Minicourse Descriptions An emphasis will be placed on creating fractals by repeating simple sets ofinstructions. Examine the mathematics of polyhedra that pack space cube, http://www.math.washington.edu/~nwmi/sum/summer2001/mini-contents.html
Extractions: Instructors: Will Webber and Ronda Webber In this minicourse we will look at the basic concepts in fractal generation. The topics will include fractal curves such as the Koch, Hilbert, and Peano curves, "Mandelbrot" sets, Julia sets, fractal dimension, iterated function systems, chaos and others. An emphasis will be placed on creating fractals by repeating simple sets of instructions. The activities will be hands-on and include stamping, folding strips of paper, cutting pop-up fractals, building 3-dimensional models, creating computer generations of fractals, and others. Instructors: Philip Mallinson with Carol Hattan You know very well what an angle is, what a straight line is, and how to measure angles and segments and areas in the plane. But suppose your universe is not a plane but a cone or a cylinder or a cube or a sphere? This minicourse invites you to extend the these basic notions to surfaces that don't look like a flat sheet of paper. You will build your own models and also use commercial products like the Lenart sphere. As well as opening a new world of geometry, geometry on the sphere is also very practical. After all, map makers need to flatten out the world for the pages of an atlas and navigators need to sail in straight lines. How do they do it? In the Footsteps of Escher: 3-D Puzzles that Tessellate Space
Minicourse Descriptions An emphasis will be placed on creating fractals by repeating simple sets of maxmin problems, nets for polyhedra, dynamic graphs linked to models, http://www.math.washington.edu/~nwmi/sum/summer2002/mini-contents.html
Extractions: Instructors: Will Webber and Ronda Webber In this minicourse we will look at the basic concepts in fractal generation. The topics will include fractal curves such as the Koch, Hilbert, and Peano curves, "Mandelbrot" sets, Julia sets, fractal dimension, iterated function systems, chaos and others. An emphasis will be placed on creating fractals by repeating simple sets of instructions. The activities will be hands-on and include stamping, folding strips of paper, cutting pop-up fractals, building 3-dimensional models, creating computer generations of fractals, and others. Materials for this fractal course are on the web at Will Webber's website Instructors: James King Art Mabbott Linda Thornberry A new version 4.0 of The Geometer's Sketchpad has appeared with new possibilities for authoring and graphing. This software is a powerful tool in any course named "Geometry", but this minicourse will focus how Sketchpad can be used in other math courses as well, including Integrated Math courses. Sketchpad can be used for visualization, experiment, modeling, and dynamic graphing. This course will demonstrate how Sketchpad can be used to study such topics as trigonometry, conics and projectile motion, centers of mass, complex numbers, max-min problems, nets for polyhedra, dynamic graphs linked to models, simulation of physical devices.
Connect-ME - Weblinks This Math Forum Unit offers links to various investigations of polyhedra. Many of these patterns are fractals. Fractal forms are ubiquitous in Nature, http://educ.queensu.ca/connectme/weblinks/strands.htm
Hop's Gallery Kepler fractals Some Koch like fractals based on Kepler s polyhedra PerspectiveStudy Including some of MC Escher s observations http://www.clowder.net/hop/
Extractions: Abstract. Slavik Jablan reviews the second edition of Jay Kappraff's Connections: The Geometric Bridge between Art and Science for the Nexus Network Journal, vol. 4, no. 4 (Auturmn 2002). Book Review Jay Kappraff, Connections : the Geometric Bridge between Art and Science. 2nd edition. (Singapore: World Scientific, 2002). To order from Amazon, click here Reviewed by Slavik Jablan I n 1990, when the first edition of Connections The preface to the second wdition describes the fundamental changes that have occurred in the field since 1990: the ease of computer visualization; the communication through the internet; electronic math/art journals ( Nexus Network Journal Visual Mathematics ); new access to software which explores fractals, tessellations, polyhedra, and minimal surfaces; building kits (Zometool Geometry) and other constructive materials. Five new sections have also been added focusing on star polyhedra and their connection to the snub figures. Some new discoveries of the design scientist, Haresh Lalvani, have been included along with some material on the Buckminsterfullerene. In the 1990's, after the pioneering contributions of A.L. Loeb to the field of Design Science and the publication of the first edition of
Fractal Resources Fantastic fractals (Features an interactive Fractal Explorer for several different George W. Hart s Virtual polyhedra, Vladimir Bulatov s polyhedra 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) Fractals Unleashed (in English, Russian, or Ukrainian) Also has a "kid's section" and a wide variety of interactive features and many other resources. 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
Mainframe and VRML displays of complex polyhedra (including kaleidoscopic polyhedra), fractals Unleashed cited above also includes a similar application. 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).
