Products fun! Tessellations, polyhedra, fractals, MC Escher, Tangrams dissections, Kaleidoscopes symmetry, Paper folding and more Buy http://www.hoagiesgifted.org/products.htm
Extractions: accepts no paid advertising. We appreciate your donations through PayPal Donate or Amazon Honor System, and your purchases through our affiliate links. Thanks! Don't miss Smart Toys , perennial favorites of gifted kids, Materials for Gifted Classrooms , terrific educational materials, and Movies , featuring gifted kids (and adults) in a positive light. Enjoy! Create the number 24 from the four numbers on a game card. You can add, subtract, multiply and divide. Use all four numbers but use each number only once. Available from simple addition and subtraction, right up to fractions, decimals and algebra. Click for 24 Challenge tournament schedule...
Connect-ME - Weblinks Spirolaterals were first encountered while investigating space curves and fractals. polyhedra in the Classroom http//mathforum.org/alejandre/workshops/unit14 http://educ.queensu.ca/connectme/weblinks/strands.htm
Chaos And Fractals stellated and polyhedra. Uses tiny Java1.1 applets and VRML worlds. Fractal Geometry at Yale University http//classes.yale.edu/fractals/welcome.html Course http://www.directory.net/Science/Math/Chaos_and_Fractals/
Educational com/shopsite_sc/store/html/index.html Books, puzzles, posters and art gallery related to tessellations, polyhedra, fractals, anamorphic art, and MC Escher. http://www.directory.net/Shopping/Toys_and_Games/Educational/
David's Links Page works. polyhedra, fractals, chaos, curved surfaces, loops, interference, tilings big gallery with explanations of the works. http://davidf.faricy.net/links.html
Full Site History to gallery. Grouped collections into subgalleries (lego sculptures, objets d art, twysted polyhedra and snowflake fractals). http://davidf.faricy.net/history.php
Extractions: - Added Regular Convex 4-Dimensional Polytopes and Regular Star Polychora pages to polyhedra section. - Image.php is finally working again! - Added to Gallery - I'm getting tired of spam, so when you click on email link, you may now have to replace '[AT]' with '@'. - Greatly simplified Calculating the Platonic Solid Measurements in the polyhedra section - Pictures now load against a black background. - I recently had an IBM 75GXP drive failure resulting in total data loss. My most recent backup was September 2001, so I lost the tori and civilization source. - Removed WADStrip utility from the Doom II section - Added Ancient Civilization to Gallery
Fractal Polyhedra and VRMLArts by V.Bulatov Look at Fractal polyhedra with interactive Java 1.1 applet, if you didn t install a VRML plugin yet. Kepler s (Stellated) fractals. http://www.ibiblio.org/e-notes/VRML/Poly/Poly.htm
Extractions: Look at Fractal Polyhedra with interactive Java 1.1 applet, if you didn't install a VRML plugin yet. Hop David attracted my attention to Keplerian Fractals . He replaces every horn of a stellated (non-convex) polyhedron by small self-similar polyhedron. The picture shows that we can make it in two different ways (we will obtain a II-type (solid) fractal if we combine I-type ones). Interactive Kepler's Octahedron is made of 4 Tetra Flakes (hit it to get next iteration). Hop David found out that it turns into a cube under iterations. He found "Cantor's Octahedron" beneath the cube's surface too. Kepler's Stellated Dodecahedron I-type II-type (solid) Kepler's Great Stellated Dodecahedron I-type II-type (solid) . Polyhedra with many vertises are too complicated :( You will get 1D Fractal Web (may be Laces or Hedgehog :) if you start at "skeleton" of a Polyhedron. The skeleton is made of rays from the Polyhedron center to its verteses. Look at Interactive
Extractions: Team Chairs Iman Osta, Lebanese American University, Address: Beirut Campus, P.O.Box 13-5053, Chouran Beirut 1102 2801, Lebanon iman.osta@lau.edu.lb Harry Silfverberg, Department of Teacher Education, University of Tampere Address: P.O.Box 607, FIN-33014 University of Tampere, Finland harry.silfverberg@uta.fi Team Members David W. Henderson, Department of Mathematics, Cornell University, USA dwh2@cornell.edu Verónica Hoyos Aguilar, CAEMTIC, National Pedagogical University, Mexico vhoyosa@upn.mx Ewa Swoboda, Institute of Mathematics, Department of Mathematics and Natural Science, Rzeszow University, Poland eswoboda@univ.rzeszow.pl Aims and Focus Call for Papers Selection of Abstracts for Expected Papers ... Call for reaction / discussant papers Aims and Focus In Topic Study Group 10 (Research and development in the teaching and learning of geometry), we will examine and discuss recent research and developments in the teaching and learning of geometry at all levels for schooling from kindergarten to the university. The Group will incorporate short presentations on, and discussions of, important new trends and developments in research or practice, providing an overview of the current state-of-the-art in geometry teaching and learning, and expositions of outstanding recent contributions to it, as seen from international perspectives.
