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         Polyhedra Fractals:     more detail
  1. 2009 Joint Mathematics Meetings Exhibition of Mathematical Art
  2. 2008 Joint Mathematics Meetings Exhibition of Mathematical Art

61. Références Thématiques Sur Internet
Chris Fearnley's polyhedra Gallery. Fractales. software pour mac/ fractalshttp//archives.math.utk.edu/software/mac/fractals/.directory.html.
http://www.bcr-caillaud.org/artcomputer/visite/v3.html

62. POLYHEDRA
Returning this series to an octohedron three times the edge lengthof the starting octohedron. Selfrepeating, like fractals. MPEG
http://www.pandragon.com/polyhedra/tetraocto.html
Tetrahedra and Octohedra
Close packing tetrahedron and octohedron begin with an octohedron.
Adding a tetrahedron to each face of the octohedron produces a stellated octohedron.
Continuing to added octohedron to tetrahedron and tetrahedron to octohedron produces a quasi Cubo-octohedron (missing square faces).
Returning this series to an octohedron three times the edge length of the starting octohedron. Self-repeating, like Fractals.
MPEG- 141 kbytes

AVI(1.1meg) of Close Packing Tetra/Octo

VRML2.0 (1.4 megabytes) Animation

CAUITON: You must have a Vrml viewer that supports animation like Worldview

63. Geometric Figures, Math And Chaos Links
for its animations of Sierpinski's Triangle and clear descriptions of other fractals. polyhedraPastimes is a great links page about polyhedra and Tesselations
http://ebeltz.net/niftylinks/mathlinks.html
Geometric Figures, Math and Chaos Links
Build Platonic Solids by copying these patterns or use the links below for more help. Click here for a printer-ready .pdf file.
Volume and Surface Area of Platonic Solids Shape # of sides Volume (Cubic Inches) Surface Area (Square Inches) Tetrahedron Cube Octahedron Dodecahedron Icosahedron Sphere infinite
Links

64. Jim Blowers' Workshops At SUUSI 2002
2. The second Three Hats problem 3. Polytopes (I showed the class how to weave polyhedra,thus bringing part of that workshop into this one) 4. fractals 5. The
http://jimvb.home.mindspring.com/MyShops2002.htm
My Own Workshops I gave only two workshops this year; Weaving Paper Polyhedra was not offered. But the two workshops I gave had some interesting moments. 210 SUUSImatics This workshop will show that mathematics is fun, beautiful, and at times uncertain, using as examples fractals, fibonacci numbers, magic and Latin squares, paradoxes, and examples from SUUSI itself, such as the mathematics behind contra dancing, and other topics. This workshop includes both lecture and participatory exercises. Recommended Reading: http://www.mindspring.com/~jimvb/ mathematics.htm Jim Blowers earned his Ph.D. in Mathematics at Northwestern University in 1972. He has always approached mathematics as something that is fun to do and would like to deliver some of that enthusiasm to others. The topics I covered this year were: The Monty Hall problem.
The second Three Hats problem

3. Polytopes (I showed the class how to weave polyhedra , thus bringing part of that workshop into this one)
Fractals

The Unexpected Math Quiz
(no, there are no quizzes at SUUSI. I simply explain part of life at Virginia Tech when SUUSI is not around.)

65. Math Education Resources
A good website for instructors who would like to introduce their students to fractals. polyhedrals Welcome to my personal pavilion of practical polyhedra!
http://libweb.sonoma.edu/search/web/math.html
Skip Navigation Library Catalog
Web Searches

Library Collections
... University Library Search for Information Subject Guides to Web Resources Math Education Resources
Math Education Resources
The world wide web sites listed below were collected by Mary Anne Sobieraj and Jeff Silverman for the Math Colloquium Series at Sonoma State University. Use these sites as a starting point for your own web research.
General Math Sites and Subject Indexes
    Mathematical Association of America - MAA organizational information as well as links to professional development workshops via the Web, their Interactive Teaching Exchange, and much more. Mathematics by Nerd World Media (tm) - A great subject index and links to topics in calculus, geometry, statistics, etc. Math Forum - wonderful resource for all aspects of math education, including specific lesson plans for K-12 through college and advanced math, as well as links to issues of interest and concern for math educators and the mathematics community in general. Includes Dr. Math, which allows students (elementary school through college level and beyond) to e-mail questions to Dr. Math and receive answers in response. The math doctor(s) are in reality math students from Swarthmore college who enjoy answering math questions. World of Mathematics - a "comprehensive, and interactive mathematics encyclopedia intended for students, educators, math enthusiasts, and researchers."

