• Happenings – 2012 Dec 29

    Updated: 2012-12-29 16:24:38
    Christmas vacation continues. I was away from home over Xmas, from the Saturday afternoon before until the Wednesday evening afterwards… I visited an old friend in Sedona AZ, driving there in two cars with two other friends, but returning alone. It amounted to 500 miles of my driving on Sunday, and 750 on Wednesday. Whew! [...]

  • Infinitude of Primes - An Impossible Injection

    Updated: 2012-12-28 02:23:18
    Proofs, the essence of Mathematics, Infinitude of Primes - An Impossible Injection. An application of the prime factorization and the pigeonhole principle

  • Infinitude of Primes - via Bertrand's Postulate

    Updated: 2012-12-23 03:15:09
    Proofs, the essence of Mathematics, Infinitude of Primes - via Bertrand's Postulate. Besides the obvious derivation, there is one with a by far more subtle result

  • Infinitude of Primes - via Fibonacci Numbers

    Updated: 2012-12-23 03:15:08
    Proofs, the essence of Mathematics, Infinitude of Primes - via Fibonacci Numbers. Some Fibonacci numbers would not fit the required pattern

  • Happenings – 2012 Dec 22

    Updated: 2012-12-22 15:26:54
    I’ve been doing holiday stuff and work, of course, this past week… now I’m off until Jan. 2… but I have lots of holiday stuff to do. Oh, so much for the Mayan apocalypse – but did you (a reader of a math blog) really expect the world to end yesterday? I’ve started a computational [...]

  • Lemniscate Linkage

    Updated: 2012-12-21 15:58:12
    8446 TOPICS LATEST ABOUT AUTHORING AREA PARTICIPATE Your browser does not support JavaScript or it may be disabled Lemniscate Linkage The midpoint of the middle bar of a 3-bar linkage traces out a curve known as a lemniscate . It is interesting to note that a lemniscate is a cross section of a . torus Contributed by : Ed Pegg Jr SNAPSHOTS RELATED LINKS Lemniscate Wolfram MathWorld PERMANENT CITATION Ed Pegg Jr Lemniscate Linkage http : demonstrations.wolfram.com LemniscateLinkage Wolfram Demonstrations Project Published : September 28, 2007 : Share Embed Interactive Demonstration New Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site . More details Download Demonstration as CDF Download Source Code preview Files require

  • Fundamental Theorem of Arithmetic

    Updated: 2012-12-19 16:33:21
    8436 TOPICS LATEST ABOUT AUTHORING AREA PARTICIPATE Your browser does not support JavaScript or it may be disabled Fundamental Theorem of Arithmetic The fundamental theorem of arithmetic or unique factorization theorem states that every natural number greater than 1 can be written as a unique product of ordered primes . Most numbers have only three or four prime factors . Contributed by : Hector Zenil THINGS TO TRY Slider Zoom Gamepad Controls Automatic Animation SNAPSHOTS RELATED LINKS Fundamental Theorem of Arithmetic Wolfram MathWorld PERMANENT CITATION Hector Zenil Fundamental Theorem of Arithmetic http : demonstrations.wolfram.com FundamentalTheoremOfArithmetic Wolfram Demonstrations Project Published : September 28, 2007 : Share Embed Interactive Demonstration New Just copy and paste

  • Morse-Novikov number and tunnel number

    Updated: 2012-12-18 14:33:43
    Someone recently pointed out to me a paper by A. J. Pajitnov [1] proving a very interesting connection between circular Morse functions and (linear) Morse functions on knot complements. (A similar result is probably true in general three-manifolds as well.) Recall that a (linear) Morse function is a smooth function from a manifold to the line [...]

  • Happenings – 2012 Dec 15

    Updated: 2012-12-15 17:27:37
    There’s not a lot to talk about today. Most of my free time this week went toward the Coursera class on computational investing… as I said before, the instructor didn’t manage to deliver all that he had hoped… but it forced me to look elsewhere for the CAPM (Capital Asset Pricing Model), and it introduced [...]

  • Mixing for progressions in non-abelian groups

    Updated: 2012-12-12 05:03:57
    I’ve just uploaded to the arXiv my paper “Mixing for progressions in non-abelian groups“, submitted to Forum of Mathematics, Sigma (which, along with sister publication Forum of Mathematics, Pi, has just opened up its online submission system). This paper is loosely related in subject topic to my two previous papers on polynomial expansion and on [...]

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