Fractal Resources 3D fractals (Using Java applets, this site allows a variety of forms such as fractal mountains, mandelbrot and julia sets, complex fractal polyhedra, etc. http://home.att.net/~Novak.S/resources.htm
Extractions: Introduction to Fractals Chaos and Fractals: A Search for Order (A brief introduction to the history and basic concepts of the topic. Excellent for beginners!) Fantastic Fractals (an outstanding comprehensive site featuring tutorials on fractal images and music, an illustrated "Just for Kids" section, interactive online fractal generators, free fractal software, newsletter, and other resources.) Our Fractal Universe: Mandelbrot and More (in English, French, or Spanish) The Fractory (An outstanding and mathematically detailed comprehensive site with excellent explanatory graphics!) Robert L. Devaney's The Dynamical Systems Technology Project At Boston University (Funded by the National Science Foundation, this site was specifically developed to introduce these topics into secondary and college level courses. Also on this site is a section on Chaos, Fractals, and Arcadia which examines the use of concepts in chaos theory in Tom Stoppard's play "Arcadia" to facilitate interdisciplinary studies. This section also provides links to similar "Arcadia" related sites.) Michael Frame's, Benoit Mandelbrot's, and Nial Neger's site for their course on
Mainframe 3D fractals. Using Java applets, this site allows a variety of forms (eg, fractal mountains, terrains, mandelbrot and julia sets, complex fractal polyhedra, etc http://home.att.net/~Novak.S/main.htm
Extractions: with the home page of Stanley Novak Now That You're Here The primary purpose of this site is to exhibit my images and music compositions. In addition, I wish to provide some personal suggestions for creating fractal images and music depending on different levels of technical knowledge. The "thumbnail" Galleries contain a number of fractal images or fractal-derived images created by programs requiring different levels of technical experience. The program used is indicated below each image and "clicking" on the image will link you to an enlarged version. Some enlarged images in Gallery-1 are also accompanied by fractal music compositions. In some instances, fractal images may have undergone additional processing with an image editor (i.e., post-processing) after being generated by the indicated program. The MIDI music for this page was composed with the full MusiNum program discussed below. Media Player (available on Windows Update) is the MIDI player used for Internet Explorer. Crescendo (operating in detached mode) is the MIDI player plugin I am using for . A basic version is available from the Crescendo homepage (freeware).
Extractions: This list comes from a gifted students' resource, but these are not just for gifted students. Every student is gifted in some way. Check them out: Educational Products Don't miss Smart Toys (Smart Toys for Gifted Kids) http://www.hoagiesgifted.org/smart_toys.htm Lists perennial favorites of gifted kids The 24 Game http://www.math24.com/ Create the number 24 from the four numbers on a game card. You can add, subtract, multiply and divide. Use all four numbers but use each number only once. Available from simple addition and subtraction, right up to fractions, decimals and algebra. Click for 24 Challenge tournament schedule... Arbor Scientific http://www.arborsci.com/ Great science supplies, with good prices Calculus By and For Young People http://www.shout.net/~mathman/ by The Mathman - Don Cohen and lots of related math materials... Carolina Supply Company http://www.carolina.com/ Science (and some math) supply company, with products in a reasonable price range... Challange Math For the Elementary and Middle School Student http://www.challengemath.com/
Efg's Fractals And Chaos -- Von Koch Curve Lab Report Fraktaler www.e.kth.se/~e97_llj/fraktal.html. Koch s Flakes in fractals polyhedra, Flakes Ltrees www.people.nnov.ru/fractal/VRML/3dLsys/3Dtree.htm. http://www.efg2.com/Lab/FractalsAndChaos/vonKochCurve.htm
Extractions: The purpose of this project is to show how to create a von Koch curve, including a von Koch snowflake. Mathematical Background Swedish mathematician Helge von Koch introduced the "Koch curve" in 1904. Starting with a line segment, recursively replace the line segment as shown below: The single line segment in Step 0, is broken into four equal-length segments in Step 1. This same "rule" is applied an infinite number of times resulting in a figure with an infinite perimeter. Here are the next few steps: If the original line segment had length L, then after the first step each line segment has a length L/3. For the second step, each segment has a length L/3 , and so on. After the first step, the total length is 4L/3. After the second step, the total length is 4 L/3 , and after the k th step, the length is 4 k L/3 k . After each step the length of the curve grows by a factor of 4/3. When repeated an infinite number of times, the perimeter becomes infinite. For a more detailed explanation of the length computation, see [ , p. 107] or
Efg's Mathematics Page html. polyhedra Database www.netlib.org/polyhedra/index.html. html. F. fractals and Chaos Also see efg s fractals and Chaos Projects Page. http://www.efg2.com/Lab/Library/mathematics.htm
Extractions: Fractals and Chaos Contents A. Reference D. Functions G. Wavelets E. Fourier Analysis, FFTs ... F. Fractals and Chaos also see efg's Delphi Math Info and Links Delphi Math Functions Math Projects A. Reference Calculators The Calculator Home Page. Calculator.org has a number of calculator related resources, including an online scientific calculator, units conversion and constants database, and other information. www.calculator.org Calculators Online Center. Part II. Mathematics
Tessellations' Ordering Page Mathartfun.com carries a variety of books, puzzles, posters, videos and software related to tessellations, polyhedra, fractals, kaleidoscopes, anamorphic art http://members.cox.net/tessellations/Ordering.html
Extractions: If you are interested in purchasing online, we recommend our sister company, Mathartfun.com. In addition to Tessellations' products, Mathartfun.com carries a variety of books, puzzles, posters, videos and software related to tessellations, polyhedra, fractals, kaleidoscopes, anamorphic art, and more! Click on the logo below to go to Mathartfun.com.
