Mathematical and Generative Graphics. Build your own one. Fast and usable calculator. Microsoft Windows Download the installer: SpeedCrunch-0.10.1.exe (2.5 MB) To perform the installation, just click on the file to run it and then follow the step-by-step instructions. After installed, run SpeedCrunch using menu, , . Now you can also run SpeedCrunch without the need of installing it. So if you don't have permission to install it on your system or you want to take it everywhere with you on your pen drive, for instance, just download the archive below, extract it and click on the executable file inside the directory.
You can move the directory to any place and still run the application. SpeedCrunch-0.10.1.zip (2.4 MB) Mac OS X Download the bundle: SpeedCrunch-0.10.1.dmg (6.6 MB) This bundle is Universal Binary and should work on Mac OS X 10.3 (Panther), 10.4 (Tiger), and 10.5 (Leopard). Linux SpeedCrunch is packaged by the following Linux distributions. For other Linux distributions, you can install SpeedCrunch by compiling it from source code. Source code fixed potential crashes. Geometry in Action. This page collects various areas in which ideas from discrete and computational geometry (meaning mainly low-dimensional Euclidean geometry) meet some real world applications. It contains brief descriptions of those applications and the geometric questions arising from them, as well as pointers to web pages on the applications themselves and on their geometric connections. This is largely organized by application but some major general techniques are also listed as topics. Suggestions for other applications and pointers are welcome.
Geometric references and techniques Design and manufacturing Graphics and visualization Information systems Medicine and biology Physical sciences Robotics Other applications Recent additions. What's special about this number? (1) Is the only prime 1 less than a perfect square. - Robin Regan is the number of spatial dimensions needed to mathematically describe a solid. are the primary colors. are the geometric constructions you cannot build using just a ruler and compasses: 1. You cannot trisect - divide into three equal parts - a given angle; 2. Double a cube; and 3. Square a circle.
A number is divisible by 3 when the sum of its digits can be divided by 3. If the denominator of a rational number is not divisible by 3, then the repeating part of its decimal expansion is an integer divisible by 9. 3 + 2 = log2 32 5 (sum of two square roots)= 4! 4) = XV/V = CL/L = MD/D = 4 + 4 – 5 = 43 + 43 – 53= 17,469 / 5,823 (this division contains all digits 1 through 9 once) 3 x 51249876 = 153749628 (the multiplication uses all 9 digits once - and so does its product!) 3 x 37 = 111 33 x 3367 = 111,111 333 x 333667 = 111,111,111 3333 x 33336667 = 111,111,111,111 33333 x 3333366667 = 111,111,111,111,111 3 x 1.5 = 3 + 1.5. American Mathematical Society :: Feature Column.
Voronoi diagrams have been used by anthropologists to describe regions of influence of different cultures; by crystallographers to explain the structure of certain crystals and metals; by ecologists to study competition between plants; and by economists to model markets in the U.S. economy... Introduction Suppose that you live in a desert where the only sources of water are a few springs scattered here and there. For each spring, you would like to determine the locations nearest that spring. The result could be a map, like the one shown here, in which the terrain is divided into regions of locations nearest the various springs.
Maps like this appear frequently in various applications and under many names. To mathematicians, they are known as Voronoi diagrams. Voronoi diagrams are rather natural constructions, and it seems that they, or something like them, have been in use for a long time. Constructing Voronoi diagrams and as from and the other containing the points that are closer to . . . Scilab Home Page. HIOX FREE Online Math Calculator, Converter. Mathematics Calcula. Project Euler. Chaos Theory. The trouble with five. December 2007 We are all familiar with the simple ways of tiling the plane by equilateral triangles, squares, or hexagons. These are the three regular tilings: each is made up of identical copies of a regular polygon — a shape whose sides all have the same length and angles between them — and adjacent tiles share whole edges, that is, we never have part of a tile's edge overlapping part of another tile's edge.
Figure 1: The three regular tilings. In this collection of tilings by regular polygons the number five is conspicuously absent. Figure 2: Three pentagons arranged around a point leave a gap, and four overlap. But there is no reason to give up yet: we can try to find other interesting tilings of the plane involving the number five by relaxing some of the constraints on regular tilings. Is it now possible to find a set of shapes with five-fold symmetry that together will tile the plane? Going for simple shapes Figure 3: Constructing a tiling piece by piece. Dividing monsters forever. Evil Mad Scientist Laboratories - Iterative Algorithmic Plastic. One of our favorite shapes is the Sierpinski triangle. In one sense, a mere mathematical abstraction, on the other, a pattern that naturally emerges in real life from several different simple algorithms.
