81. Mathartfun.com Shop for learning products that combine math and art. Includes puzzles, manipulatives, fractals, kaleidoscopes and paper folding and books. http://redirect-west.inktomi.com/click?u=http://www.looksmart.com/og/pr%3Dcdd%3B

82. Favorisierte Links Von Andrea Und Friedrich Lohmueller - Raytracing, Fractals, A Translate this page George Hart's Pavilion of Polyhedreality von George W. Hart neu ! “Virtual polyhedra”- Die Enzyklopedie der Polyeder, auch viele Geometrie-Links! (en). http://www.f-lohmueller.de/links/index_sd.htm

Unsere Links Raytracing Kunst Raytracing + POV-Ray Raytracing + Wissenschaft Mathematik, Geometrie Chemie, Biologie, Astronomie Architektur POV an Schulen ... Andere Links letztes Update 25. Jan. 2003 English version Mathematik, Geometrie, Technik: Tsutomu Higo - Gallery Cyberbust Shuhei Kawashu Exzellente Galerie kreativer mathematischer und geometrischer Kunst - mit einigen Beschreibungen!(en, jp) Paul Bourke Astrophysik und Supercomputing an der Swinburne University of Technology, Australien. Juno’s World Herman Serras Vom Golden Schnitt und Polyeder zu elliptischen Billiard-Tischen - faszinierende geometrische Spiele! (en) Homepage of Xiao, Gang Zoo of mathematical Surfaces The Geometry Junkjard von David Eppstein neu ! Eine riesige Sammlung von unterhaltsamen Geometrie-Links! (en). George Hart's Pavilion of Polyhedreality von George W. Hart neu ! “Virtual Polyhedra” - Die Enzyklopedie der Polyeder, auch viele Geometrie-Links ! (en). Tore Nordstrand Xah: Mathematics Graphics Gallery Eine systematische Galerie mit detailierten Beschreibungen von mathematischen Grafiken. Parkettierungen, Musterungen, Kurven, Schleifen. Tom Longtin - 3D Modeling, Visualization and Illustration

83. Space Spacial Patterns fractals fractals From CoolMath4Kids. Pattern Blocks TessellatedPolyhedra Nets to print from Invesigating Patterns by Jill Britton. http://www.argotlibrary.com/maths_space.html

General Sites Number Measurement Problem Solving Space Geometry Fractals Knots Online Activities ... Geoboard using manipulatives Year 4: Place an object on a grid, using columns and rows. Year 5: Relate perimeter and area of rectangles, using manipulatives and diagrams. Year 6: Estimate and measure angles, using a circular protractor. By Craig Loewen, University of Lethbridge, Alberta. Geometry All About Geometry Contains geometry facts covered in K8 math courses. Each page has an explanation, interactive practice and challenge games about geometry. Includes Area, Perimeter and Circumference, Surface Area, and Volume of solids Geometry Comics To help us keep our sense of what is really important Geometry Online Activities Geometry Online Activities From the National Council of Teachers of Mathematics (US). Grades PreK - 2 Grades 3 - 5 ; and Grades 6 - 8 Each level contains an annotated links list of 18+ online interactive activities. Geometry Online Manipulatives From the National Library of Virtual Manipulatives for Interactive Mathematics Pre-K - 2 Includes: Geoboards; Ladybug Leaf and Mazes; Platonic Solids; Pythagorean Theorem; Similar Triangles; Tessellations; and Transformations - Composition and Isometry

84. Books fractals. fractals The Patterns of Chaos A New by John Briggs. Chaosand fractals New Frontiers of by HeinzOtto Peitgen, Dietmar Saupe. http://geometricarts.freeyellow.com/books.htm

Welcome to my little bookshop.I have tried to compile some useful books to help you to enrich your understanding of geometry and to get full enjoyment out of this wonderful arena: Geometric Arts. Good hunting! Index Op art (optical art) Escher Geometry Fractals ... Geometrical Patterns Fractals Fractals : The Patterns of Chaos : A New... by John Briggs Scientists have discovered that systems in transitional states between order and chaos possess certain patterns with unique, predictable qualities. These patterns are called "fractals." In essence, they are visual images or pictures of chaos at work. Now comes a breathtaking visual tour of this exciting new scientific frontier. 207 photographs, 178 in full color; 49 line drawings Chaos and Fractals : New Frontiers of... by Heinz-Otto Peitgen, Dietmar Saupe Fascinating and authoritative, Chaos and Fractals: New Frontiers of Science is a truly remarkable book that documents recent discoveries in chaos theory with plenty of mathematical detail, but without alienating the general reader. In all, this text offers an extremely rich and engaging tour of this quite revolutionary branch of mathematical research. The Computational Beauty of Nature :...