Shiki.archive.9512: Fractals fractals are the opposite of optimal. Intervals, straight lines, planes, smooth surfaces, smooth curves, polyhedra are not fractals. http://haiku.cc.ehime-u.ac.jp/~shiki/shiki.archive/html/9512/0172.html
6. Other Polyhedra Dodecahedron 6. Other polyhedra. In principle our algorithm should create quantum fractals for each of the regular polyhedra. The http://www.cassiopaea.org/quantum_future/papers/qfract/node16.html
Extractions: Next: 4. Notes Up: 3. The Five Platonic Previous: 5. Dodecahedron In principle our algorithm should create quantum fractals for each of the regular polyhedra. The only restriction on the array of vectors is that they are all of unit length, and their sum is a zero vector. We added, for comparison with the Platonic solids configurations, two additional simple yet regular figures: double tetrahedron and icosidodecahedron. Notice that tetrahedron is self-dual, while dodecahedron and icosahedron are dual to each other. Double tetrahedron array is obtained by combining with - that is with the inverted configuration. Figure: Quantum Double Tetrahedron. Icosidodecahedron has particularly simple and elegant expression for its 30 vertices: they are of the form: and its cyclic permutations, and and its cyclic permutations, where is the golden ratio. All of its edges are of length . For its 30 vertices was needed to resolve the atrractor's fine structure. Figure: Quantum Icosidodecahedron.
Generation Of 3D Fractals For Web Unlike the well known Lsystems fractals, this algorithm does not need a rather complicated string parser and 3D turtle for its Fractal Trees and polyhedra. http://www.people.nnov.ru/fractal/VRML/Web3D/Web3D.htm
Extractions: A wide variety of amazing 3D fractals can be obtained by iteration of very simple rules many times. The simple rules lead to very small (1-3kb) algorithms and scripts realized in Java, JavaScript or VRML. The scripts are flexible and can be combined in a library of fractals for application in complex scenes. It is well known, that as since fractals possess self-similarity on scaling, therefore they can be made by iterations of scaling transformations. In Figure 1 it is shown how the famous Koch's snowflake is obtained by repetition of simple transformations: scaling, rotations and translations. Figure 1. Generation of the Kochs snowflake. The initial segment 1 is shrunk three times, then three small copies are translated upward and two of them rotated by +-60 degrees. Then this procedure is applied again to the entire curve 2 to get the next curve 3 and so on. Unlike the well known L-systems fractals, this algorithm does not need a rather complicated string parser and 3D turtle for its realization. It uses "natural" 3D operations: scaling, rotations and translations and it can be used with any "3D engine" (VRML, Java3D or Java1 applets). Unfortunately, there is no such "built in" 3D engine in present-day browsers. It turns out that very realistically looking 3D Trees and other Plants can be obtained just as the Kochs snowflake by repetition of scaling, rotations and translations. Generation of a simple tree is shown below.
Web Resources: Teens: Homework - MCPL Lessons on tesselations, polyhedra, fractals, etc. Also, supercool demos. and brain-benders. Author CoolMath.com, Inc. (71 hits) Create a Graph new! http://www.mcpl.lib.mo.us/Links/Teens/Homework/
WebGuest Directory - Math : Chaos And Fractals Interactive 3D fractals Shows how to create fractal mountains, 3D Mandelbrot and Julia sets, convex, stellated and polyhedra. http://directory.webguest.com/Science/Math/Chaos_and_Fractals
Extractions: 3D Fractals using Bicomplex Dynamics - The Tetrabrot is the bicomplex generalization of the Mandelbrot set as realized by Dominic 'Ramdam' Rochon. Articles, pictures, news and other downloads. A Sketchbook on L-systems - Modeling and visualization of plants using parametric L systems. An Introduction To Fractals - Gives definition and explains the different types of formulas used. Includes illustrations and bibliography. Chaos Theory Resources - Fractals - Directories - Links - A Directory of Internet resources on chaos theory and fractals. Chaos Theory and Fractals - History of chaos as well as extensive information on Chaos Theory and fractals. Contains several pictures of fractals and links to other Chaos Theory and fractals pages. Chaos, Fractals And Attractors In Science - Chaos theory is a popular name for the theory of Dynamical Systems (DS), mainly for non-linear systems. The theory covers many aspects of the life of DS, all of them have the same characteristics, they were born, they lived and they died. Climate Dynamics - Explains a general systems theory for chaos, quantum mechanics and gravity as applied to weather patterns.
