 Mobius  Paul Doherty
A Mobius strip is a band of paper that's deceptively simple in its appearance and exceptionally twisted in its properties. This activity is organized into an introduction, materials required, warming up, "what's going on?" and tools for further study,
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 Modularity in Art  Slavik Jablan, Mathematical Institute, Belgrade
Jablan uses the word "modularity" to refer to the process of making art by repeating a simple block, tile, or motif to make a more complicated design, by symmetry/reflection and/or tessellation. This site includes a paper on such art and its math, linked
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 The Moebius Strip  Jan Garner
An exercise on making a Moebius strip (a loop of paper with a half twist in it). How to make it, what to do with it, where to find it on the Web.
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 The Moebius Strip (SMILE)  Arnita Newton, Kenwood Academy
A lesson that investigates mathematical patterns using the Moebius Strip. From the Recreational and Creative Math section of a collection of almost 200 single concept lessons by the Science and Mathematics Initiative for Learning Enhancement.
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 Monocosm: Introduction to Linear Xenology  Vladimir Trifonov; American Mathematical Society (AMS)
A ToposTheoretic Approach to the Foundations of Physics. The FourDimensionality Problem: Why does observable spacetime look fourdimensional? is related to the Compactification Problem. The Effective Metric Signature Problems: Why is the metric of signature
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 More than Just a Plane Game  Ivars Peterson (MathTrek)
When topologists started to explore the world of geometric forms in higher dimensions, they found that neither the intuition nor the vocabulary of ordinary geometry was sufficient to describe and classify the new forms they discovered. They introduced
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 Mudd Math Fun Facts  Francis E. Su; Mathematics Dept., Harvey Mudd College
A site developed as a resource for professors wishing to enrich their courses with mathematical 'fun facts': more than 100 5minute math tidbits that can be used at the beginning of class to get students interested in mathematics. They are best used in
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 New York Journal of Mathematics (NYJM)  Mark Steinberger, Editor in Chief
Fully searchable research and universitylevel articles, such as "A Mathematical Theory of Origami Constructions and Numbers." With instructions for authors.
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 NSDL Middle School Portal: Math Pathway  NSDL; the Ohio State University
A middle school portal into NSDL's math resources, browsable by topic, or choose a preselected set of resources on given subjects.
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 Numericana.com  Gérard P. Michon
The online companion of Numericana, this site contains excerpts from Michon's book, including the entire glossary of scientific terms. Browse an index with pithy summaries, browse by popularity, or search nearly two hundred of his "final answers" of readers'
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 On Randall Sundrum Model brane detuning and hyperspace drives  Doctor Paul Karl Hoiland
By invoking known constraints on Brane Models in general that follow current Standard Model requirements of Supersymmetry I will show that some of the more recent modification to the RandallSundrum Model do not actual predict the ability to exist off
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 On the Minimax Sphere Eversion  Rob Kusner, Mathematics and GANG, Univ. of Massachussetts at Amherst
A brief paper describing the evolution of the animation of the minimax sphere eversion. Does not include the animation itself.
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 Optical Illusions (SandlotScience.com)  SandlotScience
Interactive explorations of optical effects, illusions, distortions, animations, artwork, stories, PDF projects, games, and more. Impossible objects include columns, an endless staircase and animated stairs, Java triangle models, an interlaced tribar,
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 Other Maths  Jon Perry
Notes, applets, and proofs on a variety of open problems and conjectures: roots of x^p, highest power of 2 that divides ab + bc + ca, a prime product paradox, consecutive integers, (n + 1)!, Collatz, nsecting a line, the first lower digit, Fibonacci,
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 Papers on Riemannian Geometry  Alan Weinstein
Papers written by graduate students in the course Math 240, Riemannian Geometry, in the Spring Semester of 1995 at the Univ. of California at Berkeley. Each paper is either a survey of an area or a tutorial essay in a topic related to riemannian geometry.
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 Parallel Coordinates  Alfred Inselberg
Download articles, read a course syllabus, and see images about a method for visualizing multidimensional spaces with industry applications that have included visual and automatic (classification) data mining, optimization, GIS, process control, decision
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 Pass Calculus  Le Site PassCalculus.com
Calculus question solution service. Solutions offered via email, phone, or fax; quotes are free; payment by credit card. Sample solutions and FAQ online.