On paper, one can play the Chaos Game to generate the shape (or cheat and just use the java applet). You can also generate a Sierpinski triangle in what is perhaps a more obvious way: by exploiting its fractal self-similarity. Beginning with a single triangle, replace that triangle with three half-size copies arranged so that their outer border form a new triangle of the same size as the original. Then, replace each of those three triangles with three triangles half that size, and so forth. We begin with a few packages of polymer clay– two colors of Fimo Soft, in this case.
Form the two clay colors into long triangular shapes. Press the stack of triangles together to make sure that the edges fuse well. Cut the stretched “first iteration” piece into four pieces of equal length. World's Hardest Easy Geometry Problem. Magical Square Root Implementation In Quake III. Any 3D engine draws it’s power and speed from the mathematical models and implementations within, and trust John Carmack of ID software for using really good hacks. As it turns out, a very interesting hack is used in Quake III to calculate an inverse square root.
Preface ID software has recently released the source code of Quake III engine with a GPL license. In this article we’ll see Carmack work his black magic to calculate the square root of a floating point number blazingly fast. Carmack’s Unusual Inverse Square Root A fast glance at the file game/code/q_math.c reveals many interesting performance hacks.
Observe the original function from q_math.c: float Q_rsqrt( float number ) { long i; float x2, y; const float threehalfs = 1.5F; x2 = number * 0.5F; y = number; i = * ( long * ) &y; // evil floating point bit level hacking i = 0x5f3759df - ( i >> 1 ); // what the fuck? In another file, code/common/cm_trace.c , a neater implementation of the same hack can be found. A Witchcraft Number. The Algorithm Design Manual. The Stony Brook Algorithm Repository. This WWW page is intended to serve as a comprehensive collection of algorithm implementations for over seventy of the most fundamental problems in combinatorial algorithms. The problem taxonomy, implementations, and supporting material are all drawn from my book The Algorithm Design Manual.
Since the practical person is more often looking for a program than an algorithm, we provide pointers to solid implementations of useful algorithms, when they are available. Because of the volatility of the WWW, we provide local copies for many of the implementations. We encourage you to get them from the original sites instead of Stony Brook, because the version on the original site is more likely to be maintained. Further, there are often supporting files and documentation which we did not copy, and which may be of interest to you.
The local copies of large implementations are maintained as gzip tar archives and, where available, DOS zip archives. Use at your own risk. An Intuitive Explanation of Fourier Theory. Steven Lehar slehar@cns.bu.edu Fourier theory is pretty complicated mathematically. But there are some beautifully simple holistic concepts behind Fourier theory which are relatively easy to explain intuitively. There are other sites on the web that can give you the mathematical formulation of the Fourier transform. I will present only the basic intuitive insights here, as applied to spatial imagery. Basic Principles: How space is represented by frequency Higher Harmonics: "Ringing" effects An Analog Analogy: The Optical Fourier Transform Fourier Filtering: Image Processing using Fourier Transforms Basic Principles Fourier theory states that any signal, in our case visual images, can be expressed as a sum of a series of sinusoids.
These three values capture all of the information in the sinusoidal image. The magnitude of the sinusoid corresponds to its contrast, or the difference between the darkest and brightest peaks of the image. Back to top Higher Harmonics and "Ringing" effects. Spatial references, coordinate systems, projections, datums, ell. People are often mixing the above as if they were one and the same, so here’s a recap of them. One of the things you often find people saying is that “my data is in the WGS84 coordinate system”.
This doesn’t really make sense, but I will get back to this later. This is a very confusing subject, and I might have gotten a few things wrong myself, so please add a comment and I’ll update it ASAP. Coordinate systems A coordinate system is simply put a way of describing a spatial property relative to a center. The Geocentric coordinate system is based on a normal (X,Y,Z) coordinate system with the origin at the center of Earth. Sidenote: The geocentric coordinate system is strictly speaking a cartesian coordinate system too, but this is the general terms I've seen used the most when talking about world coordinate systems. Datums and ellipsoids This poses two immediate problems: Where is the center of the earth What is the shape of the earth?
