The Kepler Light Curves of V1504 Cygni and V344 Lyrae: A Study of the Outburst Properties. We examine the Kepler light curves of V1504 Cyg and V344 Lyr, encompassing ~736 days at one-minute cadence. During this span each system exhibited ~64-65 outbursts, including 6 superoutbursts. We find that, in both systems, the normal outbursts lying between two superoutbursts increase in duration over time by a factor ~1.2-1.9, and then reset to a small value after the following superoutburst. In both systems the trend of quiescent intervals between normal outbursts is to increase to a local maximum about halfway through the supercycle—the interval from one superoutburst to the next—and then to decrease back to a small value by the time of the next superoutburst. This is inconsistent with Osaki's thermal-tidal model, which predicts a monotonic increase in the quiescent intervals between normal outbursts during a supercycle. Also, most of the normal outbursts have an asymmetric, fast-rise/slower-decline shape, which would be consistent with outbursts triggered at large radii.
Quaternion. Related Topics: Euler's Equation Quaternion is a geometrical operator to represent the relationship (relative length and relative orientation) between two vectors in 3D space. William Hamilton invented Quaternion and completed the calculus of Quaternions to generalize complex numbers in 4 dimension (one real part and 3 imaginary numbers). In this article, we focus on rotations of 3D vectors because Quaternion implementation for 3D rotation is usually simpler, cheaper and better behaved than other methods. Background of Quaternion Euler's equation (formula) can be used to represent a 2D point with a length and angle on a complex plane. Multiplication of 2 complex numbers implies a rotation in 2D. However, the set of 3 dimensional complex numbers is not closed under multiplication. The equation c2+1=0 gives the contradiction. Later, Hamilton realized 4 dimensional complex numbers are required for multiplication to be closed by adding an additional imaginary part, k.
Definition , or, into When. THE UNREASONABLE UTILITY OF RECREATIONAL MATHEMATICS by Prof. David Singmaster. Computing, Information Systems and Mathematics 87 Rodenhurst Road South Bank University London, SW4 8AF, England London, SE1 0AA, England Tel/fax: 0181-674 3676 Tel: 0171-815 7411 Fax: 0171-815 7499 E-mail: ZINGMAST@VAX.SBU.AC.UK THE UNREASONABLE UTILITY OF RECREATIONAL MATHEMATICS by Prof.
David Singmaster For First European Congress of Mathematics, Paris, July, 1992. Amended on 24 Jan 1993 and 7 Sep 1993. Les hommes ne sont jamais plus ing‚nieux que dans l'invention des jeux. [Men are never more ingenious than in inventing games.] Last Web revision:December 22, 1998 Web page processed by Web Master - Mario Velucchi -- velucchi@bigfoot.com Mario Velucchi / Via Emilia, 106 / I-56121 Pisa - Italy Resources provided by Brad Spencer.
Carl Munck - The Code. Orrery_2006.swf (application/x-shockwave-flash Object) Jitterbug Defines Polyhedra. Appendix I: Vertex Coordinates In order to calculate the properties of the 120 Polyhedron, it is helpful to first calculate the coordinates to its vertices. But what orientation and scale of the 120 Polyhedron should be used? Is there a preferred orientation and scale which will make calculations easier or which will highlight some important features of the 120 Polyhedron? In a note published on "synergetics-l@teleport.com", Gerald de Jong showed that the regular Dodecahedron could be assigned simple coordinates expressed in terms of the Golden ratio. The Golden ratio is often represented by the Greek letter phi. However, I will use the letter "p" in this text. The Golden ratio is p = (1 + sqrt(5)) / 2 which is approximately p = 1.618033989.
Gerald showed that the Dodecahedron's 20 vertices could all be assign numbers from the set {0, -p, p, -p^2, p^2, -p^3, p^3}. This is a remarkable set of numbers. P + p^2 = p^3 In general, it can be shown that (for n an integer) p^n + p^(n+1) = p^(n+2) The Golden Geometry of Solids or Phi in 3 dimensions. Having looked at the flat geometry (two dimensional) of the number Phi, we now find it in the most symmetrical of the three-dimensional solids - the Platonic Solids. Contents of this Page The icon means there is a Things to do investigation at the end of the section. 1·61803 39887 49894 84820 45868 34365 63811 77203 09179 80576 ..More.. The five regular solids (where "regular" means all sides are equal and all angles are the same and all the faces are identical) are called the five Platonic solids after the Greek philosopher and mathematician, Plato.
Euclid also wrote about them. Dice shapes What shapes make the best dice? We need to make sure all the faces are the same shape and that all the angles and sides are equal, or some faces will be favoured more than others and so our dice will be "unfair". [There are other shapes that make fair dice if we relax these conditions a little. All sides are equal in length and all angles are equal so that all the faces are identical in shape and size. A Tisket, a Tasket, an Apollonian Gasket. Fractals made of circles do funny things to mathematicians Dana Mackenzie In the spring of 2007 I had the good fortune to spend a semester at the Mathematical Sciences Research Institute in Berkeley, an institution of higher learning that takes “higher” to a whole new extreme.
Perched precariously on a ridge far above the University of California at Berkeley campus, the building offers postcard-perfect vistas of the San Francisco Bay, 1,200 feet below. That’s on the west side. However, there was one flaw in the plan: Someone installed a screen-saver program on the computer. One day, a new design popped up on the screen (see the figure above). Before I became a full-time writer, I used to be a mathematician. As it turned out, the picture on the screen was a special case of a more general construction. Something about the Apollonian gasket makes ordinary, sensible mathematicians get a little bit giddy. » Post Comment Sending...
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