85. Links The Four Types of Symmetry in the Plane, fractals Popularized and immortalizedby a Dutch artist MC Escher, who died only recently. Books on fractals. http://geometricarts.freeyellow.com/link.htm

With the increasing amount of new websites dealing with geometry pouring into the cyberspace every day, I have tried to compile some noteworthy sites that gives me some sort of serendipity. I do hope that you find them intriguing, too. If you have good noteworthy sites that should be listed here or have any problems with the links above? Please report it here. Table of Contents Geometric Sculptures Optical Art Geometrical Patterns Fractals ... Miscellaneous Geometric Sculptures: These are the sites I draw enormous pleasure out of. They deal with unusual mathematical sculptures that titillate your imagination. I am personally inspired by some of their works. Brent Collins For many years, Collins has created sculptures composed of saddle surfaces George .W Hart A sculptor of constructive geometric forms John Robinson Symbolic Sculpture Carlo H. Sequin

86. Polyhedra, Platonic Solids, Polytopes http://astronomy.swin.edu.au/~pbourke/polyhedra/

Polyhedra, Platonic solids, Polytopes -> M a i n I n d e x Waterman Polyhedra [Steve Waterman] Star Sphere and Polar Sphere Combined ) [Dan Thomasson] Rhombic Triacontahedron Coordinates for regular polyhedra Parallelohedron Polyhedra that fill space (without holes) using only translation Platonic solids and their measured properties To see a World in a Grain of Sand, And Heaven in a Wild Flower Hold Infinity in the palm of your hand, And Eternity in an hour William Blake Photographic contribution [Gayla Chandler] Build your own Polyhedra Use these templates (postscript and gif files) to build polyhedra out of cardboard. 3D Polyhedra in Super3D geometry format A large collection of polyhedra in a format that's easy to convert into your favourite format. Regular polytope (platonic solids) in 4D Geometric descriptions for all 6 plaonic solids in 4 dimensional space. 4D Objects in VEF format Index Geometry formats Data Formats Fractals, Chaos Rendering Radiance PovRay OpenGL Modelling Terrain Geometry Projections Curves Surfaces Polyhedra Stereographics Colour Textures Papers Analysis Skytower Albert Park Fun Puzzles Other for New: Fractal dimension calculator Chladni plate simulation Multiwall and offaxis projection Waterman Polyhedra Local Date/Time: Friday, 11-Apr-2003 10:14:49 EST

87. Fractals http://astronomy.swin.edu.au/~pbourke/fractals/

F r a c t a l s , C h a o s -> M a i n I n d e x Fractal Dimension Calculator - FDC Box counting software for the Macintosh and Linux. Ruler or Compass Dimension Recurrence plots I wonder whether fractal images are not touching the very structure of our brains. Is there a clue in the infinitely regressing character of such images that illuminates our perception of art? Could it be that a fractal image is of such extraordinary richness, that it is bound to resonate with our neuronal circuits and stimulate the pleasure I infer we all feel? P. W. Atkins Rendering Wada-type basins of attraction Here's a party trick for over Christmas. Get 4 large shiny Christmas balls, some coloured wrapping paper, some lights from the Christmas tree, and you have you own fractal laboratory to amuse yourself with over the festive season. Self similarity Examples of self similarity in fractals with examples from mathematics and photos of the physical world. Duffing Attractor Random Attractors Lorenz Attractor Rossler Attractor I believe the geometric proportion served the creator as an idea when He introduced the continuous generation of similar objects from similar objects. Johannes Kepler Henon Attractor Wallpaper Gingerbread man Henon Phase Diagrams The real world was full of larger structures, smaller structures, simpler and more complex structures than the tiny portion comprising sentient creatures and their societies, and it required a profound myopia of scale and similarity to believe that everything beyond this shallow layer could be ignored.