66. Mathematics Homework
of circles spheres, fewest colors, combinatorial geometry, fractals, geometricmodels Paper Models http//www.georgehart.com/virtualpolyhedra/paper-models
http://www.litch.com/library/HomeworkSites/MathHomework.htm
Mathematics GO TO: Arithmetic
Golden Mean
History of Mathematics
ARITHMETIC: Figure This! Math Challenges for Families
http://www.figurethis.org/index40.htm
Twenty-two word problems that really make you think, including "Line Up", "Beating Heart", "Fill It Up", and "Upside Down". Explains how to think through and solve each of the problems. Flashcards for Kids
http://www.edu4kids.com/math/
What is 2 - 6 + 3? Practice addition, subtraction, multiplication, and division at this site. FunBrain.com
http://www.funbrain.com/
"Math Baseball" and "Math Car Racing" are only two of the 30 educational games you can play at FunBrain! Math Forum - Ask Dr. Math - Elementary School Level
http://forum.swarthmore.edu/dr.math/drmath.elem.html
How-to's and problems in addition, subtraction, multiplication, division, place value, fractions, decimals, the "Golden Rectangle", geometric shapes, square roots, units of measure, puzzles, and word problems are at this math mega site. Math League Help Topics
http://www.mathleague.com/help/help.htm Definitions and explanations of whole numbers, decimals, fractions, statistics, geometry, ratios, percentages, measurements, beginning algebra, and positive/negative numbers for kids in 4th through 8th grade.

67. Mathematics Archives - Topics In Mathematics - Geometry
Generalizations, Ford's touching circles, Isoperimetric Theorem and Inequality, fractals,Napoleon's Theorem, Ptolemy's Theorem, Regular polyhedra and Euler's
http://archives.math.utk.edu/topics/geometry.html
Topics in Mathematics Geometry

68. S.T.A.R. ---- Student Teacher Academic Resources
Resources fractals; JAVA 3D Viewer; Mandelbrot and Julia Set Explorer; MandelbrotExplorer; Origami Mathematics Homepage; Periodic Functions; Play a Piano; polyhedra
http://coe.etsu.edu/department/cuai/starlinks/math.htm

COE Home

Choose a quick link COE Home ETSU Home About COE Quillen Chair University School Accreditation Contacting COE Calendar of Events Alumni Early Childhood Ed STUDENT TEACHER ACADEMIC RESOURCES (S.T.A.R.)
- Categories of Educational Resources General Math Algebra Calculus

69. Math Forum Internet Collection - Mathgraphics (Outline)
Origami and Mathematics; Pascal's fractals Ivars Peterson (MathLand); Pavilionof The Platonic Solids and polyhedra - Paul Flavin; Point Plots and Space Curves
http://math.kongju.ac.kr/math/java/Java/mathgraphics.html
    Math Forum Internet Resource Collection - Outline Version
Math Graphics and Visualization
[Switch to the Annotated Version
About the Collection
Table of Contents Search the Collection ...
  • The Chryzodes: a pictorial travel into science of numbers (arithmetic).
  • Chua's Oscillator: Applications of Chaos to Sound and Music
  • Circles of Light: The Mathematics of Rainbows (Gallery of Interactive Geometry)
  • Classification of Patterns
  • The Click-n Project
  • Cliff Pickover's Creativity and Math Page ...
  • The Fractint PAR Exchange - Landon Kuhn
  • Fractint WWW
  • The Fractory - The Science and Beauty of Fractals
  • FracZoom
  • Fun with Fractals - Keith Gabryelski
  • Gallery of Fractal Images - Paul Bourke ...
  • Math Teacher Link - a NetMath Coalition Project
  • MathArt
  • Mathematica Demo
  • Mathematical Animation Gallery
  • Mathematical Java Applets - Gamelan
  • Mathematical Visualizations, Interacting with surfaces in 4-D by David Banks ...
  • MathLab 95
  • MathMadness Screen Savers for Windows and DOS
  • MathMol - K-12 Mathematics and Molecules
  • Maths Net
  • Maths with Photographs
  • MathsNet ...
  • Robotic Navigation with Constraints - Level Set Methods (Sethian)
  • Room 8 Geometry Book - Riverside Elementary, Princeton, NJ
  • Rubik's Cube: Our robot can play with The Cube!
  • 70. Internet Resources For Use In Mathematics Classes
    you to change the rules and make your own fractals. The Geometry Center offers activitiesin the following areas Triangle Tilings and polyhedra, Symmetry and
    http://www.internet4classrooms.com/math_topic.htm

