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. 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) Additionally, using these numbers for the coordinates of the regular Dodecahedron highlights the Golden ratio aspects of the polyhedron.
13 Useful Math Cheat Sheets Posted by Antonio Cangiano in Applied Math, Math Education, Software, Tutorial on September 20th, 2008 | 38 responses Cheat sheets can be very useful and make for great posters around your room. The following is a collection of 13 cheat sheets for several mathematical topics and programs: And since most of us like to show our math pride off when out and about as well, Amazon sells this awesome Math Cheat Sheet T-shirt with formulas on both sides (Also available for Science and Engineering). Sponsor’s message: Looking for online algebra homework solutions?
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. 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 The Dual of a Solid Things to do
Error Goblin 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. 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
Evil Mad Scientist Laboratories ApollianGasketNested 2-20.svg - Wikipedia, the free encyclopedia Cancel Edit Delete Preview revert Text of the note (may include Wiki markup) Could not save your note (edit conflict or other problem). Upon submitting the note will be published multi-licensed under the terms of the CC-BY-SA-3.0 license and of the GFDL, versions 1.2, 1.3, or any later version. Add a note Draw a rectangle onto the image above (press the left mouse button, then drag and release). Save To modify annotations, your browser needs to have the XMLHttpRequest object. [[MediaWiki talk:Gadget-ImageAnnotator.js|Adding image note]]$1 [[MediaWiki talk:Gadget-ImageAnnotator.js|Changing image note]]$1 [[MediaWiki talk:Gadget-ImageAnnotator.js|Removing image note]]$1
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). Background of Quaternion Euler's equation (formula) can be used to represent a 2D point with a length and angle on a complex plane. 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. Now, the above example now satisfies as ij=0+i0+j0+k1. Understanding of Quaternion Definition Definition of Quaternion operator Hamilton's motivation was to create a geometrical operator to transform from a vector to the other in 3D space. , or, to produce and
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. 0.1, is consistent with the value inferred from the fast dwarf nova decays.
ApollonianGasket-1 2 2 3-Labels.png - Wikipedia, the free encyclopedia 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... Your email has been sent