88. ENC: Curriculum Resources: Suzanne's Mathematic Lessons (ENC-011220, Full Record Also found at this site are interactive student lessons for investigating polyhedraand Mandelbrot fractals with Java Applets and four interactive games that http://www.enc.org/resources/records/full/0,1240,011220,00.shtm

Skip Navigation You Are Here ENC Home Curriculum Resources Advanced Search ... Ask ENC Explore online lesson plans, student activities, and teacher learning tools. Search Browse About Curriculum Resources Read articles about inquiry, equity, and other key topics for educators and parents. Create your learning plan, read the standards, and find tips for getting grants. URL: http://mathforum.org/alejandre/index.html ENC#: ENC-011220 Publisher: Swarthmore College Date: Grades: Languages: English; Spanish Abstract: Reviews and Awards: ENC Digital Dozen, June 1998. ( http://www.enc.org/features/dd/archive/0,,6-1998,00.shtm Additional information available at: http://www.enc.org/features/dd/about/ User Comments: None currently available. Add a User Comment for this resource. Record Created: Last Modified: Contents: Web workshop ideas page Web units Magic squares (Math, history, geography) Tessellations (Tutorials, math, connections) Interactive lessons and classroom activities Studying polyhedra Studying Mandelbrot fractals Traffic jam Bricks Locker problem Dominoes Technology in the classroom ClarisWorks graphing Bar graphs Pie charts Pictograms Exponential functions Linear functions Polynomial functions Reference page information Functions Mathematicians and scientists Number systems Patterns Math 7 introduction Unit 7 Unit 8 Unit 9 Unit 10 Unit 11 Unit 12 Interdisciplinary activities Curriculum links Math 6 course Math 7 course Math 8 course Suggestion box Home The collection Help desk Quick reference Search

89. ENC: Web Links: Digital Dozen: Archive: August 1996 links to other sites with fractals, how to make fractals, and teachers Virtual polyhedraGrades Kindergarten 12 Synopsis Welcome to this growing collection http://www.enc.org/weblinks/dd/archive/0,1577,8-1996,00.shtm

Skip Navigation You Are Here ENC Home Web Links Digital Dozen Archive ... Frequently Asked Questions Find detailed information about thousands of materials for K-12 math and science. Read articles about inquiry, equity, and other key topics for educators and parents. Create your learning plan, read the standards, and find tips for getting grants. Archive Current and past selections of exemplary sitesbrowse month by month through every year. When sites are no longer available, they are not listed as Digital Dozen winners. August 1996 A fractals lesson for elementary and middle school students Grades: Synopsis: This lesson plan includes links to other sites with fractals, how to make fractals, and teachers' notes. (For more details see Brief ENC Record or Full ENC Record Gryphon House Books Free learning activities Grades: Pre-kindergarten - 6 Synopsis: Come here to find great activities from Gryphon House's catalog of books for children. (For more details see Brief ENC Record or Full ENC Record Classrooms of the 21st century Grades: Kindergarten - 12 Synopsis: This site serves as an excellent introduction to using alternative assessment in science.

90. 3. The Five Platonic Fractals Transition probabilities 3. The Five Platonic fractals. As we notedabove, different values of give different fuzziness. To produce http://www.cassiopaea.org/quantum_future/papers/qfract/node10.html

Next: 1. Tetrahedron Up: Quantum Jumps, EEQT and Previous: 5. Transition probabilities 3. The Five Platonic Fractals As we noted above, different values of give different fuzziness. To produce representative pictures, one for each solid, we adjusted so that, as a rule, the more vertices, the higher value of - thus higher resolution of details. While rendering the pictures, for obtaining grayscale value for a given picture we were using either the formula or, to get more details at the peak values, even Subsections 1. Tetrahedron 2. Octahedron 3. Cube 4. Icosahedron ... 6. Other Polyhedra ark@cassiopaea.org

91. Reference Links On Geometry And Fractals - Tech Observer Tech Observer Kenneth Hunt January 30, 2003 Reference Links On Geometryand fractals Paul Bourke Personal Pages Comprehensive http://kennethhunt.com/archives/000591.html

Tech Observer Kenneth Hunt January 30, 2003 Reference Links On Geometry and Fractals Paul Bourke - Personal Pages Comprehensive collection of pages on fractals, geometry and various terrain and rendering issues. I hope you find what you're looking for or something else that interests you. These pages come in a number of flavours: reports on projects I've been involved in, notes that I've put on the WEB instead of in a paper notebook, tutorials to assist others get started in various technical areas, papers that I've published or collaborated on, various image galleries, and finally some pages that are simply for amusement. Geometry formats Data Formats Fractals, Chaos Rendering ... Main Comments Post a comment Name: Email Address: URL: Comments: Remember info? Related Entries CAD package written in Python Mar 03, 2003 Blender 2.26 is out first GPL version Feb 13, 2003 OpenEXR is high dynamic-range 16-bit floating-point pixels format Feb 02, 2003 DivX 5.3 is out :: for Win32 Jan 25, 2003 JPhotoBrush Image Editing Tool :: java image manipulation Jan 19, 2003 Snowflakes from Fractal Patterns Dec 28, 2002