    Daily Dose of the Web
    Links for K-12 Teachers On-Line Practice Modules Mathematics Topics
    submit a site Top 10 General Math Elementary ... Secondary Topical
    Links verified 2/19/03 Mathematics activities related to:
    • Number Sense, Concepts, and Operations
    • EdHelper.com offers a wide range of fraction worksheets. Each time you request a worksheet an entirely new set of problems is generated. Fractions - This math review is targeted toward those individuals who have forgotten what they once knew about fractions. You may need the entire review or just portions of the review. Subjects covered are: Simple Fractions Complex Fractions Compound Fractions Decimals ... Percentage and Rules Multiplication: An Adventure in Number Sense - Multiplication tips; click on any underlined fact on the table to learn about a reason why you do not have to memorize it. You should also check out the multiplication index for other valuable information. Plane Math Activities - Aviation related math activities requiring genuine real world application. There are nine excellent lessons here. Check this out! But wait! That's not all! If you have

    71. Chaos And Fractals
    Mandelbrot and Julia sets, convex, stellated and polyhedra. Uses tiny Java1.1 appletsand VRML worlds. Category Science Math Chaos and fractals http//www
    http://www.ad.com/Science/F/__Fractals/
    search
    Top
    Categories:
    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.
    Category: Science > Math > Chaos and Fractals
    http://www.3dfractals.com/
    A Sketchbook on L-systems
    Modeling and visualization of plants using parametric L systems.
    Category: Science > Math > Chaos and Fractals
    http://coco.ccu.uniovi.es/malva/sketchbook/
    An Introduction To Fractals
    Gives definition and explains the different types of formulas used. Includes illustrations and bibliography. Category: Science > Math > Chaos and Fractals http://www.swin.edu.au/astronomy/pbourke/fractals/fracintro/ Aunty Pear's Art of Heart Features basic, Sterling and Photo Impact tutorials. Also has graphic sets and calling cards.  Category: Science > Math > Chaos and Fractals http://auntypear1.topcities.com/menu.htm Cassiopaea Explains how quantum jumps generate new family of fractals on the spherical canvas S^2. Includes graphics of the five Platonic fractals in several formats. Category: Science > Math > Chaos and Fractals http://www.cassiopaea.org/perseus/qfractals.htm

    72. Listings Of The World Science Math Chaos And Fractals
    Added Nov27-02; Interactive 3D fractals Post Review Shows how to create fractalmountains, 3D Mandelbrot and Julia sets, convex, stellated and polyhedra.
    http://listingsworld.com/Science/Math/Chaos_and_Fractals/

    73. Mathematical Miscellany Centre For Research In Mathematics Education - Southampt
    Combinatorial Geometry, Covering and Packing, Dissection, fractals, Geometric Models NearestNeighbors and Voronoi Diagrams, Origami, polyhedra and Polytopes
    http://www.soton.ac.uk/~crime/miscellany/
    MATHEMATICAL MISCELLANY
    The Calculus Hater's Home Page In the summer of 1665, Isaac Newton first came up with the idea of calculus, after being hit over the head with a soft, blunt object. If it had been a hard blunt object, he may have forgotten the whole idea, and thus would have saved millions of college students from much excruciating pain and suffering. Unfortunately he didn't, and after publishing most of his findings, suffered a nervous breakdown in 1693. This page has some good calculus links
    Chaos: A pictorial introduction. This presentation illustrates some essential features of the theory of "chaos" which has received media attention in recent years. It also tells the story of a contribution to the theory by the School of Mathematics at La Trobe University. This pictorial introduction is best viewed by a web browser that supports gif animations. The presentation was devised by John Banks . See, also, this department's Quicktime movies of surfaces . Quicktime movie viewers for Macintosh OS and Windows are downloadable via this site.
    This is a National Science Foundation sponsored project designed to help secondary school and college teachers of mathematics bring contemporary topics in mathematics (chaos, fractals, dynamics) into the classroom, and to show them how to use technology effectively in this process. At this point, there are several interactive papers available. These are designed to help teachers understand the mathematics behind such topics as iterated function systems (the chaos game) and the Mandelbrot and Julia sets.

