Math Forum: Alejandre: Math Lessons: Geometry draw reflections. Studying Mandelbrot fractals What is a fractal?A middleschoolers. Studying polyhedra What is a polyhedron? A http://mathforum.org/alejandre/geometrylist.html
Extractions: Suzanne's Mathematics Lessons aligned to the NCTM Standards - Geometry: Grades 6-8 Bricks Activity Classroom activity (also called the Masonry Problem; a variation on polyominoes) to be explored through manipulatives (dominoes). Students explore different possibilities of making brick walls with and without fault lines, using diagram, process, and solution in their problem solving. Crystals Students studying polyhedra enjoy seeing the structures as they occur in the real world. Crystalline structures can be categorized into seven crystal systems: see photographs of beautiful crystals or make paper models of crystals by printing out nets of crystals and constructing the models. CrystalMaker software gives students experience with ball-and-stick, space-filling, wire-frame, stick, dot surface cloud, and polyhedral models of crystals. Also Java applets that show some of the major forms for the hexoctahedralclass (symmetry 4/m3bar2/m) of crystals; and links to Web sites about crystals.
Math Forum: Suzanne Alejandre: Math Lessons polyhedra Speech Using KaleidoTile Quadrilaterals Regular Tessellations Sonya's SymmetryStudying Mandelbrot fractals Studying polyhedra Tangrams Tessellation http://mathforum.org/alejandre/index1.html
Ivars Peterson's MathTrek -Mathematical Art On Display store/html/index.html offers an introduction to mathematical art and a selectionof products related to tessellations, polyhedra, fractals, and much more. http://www.maa.org/mathland/mathtrek_11_4_00.html
Extractions: Ivars Peterson's MathTrek November 4, 2000 The term "mathematical art" usually conjures up just one namethat of Dutch graphic artist M. C. Escher (1898-1972). Many people are familiar with Escher's endless staircases, hyperbolic tilings, Möbius ants, intricate tessellations, and other creations. They may also be aware of the intertwining of mathematics and art during the Renaissance, with the development of perspective painting and eye-teasing stagecraft. A few might add the names of Piet Mondriaan (1872-1944), Salvador Dali (1904-1989), Victor Vasarely, or Frank Stella. But the realm of mathematical art is far wider and more diverse than most people realize. A surprising number of contemporary artists count mathematicsfrom Fibonacci numbers and the digits of pi to tetrahedra and Möbius stripsas the inspiration for their creations. For those fortunate enough to be in New York City, the exhibit offers a rich sampling of artworks inspired by mathematics, ranging from the gracefully curved sculptures of Brent Collins and tensegrity structures of Kenneth Snelson to the playful polyhedra of George Hart and the wavy painted grids of Doug Pedens. The show runs from Nov. 7 to Dec. 15, 2000, at the Cooper Union for the Advancement of Science and Art, Humanities Gallery and Brooks Design Center, Albert Nerken School of Engineering, 51 Astor Place, New York City (
IDE Corp. - Innovative Designs For Education the mood ), AND several different downloadable software programs to enable studentsto challenge themselves and create their own fractals!!! polyhedra Lighting. http://www.idecorp.com/link_math.htm
Extractions: Math Click here to return to Archive Links Table of Contents. Click here to see the current month's links. NOTE: The links provided here are suggestions only and have not been thoroughly reviewed for appropriateness in school. Educators should review a site before directing students to it. Remember that sites change frequently and might contain different content than on previous occasions. Authentic Math UBUYACAR