Read more on Datums and Spheroids. Projections. MathWorld: The Web's Most Extensive Mathematics Resource. Archimedean Solid. The 13 Archimedean solids are the convex polyhedra that have a similar arrangement of nonintersecting regular convex polygons of two or more different types arranged in the same way about each vertex with all sides the same length (Cromwell 1997, pp. 91-92). The Archimedean solids are distinguished by having very high symmetry, thus excluding solids belonging to a dihedral group of symmetries (e.g., the two infinite families of regular prisms and antiprisms), as well as the elongated square gyrobicupola (because that surface's symmetry-breaking twist allows vertices "near the equator" and those "in the polar regions" to be distinguished; Cromwell 1997, p. 92).
The Archimedean solids are sometimes also referred to as the semiregular polyhedra. The Archimedean solids are illustrated above. Nets of the Archimedean solids are illustrated above. The following table lists the uniform, Schläfli, Wythoff, and Cundy and Rollett symbols for the Archimedean solids (Wenninger 1989, p. 9). , edges where. Quantum Random Bit Generator Service. Handy Mathematics Facts for Graphics. Email scd@cs.brown.edu with suggested additions or corrections Eric Weisstein's world of Mathematics (which used to be called Eric's Treasure Trove of Mathematics) is an extremely comprehensive collection of math facts and definitions.
Eric has other encyclopedias at www.treasure-troves.com S.O.S. Mathematics has a variety of algebra, trigonometry, calculus, and differential equations tutorial pages. Dave Eberly has a web site called Magic Software with several pages of descriptions and code that answers questions from comp.graphics.algorithms. Steve Hollasch at Microsoft has a very comprehensive page of graphics notes which he would like to turn into a graphics encyclopedia. Vector math identities and algorithms from Japan. Paul Bourke has a variety of pages with useful tidbits, many of which are linked to from Steve Hollasch's page. The graphics group at UC Davis also has notes about computer graphics. Peter H. Josh Levenberg has a page of links to yet more graphics algorithm resources. e pi. A 10 minute tutorial for solving Math problems with Maxima. Posted by Antonio Cangiano in Essential Math, Software on June 4th, 2007 | 132 responses About 50,000 people read my article 3 awesome free Math programs.
Chances are that at least some of them downloaded and installed Maxima. If you are one of them but are not acquainted with CAS (Computer Algebra System) software, Maxima may appear very complicated and difficult to use, even for the resolution of simple high school or calculus problems. This doesn’t have to be the case though, whether you are looking for more math resources to use in your career or a student in an online bachelor’s degree in math looking for homework help, Maxima is very friendly and this 10 minute tutorial will get you started right away. Maxima as a calculator You can use Maxima as a fast and reliable calculator whose precision is arbitrary within the limits of your PC’s hardware. (%i1) 9+7; (%o1) (%i2) -17*19; (%o2) (%i3) 10/2; (%o3) (%i4) % - 10; (%o4) (%i5) %o1 * 3; (%o5) float(1/3); => float(26/4); => sqrt(81); => 3 awesome free Math programs. Posted by Antonio Cangiano in Software on June 2nd, 2007 | 109 responses Mathematical software can be very expensive.
Programs like Mathematica, Maple and Matlab are incredibly powerful, flexible and usually well documented and supported. Their price tags however are a big let down for many people, even if there are cheap (in some cases crippled) versions available for educational purposes (if you are a student or a teacher). The secondary disadvantages are those caused by the fact that such programs are proprietary.
This can also affect or limit a “sharing oriented” environment like the academic and research fields. 1. A general purpose CAS (Computer Algebra System) is a program that’s able to perform symbolic manipulation for the resolution of common problems. Valuable mentions are: 2. Matlab is the standard for numerical computing, but there are a few clones and valid alternatives that are entirely free. Valid alternatives are:
Ulam spiral. Ulam spiral of size 200×200. Black dots represent prime numbers. Diagonal, vertical, and horizontal lines with a high density of prime numbers are clearly visible. The Ulam spiral, or prime spiral (in other languages also called the Ulam Cloth) is a simple method of visualizing the prime numbers that reveals the apparent tendency of certain quadratic polynomials to generate unusually large numbers of primes. It was discovered by the mathematician Stanislaw Ulam in 1963, while he was doodling during the presentation of a "long and very boring paper" at a scientific meeting. Shortly afterwards, in an early application of computer graphics, Ulam with collaborators Myron Stein and Mark Wells used MANIAC II at Los Alamos Scientific Laboratory to produce pictures of the spiral for numbers up to 65,000.
In an addendum to the Scientific American column, Gardner mentions work of the herpetologist Laurence M. Construction[edit] All prime numbers, except for the number 2, are odd numbers. Shell Space: Flare, Verm, and Spire - Wolfram Demonstration. Introduction.