    74. Changes
    Resources by Topic Space - Chaos and fractals fractals - MathWorld. Resourcesby Topic - Space - polyhedra polyhedra contructed by Fr.
    http://michaelshepperd.tripod.com/changes.html
    Mathematics Resources
    Recent Changes and Additions Home Resources by Topic Calculators and Plotters Reference ... More Stuff 26 January

    Resources by Topic - Space - Symmetry
    Ambigrams
    Ambigram.Com - David Holst

    AmbiGallery

    Ambigram.Matic

    AmbiLinks
    ...
    links - Punya Mishra
    18 January
    Resources by Topic - Networks and queueing
    new page created Resources by Topic - Numbers Skillswise Number Quizzes - BBC Resources by Topic - Space - Chaos and fractals Fractals - MathWorld Resources by Topic - Space - Symmetry Dream-Catcher Mandalas - Louis Talman Resources by Topic - Space - Symmetry patterns / Groups Pattern - Course from Dartmouth College Resources by Topic - Space - Tessellations Student Tessellations - links Reference Michigan Teacher Network Learning Technology - Web tools new page created 9 January Resources by Topic - Groups drawing friezes with LOGO two colour friezes - Slavik Jablan Symmetry and Ornament - Slavik Jablan Discrete Plane Symmetry Groups - Ana Kozomara ... photos - Clifford Reiter Resources by Topic - Space - Symmetry photos - Clifford Reiter Reference 7 January Resources by Topic - Groups plaster friezes - Felber Ornamental Plastering Corporation SculptStone Friezes - Pineapple Grove Designs woven rope friezes - Nils Kristian Rossing frieze applet - Frank Farris ... 17 wallpaper patterns - Escher Resources by Topic - Space - Symmetry plaster rosettes - Felber Ornamental Plastering Corporation plaster ceiling medallions - Felber Ornamental Plastering Corporation The Doors in Al-Hoceima (and other works) - Tim Backhouse Reference

    75. Algorithmic Art
    BACK. References and links. Introducing fractals By Cynthia. Spiglette’s fractals.Wallpaper Groups. Index Of polyhedra. Paper models Of polyhedra. Escher Gallery.
    http://www.pythagoras.org.uk/page76.html
    Algorithmic Art
    Home Page

    Tutorials

    Virtual Art Gallery
    ... References and links
    Stanley Spencer’s Web Site
    Stanley J Spencer
    Last updated
    January 2003
    NEXT
    BACK
    References and links Introducing Fractals By Cynthia Spiglette’s Fractals Wallpaper Groups Index Of Polyhedra Paper models Of Polyhedra Escher Gallery Whitwell The Centre of the Universe But not as we know it Jim Proofs For Pythagoras References 1. Fractals images of Chaos - Hans Lauwerier A good read. A comprehensive introduction to fractals. A good source of geometric ideas. A book I often dip into and re read. 2. The Penguin Dictionary of curious and interesting Geometry - David Wells Again, a good source of ideas from the world of geometry. Each section contains a list of references for further reading. I always take this on holiday. A good source of basic geometry and other mathematical work. 4. http://mathforum.org/dr.math/ for the Golden triangle 5. The Internet, generally is a good source of ideas and information. Plug in the key words into a search engine and follow up the leads. Algorithmic Artists

