 The Butterfly Theorem  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
Ten proofs (and a few variations) of the beautiful Butterfly theorem, with illustrations and remarks. Links to some generalizations: A Better Butterfly theorem, 2NWinged Butterfly theorem, several pages on the Two Butterflies theorem. Several of these
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 The Butterfly Website Picture Galleries  Mikula Web Solutions, Inc.
Symmetry in nature: butterfly and moth images from a variety of sources. In most cases, a small picture is included for speed of transmission, and a larger picture is available by clicking on the small picture.
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 Calculus Animations and Lecture Notes  Kelly Liakos
Computer animations, labs, and graphics developed by a college teacher for use in classes from precalculus and trigonometry through the calculus sequence and elementary differential equations. Yearly subscription fee applies. Samples available on the
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 Calculus graphics  Douglas N. Arnold; Institute for Mathematics and its Applications
Excerpts from a collection of graphical demonstrations developed for a class in first year calculus in the McAllister Technology Classroom. Derivatives and differentials; Computing the volume of water in a tipped glass; Archimedes' calculation of pi;
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 Calendrical Calculations  Nachum Dershowitz and Edward M. Reingold
A book about the algorithms used to calculate different calendars (Gregorian, Julian, Mayan, Hebrew, Persian, and more.) The preface, table of contents, index, and a sample chapter are available in PDF and PostScript formats. Other book resources include
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 Carlson's Fractal Gallery  Paul Carlson
Fractal images in the following categories: 3D Phoenix Spirals; Atan Method (produced by a variety of methods, mostly transcendental functions); 3D Stalks (produced by a variation on a method by Clifford Pickover); Bubbles (standard Mandelbrot); Pokorny
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 Cartesio  Camillo Trevisan
CARTESIO is an educational computer graphics freeware program for high school and college students exploring and analyzing geometric projections and CAD (computer aided design) principles. Site is in Italian and English, with links to the author's homepage
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 Category Theory Demonstrations  Jocelyn Paine
This is a Web page with buttons that generate examples, with diagrams, of concepts in category theory. These include: initial and terminal objects, products and coproducts, equalisers and coequalisers, pullbacks and pushouts, and limits and colimits.
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 Cédric Villani
For mathematicians, the 2010 Fields Medalist offers his publications, lecture notes for students, errata sheets, and his research into collisional kinetic theory (Boltzmann type), collisionless kinetic theory (Vlasov type), and optimal transport. "For
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 Cellular Automata Dynamics  Rafael Espericueta
Explorations of 0, 1, and 2dimensional cellular automata; and applications of cellular automata to ecosystem modeling. A slide show of the table of contents of the book is available here, as well as the full text of the book, in pdf format.
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 Center for Technology and Teacher Education  Curry School of Education, University of Virginia
An interdisciplinary group that develops materials to prepare teachers to use technology to enhance and extend students' learning of mathematics. This site offers activities using graphing calculators, The Geometer's Sketchpad, Microsoft Excel, the ExploreMath.com
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 Centre for the Popularisation of Mathematics  Ronnie Brown, School of Mathematics, University of Wales, Bangor
The Centre's goal is to present Mathematics to as wide as possible an audience, and to give an impression for mathematics of its objects of study, methodology, successes and applications, enjoyment, and the wider context. Includes the WWW version of the
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 Chaos and Fractals  Joakim Linde; Chalmers Tekniska Högskola
A small fractal image gallery gallered with Fractus software, Fractint parameter files, a fractal icon archive, and links to other fractal sites.
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 Chaos and Fractals  ThinkQuest 1996
Chaos is an advanced field of mathematics that involves the study of dynamical systems or systems in motion. Chaos Theory consists of the mathematical proofs and theories that attempt to describe processes in motion. Think of any
mathematical system
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 Chaos at Maryland  The Chaos Group, the University of Maryland at College Park
Research in chaotic dynamics: the theory of dimensions, fractal basin boundaries, chaotic scattering, controlling chaos, and more. Read research papers, link to Daniel P. Lathrop's Nonlinear Dynamics Lab and the Pattern Formation Laboratory, learn about
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 Chaoscope  Nicolas Desprez
Software to render 3D strange attractors such as IFS, Julia, Lorenz, and pickover. Browse the gallery, participate in the monthly contest, check the freeware's manual, learn from tutorials. Also available at http://www.btinternet.com/~ndesprez/.