92. Grain Structures It was found out, that the stochastic net of Voronoi polyhedra satisfies the stereologicalprinciple of geometric model correspondence with the real object. http://siams.com/modeling/ngrgr/thdgr/default.htm

Up Developers Software Web-soft ... Gallery Categories: Close Packings Sintering Grain Structures Fractals ... Contact us Category: Grain Structures Three-Dimensional Geometric Monocrystal Structure. Authors: Alievsky D.M., Kamenin I.G., Kadushnikov R.M., Alievsky V.M. The problem is linked with building the three-dimensional geometric monocrystal structure in the material science. It was found out, that the stochastic net of Voronoi polyhedra satisfies the stereological principle of geometric model correspondence with the real object. The distribution law of the polyhedra characteristic sizes is linked with the spheres diameter distribution law. This law gives a possibility to perform the three-dimension statistical reconstruction of the microstructure in correspondence with the known function of the grain size distribution on the ground edge. Computer realization of these models allows to effectively perform the statistic analysis of the polyhedra structures with the purpose of checking their adequacy to the real materials and serves as an initial base for calculating the geometric structure for the material with the specified properties. We consider 2 kinds of skeletal model based on Voronoi polyhedra and 3D Delaunay triangulation. These geometrical concepts are some generalization of the classic concepts described, for example, in Preparata, Shamos, 1985. These models allow to transit from the set of spheres to polyhedral description of the system naturally.

93. Efg's Mathematics Page solids polyhedra www.georgehart.com/virtualpolyhedra/vp.html. Math html.polyhedra Database www.netlib.org/polyhedra/index.html. Geometery http://plum.ia.polsl.gliwice.pl/~DIP/efg/Library/mathematics.htm

Mathematics in look for Mathematics 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 Ask Dr. Math Have a K-12 Math Question? http://forum.swarthmore.edu/dr.math The Math Forum http://forum.swarthmore.edu Calculators Online Center Part II. Mathematics http://www-sci.lib.uci.edu/HSG/RefCalculators2.html Geometry Geometry (offline now because of a legal fight between CRC Press and Eric Weisstein) http://mathworld.wolfram.com/topics/Geometry.html Géométrie http://perso.wanadoo.fr/jpq/geometrie/index.htm Famous Curves http://www-groups.dcs.st-and.ac.uk/~history/Curves/Curves.html Geometry, Solid The 5 Platonic Solids and the 13 Archimedean Solids www.scienceu.com/geometry/facts/solids Polyhedra www.georgehart.com/virtual-polyhedra/vp.html Math Reference Tables math2.org (formerly Dave's Math Reference Tables) General, Algebra, Geometry, Trig, Discrete/Linear, Other, Stat, Calc, Advanced www.math2.org/index.xml

94. AM I'm sorry, but I can't provide any Escherlinks. Math art gallery VirtualPolyhedra See also fractals. Associations. See Organisations. Awards. http://cage.rug.ac.be/~hvernaev/catA-M.html

The Math Catalog: A-M A-M N-Z Algebra The Axiom of Choice (from the Math-FAQ) Pi ( History from the Math-FAQ The Gauss-Legendre Algorithm to compute digits of pi (a local version is behind this button) See also: Number Theory Topology Programs Analysis Famous Curves Some special numbers and functions (from the Math-FAQ) Archive See also: Nonstandard Analysis Programs Art All links to Escher I'm sorry, but I can't provide any Escher-links. Math art gallery Virtual Polyhedra See also: Fractals Associations See: Organisations Awards Fields Medal (from the Math-FAQ) Fields Medal (from the University of Toronto) Basics See: Elementary Biographies of famous Mathematicians Mactutor History of Mathematics The World Great Mathematicians Books See: Publications Calculus See: Analysis Chaos-theory Introduction to ~ See also: Fractals Combinatorics The Electronic Journal of Combinatorics See also: Games Commercial Cray MathPro Press (obsolete?) MathSoft MathWorks TCISoft Texas Instruments Competitions See: Contests Computer Programs See: Programs Contests Kiran's Math Page (contains links to Math olympiads and contests) Links to See also: Olympiads Definitions See: Glossary Dictionary See: Glossary Discrete Mathematics ~ index Materials in Dutch A newspaper-article about Fermat's Last Theorem University Of Nijmegen University Of Twente An excerpt from questions (mostly) from the Dutch Math Olympiad Pythagoras -magazine Education Prime numbers (introduction to number theory) Mega Math (elementary introductions to mathematical items, for educational purposes)