DISCUSSIONS INDEX Plane Figure fractals, Compares fractals with one and two dimensional generators . polyhedra, Questions about dice lead to a discussion of polyhedra and http://www.shodor.org/interactivate/discussions/
Extractions: These discussions are designed to give teachers ideas for how to introduce or explain a concept with a student or with a class. Informal and formal definitions of concepts as well as common student misconceptions are included in the dialogue. These discussions are best accessed from the lessons in which they are used, but are listed here for quick reference. Teachers who develop discussions similar to these for other topics are encouraged to submit them to the Project Interactivate. Use this form to contact the Interactivate Team for details. They are arranged according to the NCTM Principles and Standards for School Mathematics Number and Operation Concepts Geometry and Measurement Concepts Function and Algebra Concepts ... Search Interactivate Number and Operation Concepts Discussion: Description: Integers Introduces the concept of an Integer. Integer Addition and Subtraction Introduces the Addition and Subtraction of Integers. Integer Multiplication Introduces the Multiplication of Integers. Integer Division Introduces the Division of Integers.
Shiki.archive.9512: Fractals polyhedra are not fractals. There are two notions of dimension in geometry (in fractals are mostly irregular, and they are never as simple as polyhedra. http://haiku.cc.ehime-u.ac.jp/~shiki/shiki.archive/html/9512/0172.html
David's Links Page polyhedra, fractals, chaos, curved surfaces, loops, interference, tilings big gallery with explanations of the works. http://davidf.faricy.net/links.html
IDE Corp. - Innovative Designs For Education This WebQuest is, essentially, an onlineassigned report on fractals. Not veryhigher order, Looking for interesting activities to explore polyhedra? 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. Algebra Active Algebra
Xah: Great Math Programs PDF on various geometry topics on curves, surfaces, comlex mappings, fractals . You can see how some polyhedra can be generated by mirroring tiles in http://www.xahlee.org/PageTwo_dir/MathPrograms_dir/mathPrograms.html
Extractions: If you spend more than 30 minutes on this site, please send $1 to me. Go to http://paypal.com/ and make a payment to xah@xahlee.org. Or send to: P. O. Box 390595, Mountain View, CA 94042-0290, USA. â back to Xah's home Xah Lee. Last major update: 2004. This is a list of fun math programs i have played over the years. They are mostly shareware or freeware. For Mac, Windows, or Linux. A star sign â means it is an excellent software that can be enjoyed without any math study. If you think your program should be listed here, please submit a copy for review. (email me first). There are about 700 unique visitors to this page each week. Graphing Calculator by Ron Avitzur. Imagine your hand-held graphing calculator with the power of a desktop computer, then you get the idea of what this program is about. Out of 10 or 20 programs that plots curves and surfaces i've tried, I think this is the best. Most versatile and most easy to use. Go download a demo and see for yourself. If you want a plotting program for your highschool or college installation, I suggest this one. URL: http://www.nucalc.com/
Mathematics For The Non-Mathematician Something of a modern classic by the man who helped develop fractals into an There is a wealth of historical information on the study of polyhedra, http://math.bard.edu/bloch/biblionm.htm
Extractions: 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. 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 youre at it. Kline has a similar book in a Dover edition. Ivars Peterson, The Mathematical Tourist, W. H. Freeman, 1988.
Spidron System ÷ Polyhedra 1. General Concept 2. Tilings 3. Reliefs 4. fractals and Variations. 5.polyhedra. 6. Dissections 7. Spacefilling 8. Transformations 9. Extra. http://www.szinhaz.hu/edan/SpidroNew/polyhedra.htm
Spidron System ÷ Fractals And Variations 1. General Concept 2. Tilings 3. Reliefs. 4. fractals and Variations. 5.polyhedra 6. Dissections 7. Spacefilling 8. Transformations 9. Extra. http://www.szinhaz.hu/edan/SpidroNew/fractals.htm
Mathematics Archives - Topics In Mathematics - Geometry Ford s touching circles, Isoperimetric Theorem and Inequality, fractals,Napoleon s Theorem, Ptolemy s Theorem, Regular polyhedra and Euler s Theorem, http://archives.math.utk.edu/topics/geometry.html
Extractions: ADD. KEYWORDS: Two Dimensional Tilings, Three Dimensional Tilings, Face-Transitive Tilings, Periodic Delone Tilings, Orbifold Graphs, Classification of 3-Dimensional Tilings, Tiling Space by Platonic Solids, Enumeration of Polyhedral Crystal Structures The Computation of Certain Numbers Using a Ruler and Compass
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.
Double Helix Mathematics Websites Dynamical Systems and fractals www.math.okstate.edu/~wrightd/ Systems andTechnology Project, fractals, Math in Daily Life, Paper Models of polyhedra http://www.csiro.au/helix/websites/maths.shtml
Extractions: Like to surf to some cool science sites? Below are some of the links that have appeared in past issues of The Helix and Scientriffic . Some of our particular favourites are marked with a Is based on the 1970's IBM film Powers of 10. You begin your journey 10 million light years from our solar system and finish it face-to-face with a proton. Exercise your brain with puzzles and brain busters. This site includes an arcade section, brainy games, mental madness, fantasy games and strategy and board games. Its sure to keep you busy for hours! Cricinfo www.cricinfo.com/
Alexa - Browse: Chaos and Fractals Search in Chaos and fractals Shows how to create fractal mountains,threedimensional Mandelbrot and Julia sets, convex, stellated and polyhedra. http://www.alexa.com/browse?&CategoryID=26913
