Art, Mathematics, Music and the Physical Universe Art, Mathematics, Music and the Physical Universe B. L. Moiseiwitsch Contents 1. 2. 3. 3.1 Introduction 3.2 Primitive Art 3.3 Music 3.4 Islamic Art 3.5 Renaissance Art 3.6 Modern Art 3.7 Summary 4. 4.1 Geometry 4.2 Time 5. 5.2 Unification of the Forces of Nature 5.5 Space-time and the Uncertainty Principle Appendices Appendix A. Appendix B. Appendix C. Appendix D. Appendix E. References Moonlight Sonata 1. Our knowledge of the external physical universe obviously comes entirely from our senses, mostly by seeing, hearing and touching. As a beginning let us consider the sense of vision. A truly interesting manifestation of this has been produced by the Magic Eye pictures1, or Single Image Random Dot Stereograms, that give rise to remarkable visions of three-dimensional objects by employing coloured dots, the ‘Salitsky Dots’, on a flat piece of paper. As in the case of vision, there are no actual sounds in the physical world. In the past this led to many misunderstandings about the universe. 2. 3. Table 1.
Models help you understand why you disagree Models help you understand why you disagree In a blog post yesterday, I advocated very strongly that rather than simply bloviating about political (and other) topics, we should instead build mathematical models to clearly express our thinking. There was a lot of disagreement on this. But quite a few people took the point to heart, and several actually decided to modify my model to illustrate their thinking. One in particular was Jeremy Scheff, who who forked my model and came up with his own. His model has a very different answer. I’m going to briefly address his model to demonstrate how models help us have a rational discussion. Jeremy alters my model in several ways. In Chris’s model, basic income is paid to everyone. He is very explicit about this. This is a major point of disagreement between us. A second place where his model disagrees with mine is that he believes a largeish number of people are not really disabled, and a Basic Income would induce them to engage in productive work:
User:LucasVB/Gallery Below is a mostly comprehensive gallery of all images — illustrations, diagrams and animations — that I have created for Wikipedia over the years, some of which have been selected as featured pictures, or even picture of the day. As you'll probably notice, they're mostly related to physics and mathematics, which are my main areas of interest. If you have any comments, requests, suggestions or corrections, feel free to drop me a message on my talk page. You can also follow me on tumblr for WIPs, current and failed projects and other creations. If you appreciate my work, consider making a donation. Animations Waves Wave-related animations. Fourier series integral identitiesPeriodic identity functionApproximating a sine curve from square wavesAdditive synthesis (sawtooth wave)Additive synthesis (square wave)Additive synthesis (triangle wave) Pendulums A series of images illustrating the oscillation of a pendulum. Blue Solids Static 2D Distance between Earth and Sun
Projections and Coordinate Systems Projections and Coordinate Systems Discussion Projections and coordinate systems are a complicated topic in GIS, but they form the basis for how a GIS can store, analyze, and display spatial data. Understanding projections and coordinate systems important knowledge to have, especially if you deal with many different sets of data that come from different sources. ProjectionsDistortionCoordinate SystemsDatumsExamples of different projections Projection Storage vs. Projections The best model of the earth would be a 3-dimensional solid in the same shape as the earth. Globes are large and cumbersome. Here is an image of a globe, displaying lines of reference. Positions on a globe are measured by angles rather than X, Y (Cartesian planar) coordinates. [Image from ESRI] For this reason, projection systems have been developed. Here is a simple schematic designed to show how a projection works. [Image from ESRI ] [Images placed with permission of Peter Dana] Distortion Coordinate Systems Datums
Developer API :: TheBigDB 20 Personal Website Examples for Your Design Inspiration | Webdesignersblog - Designers Daily Resource Magazine it’s important to make your online portfolio as impressive as you can. Portfolio websites can be used effectively for Personal Branding, Job Searches, most valuable Marketing Tools, and show off their awesome skills to stand out in this Tough Design Industry. Portfolio Sites are clean and minimal, there are a lot of possible design Styles and Approaches. In this article, we have collected 20 Personal Website Examples for Your Design Inspiration. Don’t forget to subscribe to our RSS or Follow us on Twitter if you want to keep track of our next post. 01. 02. 03. 04. 05. 06. 07. 08. 09. 10. 11. 12. 13. 14. 15. 16. manuel-rueda 17. 18. 19. 20. gopir13
Stereographic Projection - Math Images From Math Images Stereographic Projection of a Sphere Stereographic projection maps each point on a sphere onto a plane. Figure 1An example of a stereographic projection. Two points, P1 in the upper hemisphere and P2 in the lower hemisphere, are projected onto the x-y plane. Stereographic projection is a map from the surface of a sphere to a plane. A map, generally speaking, establishes a correspondence between a point in one space and a point in another space. The main image shows this process more concretely. The following applet demonstrates how a sphere is projected onto a plane. [Click to view A More Mathematical Explanation] Definition A stereographic projection maps the points of a sphere onto a plane. UNIQ36eed [...] [Click to hide A More Mathematical Explanation] Figure 2Cross section of a sphere. Specifically, Let S be the unit sphere centered at the origin; that is, the set of all points (x, y, z) that satisfy the equation Rectangular Coordinates That is, Eq. 1 [Click here to show.] Eq. 2
Reinventing Explanation The Babylonian Map of the World is one of the world's oldest extant maps, dating to 600 BCE. It's a crude map, difficult to read at a glance, but fortunately an accompanying cuneiform text describes the features on the map, including Babylon, seven other cities, a canal, and a mountain: Modern maps are, of course, far better than this early map. They improve on it by taking advantage of the many map-making techniques developed since 600 BCE, such as: surveying to get proportions correct; projections to correct for the curvature of the Earth; methods to depict topographic features; and so on. Even ideas such as showing roads and nautical routes were not a priori obvious, but had to be invented. This agglomeration of ideas has turned maps into a powerful medium for thought. Using this map, an ordinary person can walk into the Underground for the first time, and within minutes know how to find their way from place to place. Why go the trouble of constructing these prototypes?
Visualized Den Haag, The Netherlands Jan Willem Tulp is a freelance information visualizer, based in Den Haag, The Netherlands. Jan Willem loves to work at the intersection of data, design and software. Math on a Sphere | An Interactive Exploration of 3D Surfaces for Public Audiences