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 chaotic nspace network  Jon Camp and Benjamin Martin
Fractals: an introduction, gallery of images, and evaluation of software for fractal creation, with links to download. Other mathematics resources include a brief introduction to the Fibonacci sequence.
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 Charted  Medium
"Beautiful, automatic charts"; just type or paste in the link to a Google Document or other data file in .csv format. Deliberately sparse in features, Charted renders line charts and stacked column charts, refetching data every 30 minutes.
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 ChartsBin  ChartsBin.com
A webbased data visualization tool for making, embedding, and exporting interactive visualizations out of your own data. Register to create your own graphic or browse ChartsBin's public gallery for "Starting Age of Compulsory Education around the World,"
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 Circles of Light: The Mathematics of Rainbows  Frederick J. Wicklin, Paul Edelman; The Geometry Center
How are rainbows formed? Why do they only occur when the sun is behind the observer? If the sun is low on the horizon, at what angle in the sky should we expect to see a rainbow? This lab helps to answer these and other questions by examining a mathematical
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 CMP Software  Connected Mathematics Project, Michigan State University
Downloadable software designed to accompany CMP units. For the Factor Game winning strategies involve distinguishing between numbers with many factors and numbers with few factors; students analyze game strategies and are introduced to the definitions
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 C*ODE*E  Mathematics Dept., Harvey Mudd College
Online archives of the newsletter of the Consortium for Ordinary Differential Equations Experiments, which provided a regular source of ideas,
inspiration, and experiments for instructors of ODEs between 1992 and 1997. Search back issues by issue, keyword,
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 Combinatorial Figures  Robert M. Dickau; Math Forum
Mathematica pictures that are interesting for elementary combinatorics. Catalan number diagrams; permutation diagrams; derangements; shortestpath diagrams; Stirling numbers of the first and second kind; Bell numbers, harmonic numbers and the bookstacking
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 Combustion Chaos  Univ. of Houston, Univ. of Texas at San Antonio
An interdisciplinary research group studying the dynamics of pattern formation in burner stabilized premixed flames. Includes graphics, movies, and Java simulations of different patterns, explanations of models and experiments, and list of related publications;
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 Complex Analysis (Graphics Archive, Special Topics)  The Geometry Center
Research involving maps of one or more complex variables.
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 Complexification  Jared Tarbell
View interactive, open source Java applets of fractals and other mathematically significant graphics.
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 Computational Geometry (Graphics Archive, Special Topics)  The Geometry Center
Understanding algorithms that solve problems in Geometry.
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 Computer Art and Tessellations  Hans Kuiper
A site about tessellations (tiles, tessels or regular patterns), infinity pictures, optical art, Islamic art, optical illusions, auto stereograms, company logos, quilt patterns and palindromes. Figures, patterns, textures and wallpaper drawings inspired
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 Computer Generated Art Gallery  Tom Ellis
Original computergenerated fractal images. Mandelbrot Sets; Mandelbrot zoom rendered onto a sphere.
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 Computer Graphics  Brad Shelton; Dept. of Mathematics, University of Oregon.
Thirty computer graphics (knots, braids, a mobius trough) and four movies (torus, spirograph) created with Mathematica.
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 Computer Science Education Week  National Computer Science Education Week
The materials from Computer Science Education Week inspire exploration of the field any time: defining documents; posters, brochures and kits; reports and presentations; data/computer science facts; curriculum; programs and ideas; videos; and contests.
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 Computing Before Computers  Brian Borchers, New Mexico Institute of Mining and Technology
Online introductions, with PostScript or PDF downloads, of Napier's Bones and of the GenailleLucas Rulers. Pictures of statistical computing devices such as the Pickett N525ES Statrule, the cumulative binomial probability computer, the General Dynamics
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 Concentric Geometric Hierarchies  Kirby Urner, 4D Solutions
Exhibit 1 is a JavaScript demo exhibit of the concentric hierarchy from the tetrahedron out to the rhombic dodecahedron. The shapes are all 2.3.4fold symmetric. A status bar shows the volumes of the shapes when you select an isolated view. A cumulative
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 Conception of the Good  Naveen Rizvi
"Insights into our current education system" by a UK classroom teacher. Rizvi, a selfdescribed "believer in teaching via direct instruction," blogs to "share ideas and model how I have implemented these ideas and then discuss the impact of the number
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 The Concinnitas Project
Aquatint collection of the ten "most beautiful mathematical expressions," as selected by Michael Atiyah (the Index Theorem), Enrico Bombieri (the Ree Group Formula), Simon Donaldson (Ampère's Law), Freeman Dyson (the MacDonald Equation), Murray
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 Contour plots with trigonometric functions  Eric Weeks
A method of making interesting nonmoiré patterns. See also his pages on Lissajou figures, Polar Flowers, and Spiral triangles.
