Math

RNGs: A double KISS
The KISS (Keep-It Simple-Stupid) principle appears to be one of the better ways to get fast and reliable random numbers in a computer, by combining several simple methods. Most RNGs produce random integers---usually 32-bit--- that must be converted to floating point numbers for applications. I offer here a pos... 17 Apr 2010 18:33

Square Roots and Sequences
Hello, let {s_n} be the sequence defined by s_0 = 2^(1/2), s_{n+1} = (2 + s_n)^(1/2), and {t_n} the sequence defined by t_0 = 2^(1/2), t_{n+1} = (2 + [(s_n)^(1/2)])^(1/2). Then it's easy to see that {s_n} and {t_n} are two strictly increasing sequences and that t_n <= s_n < 2, for every n. So they ... 15 Apr 2010 17:00

Limit of Real Analytic Functions
Hello, let sum_{n=0}^Infty (a_n)*(x^n) be a real power series with radius of convergence R > 0. Set, for every -R < x < R, f(x) = sum_{n=0}^Infty (a_n)*(x^n). Then, for every m>=0, let sum_{n=0}^Infty (b_{n, m})*(x^n) a real power series with radius of convergence R_m >= R. Set, for every -R_m < ... 14 Apr 2010 07:40

projection of knot
Let A (in R^2) is an image of circle by continuous nonconstant map on R^2. Does exist a knot in R^3 (homeomorpfic with circle) whose projection onto plane is A? ... 15 Apr 2010 11:23

parabola roulette
Hello, Im trying to write an animation in Maple that shows a parabola rlling on a line, and its focus sketching out a catenary. I was wondering what the equation was to model such a thing. Any help appreciated. ... 17 Apr 2010 16:20

I am groovy
Pentcho Valev wrote: http://www.prospect-magazine.co.uk/article_details.php?id=5538 Paul Davies: "Was Einstein wrong? Einstein's famous equation E=mc2 is the only scientific formula known to just about everyone. The "c" here stands for the speed of light. It is one of the most fundamental of the basic co... 13 Apr 2010 20:43

quaternion rotation formula
I was vague in my last question and I am very sorry about that, what I wanted to do was to take this formula: http://en.wikipedia.org/wiki/Rodrigues%27_rotation_formula and substitute z.v and zxv with z.v = (z*v + v*z) / (-2) zxv = (z*v - v*z) / 2 , where z and v are now pure quaternions and somehow obtai... 13 Apr 2010 18:29

two limits to speed: speed of light and upper limit of slow speed #596 Correcting Math
My better judgement tells me not to start something in what few days I have remaining before 15 April to end this book. I cannot help but notice that the Universe has a speed desert where most speeds conglomerate around a few Km/sec and conglomerate at the speed of light with no intermediate speeds in-between. ... 13 Apr 2010 15:05

Math and Physics of Bycicle Tires Profiles
Greetings! I'm looking for references (articles, books) about the mathematics and physics of bycicle tires profiles. How are their shapes determined? Are there any optimal/cost/safety issues involved? I've found this link: http://www.hydra-glide.com/phpBB3/viewtopic.php?f=60&t=752 Thanks in advance, Humbe... 13 Apr 2010 19:36

Asymptotics
Let a(n) be a real sequence. If sum_k=1..n [a(k)]^2 = O( 1/(n^p . log^q n)), n -> +infinity (p,q >= 0) then a(n) = O( 1/n^(p+1)/2 . log^q/2 n), n -> +infinity? ... 13 Apr 2010 11:42