95. Mathematics For The Non-Mathematician but don’t be surprised if you’ll need to look elsewhere to find out what fractalsactually are. Peter R. Cromwell, “polyhedra,” Cambridge University http://math.bard.edu/bloch/biblionm.htm

Mathematics for the Non-Mathematician An Idiosyncratic Annotated Bibliography Ethan D. Bloch General A wonderful mix of mathematics, philosophy, history of mathematics, and what might be called the psychology of mathematics as currently practiced by working mathematicians. This is one of the few books that really shows a non-mathematical audience what it's like to do serious mathematics. The authors do get involved with philosophical issues most mathematicians do not get worked up about, and it's worth keeping that in mind when reading the philosophical parts. It's also worth slogging through any technical points for the overall richness of this book. Morris Kline, “Mathematics: A Cultural Approach,” Addison- Wesley, 1962. An outstanding book covering much of mathematics in both ancient and modern times. The book discusses historical and philosophical issues without neglecting more traditional mathematical ones. Some of the interesting chapters include 8 (Ancient Greece), 10 (Renaissance Painting), 11 (Projective Geometry) and 24 (Music). Read the rest of the book while you’re at it. Kline has a similar book in a Dover edition. Ivars Peterson, “The Mathematical Tourist,” W. H. Freeman, 1988.

96. Suzanne Alejandre - Fractal Links Basic fractal information for the math teacher or interested user, with Internet resources to expand your fractal knowledge. http://forum.swarthmore.edu/alejandre/workshops/fractal/fractal3.html

Suzanne's Math Lessons Fractals Suzanne Alejandre Magic Squares Multicultural Math Fair Polyhedra ... Tessellations What is a fractal? From the Fractal FAQ: "A fractal is a rough or fragmented geometric shape that can be subdivided in parts, each of which is (at least approximately) a reduced-size copy of the whole. Fractals are generally self-similar and independent of scale." "There are many mathematical structures that are fractals; e.g. Sierpinski triangle, Koch snowflake, Peano curve, Mandelbrot set, and Lorenz attractor. Fractals also describe many real-world objects, such as clouds, mountains, turbulence, and coastlines, that do not correspond to simple geometric shapes." This Fractal FAQ was created and edited by Ken Shirriff through September 26, 1994. The current editor is Ermel Stepp. Alan Beck writes: "Basically, a fractal is any pattern that reveals greater complexity as it is enlarged. Thus, fractals graphically portray the notion of 'worlds within worlds' which has obsessed Western culture from its tenth-century beginnings." Beck further explains that when we look very closely at patterns that are Euclidean, the shapes look more and more like straight lines, but that when you look at a fractal up close you see more and more details.

97. Saturday Morning Math Group: Previous Talks http://www.ma.utexas.edu/users/smmg/PreviousTalks.html

Saturday Morning Math Group Here is a list of talks and relevant links given in years past. Fall 2002 Schedule: Organizer: Heather Lehr September 14, 2002: RLM 4.102 Dr. Michael Starbird , "INFINITY: How to Count When You Run Out of Toes" For more information about infinity, visit Ask Dr. Math The Infinity Site , or Hotel Infinity October 12, 2002: RLM 4.102 Dr. Chaim Goodman-Strauss (the original founder of SMMG along with Karen Uhlenbeck), "Up to 1,000,000 Dollars in Prize Money Will Be Given Away!" (see the poster For more information on Game Theory, visit Clever Games for Clever People The Game of Life Another explanation of the Game of Life , and Gametheory.net for lots of games, links, resources, and more on game theory. November 16, 2002: RLM 4.102 Dr. Felipe Voloch , "Barcodes!" For more information on Barcodes and related topics, visit Dr. Voloch's barcode page Clocks and Modular Arithmetic Discussion Math Alive Modular Arithmetic , and info on Casting Out Nines December 14, 2002: RLM 4.102 Dr. Vrej Zarikian : "Infinite Sums" Spring 2002 Schedule: Organizer: Melissa Macasieb February 2, 2002:

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