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 Cool Cosmos  Education and Public Outreach Group, Infrared Processing and Analysis Center and the SIRTF Science Center
To communicate the world of infrared astronomy to the public, the Cool Cosmos web site offers: classroom activities; infrared light lessons; infrared astronomy tutorial and timeline; multiwavelength astronomy; Ask an Astronomer; Cosmic Kids; image galleries,
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 coolmath.com: Cool Math  Karen
A searchable "amusement park of mathematics" for exploring math: functions, tessellations, polyhedra, limits, logs, fractals (with galleries), puzzles and problems, fun with numbers, how to succeed in math, careers in math. Also Cool Links for Math for
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 COOL School  School districts of British Columbia, Canada
COOL School is a consortium of school districts in BC, Canada, which work together to develop quality online learning resources. An LOR (learning object repository) is available on site which includes a variety of math topics, from applications to Calculus.
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 Counting Triangles  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
Division of a square by evenly spaced lines parallel to its sides yields a number of small squares which is clearly square. Interestingly, the same is true for a triangle divided by evenly spaced lines parallel to its sides. The page contains a dynamic
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 Count On  Department for Education and Employment, UK
Activities and resources  some simple and some fancy  for parents, teachers, and students. Resources offers, among other things, guides: to mathematical misconceptions; for parents helping with homework; for promoters of math fairs; and for providers
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 Count the Apples  simplyfluid.com
A free online learning tool that uses images of apples to help preschoolers
and kindergarteners learn to count up to 10 by both numbers and words. There are 4 levels of increasing difficulty for sequence and image patterns.
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 Create 2D and 3D gnuplot Graphs
Input a function, vary parameters, plot 2D, 3D Surface, or 3D Contour, vary range displayed, and plot multiple functions at once. With help on various features, and links to graphing animated plots and varying the parameters. Part of the Shodor Educational
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 The Crypto Drop Box of the American Cryptogram Association  Jerry Metzger
The American Cryptogram Association (ACA) is a nonprofit volunteer organization devoted to disseminating cryptographic knowledge. Members make up and solve their own creations strictly for the fun of it. Every two months, the ACA journal, The Cryptogram,
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 CrystalMaker
A Macintosh program to display and manipulate all kinds of crystal structures. Using the free companion program, CrystalDiffract, CrystalMaker files can be used to generate xray and neutron powder diffraction patterns. Main features: In "PhotoColour"
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 Crystals: Crystallography & Systems  Suzanne Alejandre
A Math Forum Web Unit. 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
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 Culturally Situated Design Tools: Teaching Math through Culture  Ron Eglash
Java for creating your own Mangbetu design, cornrow curves, graffiti, bead looms, SimShoBan, Yupik star navigator, Yupik parka patterns, PreColumbian pyramids, and rhythm wheels  and learning the mathematics behind them. Organized into African, African
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 Curry's Paradox  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
A bewildering dissection paradox wherein recombination of 4 pieces cut of a rectangle produces a rectangle of a different size. Borders geometry and algebra. Accompanied by a Java illustration.
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 Dadaviz  León Markovitz and Jishai Evers
Interactive data visualization curated from thirdparty sources. Infographics, which date back to April, 2014, have included "GDP per Continent & Country," "The major causes of death in the 20th Century," "4_21 Polytope Visualized," "The Changing Arctic,"
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 Daina Taimina
Hyperbolic crochet, talks, publications, and other resources from the mathematician and fiber artist. See and read more about Taimina's fiber sculptures by visiting her artwork and blog. Books by this adjunct associate professor in the Department of Mathematics
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