terms of irrational numbers, π is famous. Now write down “e” and ask people what it is. 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. Roots of quadratic polynomials are in grey; roots of cubics are in cyan; roots of quartics are in red and roots of quintics are in black.

Thomas Kuhn: the man who changed the way the world looked at science Fifty years ago this month, one of the most influential books of the 20th century was published by the University of Chicago Press. Many if not most lay people have probably never heard of its author, Thomas Kuhn, or of his book, The Structure of Scientific Revolutions, but their thinking has almost certainly been influenced by his ideas. The litmus test is whether you've ever heard or used the term "paradigm shift", which is probably the most used – and abused – term in contemporary discussions of organisational change and intellectual progress.

Chapter 5 : Repeating Decimals 1/81 = 0.012345679 ... (from 0 to 7 (one letter), last is 9. length=9) 1/891 = 0.001122334455667789 ... (from 00 to 77 (two letters), last is 89. length=18) 1/8991 = 0.000111222333444555666777889 ... (from 000 to 777 (three letters), last is 889. length=27) 1/89991 = 0.000011112222333344445555666677778889 ...

The Socratic Method The Socratic Method:Teaching by Asking Instead of by Tellingby Rick Garlikov The following is a transcript of a teaching experiment, using the Socratic method, with a regular third grade class in a suburban elementary school. I present my perspective and views on the session, and on the Socratic method as a teaching tool, following the transcript.

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