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 Pete L. Clark
Course notes, open problems, publications and preprints by Clark, who teaches at the University of Georgia, and does research primarily in number theory and arithmetic geometry. See, in particular, Clark's freely downloadable PDF expositions on commutative
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 Physics Forums
Discussions emphasize physics, but "PF" also includes an entire directory on mathematics: General Math; Calculus & Analysis; Differential Equations; Linear & Abstract Algebra; Topology & Geometry; Set Theory, Logic, Probability, and Statistics;
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 Powell's Books
Located in Portland, Oregon, USA; the largest independent bookseller in the United States, specializing in technical books and new, used, hardtofind, and antiquarian titles. An extensive subject and keyword list is available  search database of titles,
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 Problems in Topological Graph Theory  Dan Archdeacon
An ongoing list of open questions in topological graph theory, to which the author invites contributions. Classical questions on genus; coloring graphs and maps; drawings and crossings; paths, cycles, and matchings; symmetries; locally planar embeddings;
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 Problems with a Point  Education Development Center, Inc. (EDC)
A collection of problems designed to help students in grades 612 learn new mathematical ideas by building on old ones. Varying in difficulty and approaches, these problems are useful for teachers, students, parents, math clubs, homeschoolers, and others.
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 Project List  Thomas Banchoff
Projects: a remake of The Flat Torus in the ThreeSphere, a film originally created in 1968; "Complex Function Graphs"; selflinking of curves on the 3sphere; "Monge and Desargues, Identified" (requires the Geometer's Sketchpad); a "sketchpad" for spherical
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 The Quadray Papers  Kirby Urner, 4D Solutions
An Introduction to Quadrays. The game of quadrays starts with a regular tetrahedron and four rays pointing from its center to the four corners; these or any ray built from these rays are labelled 4tuples  i.e. four numbers separated by commas and enclosed
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 Query Interface to the Contents of the Mathematics Archives  University of Tennessee, Knoxville (UTK)
Search software, abstracts and reviews; teaching materials, etc. by keyword.
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 Recycling Topology  Ivars Peterson (MathLand)
It's hard to miss the triangle of three bent arrows that signifies recycling. It appears in newspapers and magazines and on bottles, envelopes, cardboard cartons, and other containers. But have you noticed that there are two versions of this ubiquitous
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 Robert Abbott's Mazes  Robert Abbott
Two very difficult puzzles programmed by Oriel Maxime and based on mazes in Abbott's books: the Sliding Door Maze, and Theseus and the Minotaur. Also a collection of reviews of the books SuperMazes and Mad Mazes, with more puzzles (but nothing interactive),
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 The Roman Press, Inc.  Steven Roman
Home page of a California mathematics professor, including research articles, books and textbooks, and software.
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 sarahmarie belcastro's home page  SarahMarie Belcastro
From one of the authors of Making Mathematics with Needlework: "I seem to have become a topological graph theorist while I wasn't looking. I am also interested in convex and combinatorial geometry, algebraic geometry, topology, algebra, the geometry of
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 Sciences exactes / Mathématiques  Encyclopédie Hachette Multimédia En Ligne
Recherche Mathématiques par thème: Mathématiciens et logiciens; Mathématiques générales; Logique; Algèbre; Topologie; Analyse; Géométrie; Cinématique; Statistiques; Probabilités;
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 Scientific Graphics Project  MSRI  David Hoffman; Mathematical Sciences Research Institute
A geometry catalogue of Minimal Surfaces (The Gauss Map, The Weierstrass Formula, Conformal Mapping, Stereographic Projection, and an extensive Minimal Surfaces Index); CMC Surfaces; Level Surfaces (Level Sets Approximating Minimal Surfaces, Curvature
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 Search for Math on the Internet  The Math Forum
Keyword search of all searchable archives, Newsgroup archives, Dr. Math archives, Problems of the Week, Internet Math Library, or any combination thereof.
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 Search New York Journal of Mathematics (NYJM)  Department of Mathematics and Statistics, State University of New York (SUNY) at Albany
Search the contents of all years of the journal, or search individual years, 1994present.
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 SHAPES  XOX Corporation
Providing advanced C/C++ libraries and applets for application developers in GeoScience, CAE, CAD, Medicine, and other industries that require geometry and topology. Their primary product is Shapes®, a geometry system. Site offers contact and product
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 SHAREWARE.COM  CNET, Inc.