Extractions: For those of you with young children thought these might be helpful. (and fun) http://www.fastq.com/~jbpratt/education/mypages/flannelstories.html http://www.bright.net/~double/feltbo.htm Steve - Without an enemy's action, there is no possibility for patience or tolerance to arise. - The Dalai Lama http://www.ies.co.jp/math/java/comp/itoi/itoi.html Just jump right in here and see what you find. Math, and it's fun. Steve - Without an enemy's action, there is no possibility for patience or tolerance to arise. - The Dalai Lama
Relevant Links polyhedra, Transformation. Program You can make simple fractals, (Digital Cats) Demonstration screen saver A program for creating fractal animation (Filmer V2 http://moscow.cityu.edu.hk/~ma4527/links.htm
Xah: Great Math Programs A collection of mathematical programs, with particular reference to geometry.Category Science Math Geometry Software explanations. Poly (v.1.05, 1999/12) Poly is another interactive 3D programthat does polyhedra. This Trudeau. (1994). fractals. fractals http://www.xahlee.org/PageTwo_dir/MathPrograms_dir/mathPrograms.html
Extractions: back to Xah's home This is a list of fun math programs i have played over the years. Most programs are for Macintosh, but Windows program is also included. They are mostly shareware or freeware. A heart means excellent. Email me if you think a program should be listed here. 2002-11-25. 3D-FilmStrip for Mac OS X is out! It is now called 3D-XplorMath. This vesion includes some 50 PDF files explaining various math objects. Super. Thanks Richard Palais. 3D-XplorMath Home Page . Now there's also a Mathematica package that convert 3D-XplorMath surface files to Mathematica graphics. Please get it here: 3dxm.tar.gz (Use StuffIt or WinZip to decompress the folder.) Here's some screen shots: breather.png costa.png enneper.png inv_boy.png ... symmetric4noid.png 2002-11-21. I'm adding a few obscure computer algebra software for those in the computing industry: Octave is a high-level language, primarily intended for numerical computations. It is somewhat compatible with MatLab. FreeSoftware. Website: octave.org
Books On Special Topics He even relates fractals to art and architecture. Unit Origami (7up) Geometryof polyhedra; Graph Problems Tomoko Fusé; Japan Publications, 1990; $19 http://dimacs.rutgers.edu/Volumes/schools/paper82/node16.html
Extractions: Marcia Ascher; Chapman and Hall, 1991; $42. This is a fascinating book, which will give you a new perspective on mathematical ideas that one often takes for granted, such as the words used for counting. Of special interest is a chapter exploring Eulerian paths, a standard topic in discrete mathematics (e.g., see [ ]), as an artistic aid to story-telling in the South Pacific islands. This is the source of some of the material in the module Drawing Pictures with One Line , described on page . The following is an excerpt from a review by Susan Picker LP `90. But Ethnomathematics explores more than the topic of graph theory as it presents the mathematical ideas of number, kin relations, games of chance and strategy, and symmetric strip decorations. ...It provides a comprehensive look at the meaning and use of similar mathematical ideas in different cultures, illuminating both the mathematics and the culture in which it appears, and through this showing the value of the study of mathematics in a multicultural setting.
Index By Grade Level. Intro to Tessellations, *; Build Your Own polyhedra, *; UnitOrigami, *; fractals for the Classroom, *; Math/Human http://dimacs.rutgers.edu/Volumes/schools/paper82/node32.html
Extractions: Next: Index by topic. Up: Recommended Resources for Teaching Previous: Web Sites In this section, for each of the grade-level ranges K-2, 3-5, 6-8, and 9-12, we list the titles of resources described in the text whose content seems especially appropriate. Within each subsection, titles are ordered (approximately) by reading level. Each title is followed by the number of the page that contains its description. See Appendix B for unabbreviated titles.