    76. Àú³Î ¼öÇлç¶û 19È£ ƯÁý Çлýµé°ú ÇÔ²²ÇÏ´Â CA¼
    Java Plot3D http//www.frontiernet.net/~imaging/pythagorean.html; Self-Similarityhttp//math.rice.edu/~lanius/fractals/self.html; polyhedra http//www.nirim.go
    http://www.mathlove.org/doc/journal2/text/19-01.html
  • Michael Serra, ¡ºDiscovering Geometry¡», Key Curriculum Press]
  • Activities for Junior High School and Middle School Mathematics, Vol.1, Vol.2, NCTM
  • 1. Åʱ׷¥(Tangram)
  • 77. Tarquin Maths Making Three Dimensional Shapes
    This splendid book gives photographs and templates for all known polyhedra and isa Fractal Cuts Exploring the magic of fractals with popup designs 0 906212
    http://www.tarquin-books.demon.co.uk/books/tarquinmathsmaki.html
    Making Three Dimensional Shapes Send for our illustrated catalogue Mathematical Models Children love making these beautiful shapes which are such fun to decorate. Each model is printed on crisp white paper ready to cut out and glue together. There are at least 12 hours of enjoyment in each book and the finished models make a fine collection. There are plenty of suggestions and ideas for colouring and decoration. Make Shapes - Book 1
    19 simple models
    Make Shapes - Book 2
    8 larger models
    Mathematical Curiosities
    To cut out and glue together
    1 899618 35 X All the colourful models in this collection, when cut out and glued together have curious and interesting properties. Some rotate, some fold and unfold, some twist and others fit together in unexpected ways. All illustrate mathematical ideas in an amusing and interesting fashion. Also included is a minibook which gives background information and further ideas. More Mathematical Curiosities
    To cut out and glue together
    A further collection of colourful models offering insights into mathematical concepts and including a minibook of background information and ideas.

    78. Math Sites
    Web Gallery of Interactive Geometry. Interactive fractals; Interactivate GeometryActivities; PBS Teacher Source - High School Geometry; polyhedra; Probability
    http://cte.jhu.edu/techacademy/web/2000/heal/siteslist.htm
    Games More Fun Puzzles Problems Algebra Sites

    79. Math
    activities and curriculum resources. Links include Calculators, fractals,polyhedra and Place Values. http//convertit.com. Convert It.
    http://www.bhsu.edu/education/edfaculty/lturner/Math.htm
    Math Abacus Algebra Fractals Fractions ... Statistics
    ABACUS
    http://www.ee.ryerson.ca:8080/~elf/abacus The Abacus. (5+) This site provides information and instruction on using the Chinese abacus to do addition and subtraction. There are also related links to other abacus sites.
    ALGEBRA
    www.algebra.com Algebra Homework Help Center Algebra and math homework online. Pre-algebra, Algebra I, Algebra II. Numerous solvers with Work shown. Links to great algebra lessons. Interactive solvers for algebra word problems. Ask questions on our question board. www.algebra-online.com Algebra Online. (9-12) Algebra Online SM is a free service designed to allow students, parents, and educators throughout the world to communicate. This includes free private tutoring live chat , and a message board , among many other features. Questions and discussions relating to all levels of mathematics (not just Algebra) are welcome. Algebra Online SM is the future in education. http://forum.swarthmore.edu/sum95/sinclair/alg1.html Algebra Resources. (9-12) This site offers algebra lessons and activities and provides links to computer resources for teaching algebra.

    80. Add A Maths Link
    Jump Maths General Schools University General Education fractals Homepages Other Worksheet Factory UK; Three puzzles with polyhedra and numbers;
    http://www.mathsisfun.com/links/links.htm
    HOME All Pages A - Z Listing Maths Menus Handling Data Miscellaneous Maths Help Discussion Forum
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    Puzzles Calculators TI Calculators Computer Programs Winlogo Programs Links Add a link
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    Add Your Favourite Maths Pages
    Below is a free for all list of links meaning you can add anything you please. Add your favourite maths, schools, university or whatever sites. If this is your home site please add a link back to http://www.mathsisfun.com on your site. These links will be sorted periodically and the best will be transferred to a permanent link page.
    Due to recent abuse of this facility links may now be sent using the form below and I will add them manually. Last link was added on Thursday, May 6 2002 Title:
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