Search more than 250,000 files in the former Virtual Software Library: first select the platform of your choice, then enter the word or filename to search for. You may also search for files in a specific archive here by first selecting the archive of
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 Sites with Problems Administered by Others  Math Forum
Problems of the week or month: a page of annotated links to weekly/monthly problem challenges and archives hosted at the Math Forum but administered by others, and to problems and archives elsewhere on the Web, colorcoded for the level(s) of the problems
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 Sliders  Cut the Knot!, Alexander Bogomolny, with Don Greenwell
A variation of the Fifteen puzzle invented by Sam Loyd in the early 1870's: puzzles on graphs, including a proof independent of Wilson's theorem that all Lucky 7 permutations are possible; and variations of Sliders, a Fifteenlike puzzle that can be played
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 Software (Mathematics Archives)  University of Tennessee, Knoxville (UTK)
An extensive collection of links to software, with abstracts and reviews, organized in four different ways: by platform (Macintosh, MSDOS) and then by subject; interactive texts (using a commercial package such as Mathematica, Maple or Mathkit to interact
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 Solid Gold Gnarly Math
A Windowscompatible CDROM for kids, homeschoolers, parents, and teachers, designed to teach algebra, geometry, numbers, trigonometry, topology, and probability. It contains games, magic tricks, and other fun things, along with a Math Lab where kids
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 Some Planar Isospectral Domains  Buser, Conway, Doyle, Semmler
A paper on isospectral pairs of plane domains, and a particularly simple method of proving isospectrality. One example is a pair of domains that are not only isospectral but homophonic, showing that one really can't hear the shape of a drum. With a gallery
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 Sommer Cube  Michael Sommer
The faces of the modular Sommer Cube (S3) feed into twisted conduits that comprise a threedimensional, tunnelling maze. The website provides example arrangements and construction questions such as "Given that a ball must exit at the lowest S3 level and
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 Sprouts for Spring  Ivars Peterson (MathLand)
The game of sprouts has a way of growing on you. This twoperson, pencilandpaper game is simple enough that children can play it. Yet its intricacies provide much food for mathematical thought. The players start with a certain number of dots scattered
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 Surfaces (Geometry and the Imagination)  Conway, Doyle, Gilman, Thurston; The Geometry Center
A surface, or 2manifold, is a shape any small enough neighborhood of which is topologically equivalent to a neighborhood of a point in the plane. For instance, a the surface of a cube is a surface topologically equivalent to the surface of a sphere.
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 Symmetry and Orbifolds (Geometry and the Imagination)  Conway, Doyle, Gilman, Thurston; The Geometry Center
Given a symmetric pattern, what happens when you identify equivalent points? You get an object with interesting topological and geometrical properties, called an orbifold... hearts, paper dolls, wave patterns, quotient orbifolds, Moebius bands.
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 Theory and Applications of Categories (TAC)  Robert Rosebrugh, Ed.; Mount Allison University
The allelectronic, refereed journal on Category Theory, categorical methods and their applications in the mathematical sciences. The scope of the journal includes: all areas of pure category theory, including higher dimensional categories; applications
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 Thinking Mathematics!  James Tanton
Tanton writes wordless volumes of creative and surprising math puzzles, accessible approaches to calculus suitable for standardized test preparation, and curriculum "tidbits." Download his free guides to fractions and "to everything quadratic," and watch
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 This is MegaMathematics! (MegaMath)  Nancy Casey; Los Alamos National Laboratory
The frontier of mathematics is an exciting place, where mathematicians experiment and play with creative and imaginative ideas, many of them accessible to young children; others (infinity is a good example) whose profound mathematical importance is not
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 Through Mazes to Mathematics  Tony Phillips; Dept. of Mathematics, SUNYStony Brook
Material about a class of mazes that have a complete mathematical description. Includes building your own labyrinth, an activity suitable for 4thgraders and up. Explores the relationship between mazes and mathematics. Examples and calculations with Simple,
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 Tony Phillips  Dept. of Mathematics, SUNYStony Brook
Ongoing Web math projects: Honors Calculus; Visualizing Women in Mathematics, the Physical Sciences and Technology; Calculus Reform; Geometry of the Binary Tetrahedral Group in SU(2); Mazes; Tides; Integrating Research and Education (RAIRE); Math Photo
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 Topological Space: Definition and Basic Theorems  Michal Wojcik
This page contains the definitions of the following concepts: topological space, open set, closed set, interior, closure. Contains the most basic theorems about these concepts together with an easytoread proof which is slightly informal in some places.
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