Coolmath4kids -- GEOMETRY There a lots of cool polyhedra AND you can spin them around! What are fractals? byCynthia Lanius http//math.rice.edu/~lanius/frac/ Learn all about fractals. http://www.coolmath4kids.com/geometrymain.html
Quantum Jumps, EEQT And The Five Platonic Fractals 5. Transition probabilities. 3. The Five Platonic fractals 1. Tetrahedron; 2.Octahedron; 3. Cube; 4. Icosahedron; 5. Dodecahedron; 6. Other polyhedra. 4. Notes1 http://www.cassiopaea.org/quantum_future/papers/qfract/
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://homepages.borland.com/efg2lab/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
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
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
Mathematiques Et Geometrie En VRML VRML with Fields amp;amp;amp;Operators Lars Schumann VRML 2.0 - polyhedra polyhedrahttp//library.thinkquest.org/19387/3D.html fractals Newton's Basins VRML http://apia.u-strasbg.fr/vrml/ressources/domaines/maths.html
Hello Homework! Mathematics an introduction to fractals for middleschoolers. Paper Models - Paper polyhedrahttp//www.georgehart.com/virtual-polyhedra/paper-models.html Shows how to http://www.tds.lib.mn.us/HMath.htm
Extractions: Eighty word problems - in English and Spanish - for middle schoolers from the National Council of Mathematics Teachers and the U.S. Department of Education that don't just give the answers to the problems, but explain how to think them through and solve them. The problems focus on measurement (eg. "Line Up") , numbers (eg. "Beating Heart"), statistics and probability (eg. "I Win!"), algebra (eg. "Which Way?), and geometry (eg. "Popcorn"). FunBrain.com - Kids Center
Math Links Knots on the Web (Peter Suber); fractals An Introduction; Beauty of fractals;3d fractals! Number Theory. The Prime Pages. polyhedra other Geometry. http://www.cs.stedwards.edu/math/links.html
Hyperlinks For Geometry Studying Mandlebrot fractals (applet with GOOD interactive info) http//forum.swarthmore.edu/alejandre/applet.mandlebrot.html.Geometer's Sketchpad. polyhedra. http://euler.slu.edu/teachmaterial/hyperlinks_for_geometry.html
Extractions: (Courtesy Dr. R Freese) Contents: Experiment with Volume (simle worksheet, estimating volume) http://math.rice.edu/~lanius/Geom/cyls.html Volume Functions: (Worksheet)Calculating volumes http://math.rice.edu/~lanius/Geom/cyls2.html Geoboard Area : a worksheet exploring area. (Based on the geoboard) Designs with Circles: construction of circles (rotation and reflection symmetry) http://forum.swarthmore.edu/alejandre/circles.html Percentage Circle http://forum.swarthmore.edu/~sarah/shapiro/gsp.percent.circle.gif Nets of crystals: paper construction of crystals, polyhedrahttp://forum.swarthmore.edu/alejandre/workshops/crystalnet.html Systems of Crystals (type of crystals, and physical examples) http://forum.swarthmore.edu/alejandre/workshops/chart.html Real World - Viewing Crystals (applications of Tesselations in the real world) http://forum.swarthmore.edu/alejandre/workshops/crystal.html Isometric Drawing http://forum.swarthmore.edu/workshops/sum98/participants/sanders/Isom.html
Pop Quiz: Further Information For Question #5 on equilateral triangles are the pages about crystals; fractals, especially the SierpinskiTriangle and the Koch Snowflake (see below); and polyhedra (try the http://www.hamilton.net/subscribers/brian/popquiz/0005.html
Extractions: Another interesting thing about equilateral triangles is that they are also equiangular , meaning all three angles are equal as well. Since there are 180 degrees in a triangle, and all three angles are the same in an equilateral triangle, each angle of an equilateral triangle measures 60 degrees. An equilateral triangle is known as a regular polygon , since all its sides are equal and all its angles are equal. Equilateral Triangles in Everyday Life Equilateral triangles are found nearly everywhere. Examples include many everyday objects, landmarks, and symbols. The Greek letter delta, and our own letter A Formulas for Equilateral Triangles Several formulas exist which are useful in finding measurements of equilateral triangles and polyhedra which contain equilateral triangles. A few are given below. The area of any triangle is given by A bh where A is the area
Math 8 - Frisbie Middle School Building Math Power, polyhedra, Graphing and Functions, Linear and ExponentialFunctions, fractals and Chaos Theory, Applied Data Analysis. http://www.rialto.k12.ca.us/frisbie/math8.html
Extractions: Math 8 As part of the Rialto Unified School District, Frisbie Middle School is using the Glencoe instructional materials to teach mathematics. Math 8 is a general mathematics course for eighth grade students not enrolled in Algebra I. Under the Curriculum Links the alignment of the course can be checked against the RUSD Math Matrix, California Framework Standards, and the NCTM Standards. Links are provided to support the Math 8 curriculum for students, teachers and parents. Some of the links are to Internet sites with information, others link to sites with interactive lessons which could be used at home as a supplement or during class and still others could be used as enrichment for students willing to work before or after school. A similar Math 7 page is available for the general mathematics course for all seventh grade students. As you use these pages, comments and/or suggestions would be appreciated. Please send them to Suzanne Alejandre Math Matrix - RUSD RUSD Course of Study CA Academic Standards Commission California Mathematics Framework
