 Advanced Topics in Mathematics  Anthony Beckwith
Page for a high school course exploring fractals, the Global Positioning System, number theory, topology, chaos theory, and the history of mathematics. Syllabus and brief description of each topic.
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 arXiv.org ePrint archive  Los Alamos National Laboratory (LANL)
A major site for mathematics preprints that has incorporated many formerly independent specialist archives including alggeom, functan, dgga, qalg, autofms, cdhg, MAGNUS, Several Complex Variables, Logic Eprints, Commutative Algebra, Dynamical Systems,
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 Bus Boarding and the Theory of Knots  Roy Lisker
This article is a humorous application of basic Knot Theory to the situations encountered when people are trying to board a bus in a great hurry. Their trajectories create braided patterns whicha are 'analyzed' with the help of the theory of knots.
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 Center for Geometry Analysis Numerics and Graphics (GANG)  Dept. of Mathematics & Statistics, Univ. of Massachusetts, Amherst
An interdisciplinary Differential Geometry research team. The GANG Geometry Archive is an online library of papers, preprints, images, animations and software connected with their research. The Library includes: Knot (energyminimizing knots and links);
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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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 Combinatorial Geometry (The Geometry Junkyard)  David Eppstein, Theory Group, ICS, UC Irvine
An extensive annotated list of links to material consisting of problems in which one starts with a geometric figure (say a polytope) but then considers abstract incidence properties of it rather than its metric properties. Most tiling and coloring problems
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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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 C.T.J. Dodson  Christopher Dodson
Dodson provides notes and Maple or Mathematica packages for many different mathematics courses, including algebra and precalculus, calculus, differential equations, using computers for mathematics and statistics, and an introductory course on curves,
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 Discovering the Art of Mathematic  Fleron, Julian, et al.
Resources to help mathematics faculty teach the subject to liberal arts and humanities undergraduates by actively involving them in authentic mathematical experiences that "provide meaningful cognitive and metacognitive gains, and nurture healthy and
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 Front for the Mathematics ArXiv  Univ. of California, Davis
U.C. Davis front end for the xxx.lanl.gov ePrint archive, a major site for mathematics preprints that has incorporated many formerly independent specialist archives including alggeom, functan, dgga, qalg, autofms, cdhg, MAGNUS, Several Complex
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 GANG Knot Library  Dept. of Mathematics & Statistics, Univ. of Massachusetts, Amherst
A library of Energy Minimizing Knots and Links. Select a knotimage or category to see more members of the knot's family. The catalog contains knots up to 8 crossings. 2,q torus knots and links; Rational link with two, three, and fourterm continued
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 The Geometry Junkyard  David Eppstein, Theory Group, ICS, Univ. of California at Irvine
A collection of usenet clippings, web pointers, lecture notes, research excerpts, papers, abstracts, programs, problems, and other stuff related to discrete and computational geometry  some serious and much also entertaining. Junk sorted into piles (Topics):
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 Geometry of Fullerenes  Slavik Jablan, Mathematical Institute, Belgrade
Fullerenes (Buckminster Fuller) are considered from the points of view of geometry, graph theory and knot theory. Contents: Introduction; General fullerenes, graphs, symmetry and isomers; 5/6 fullerenes; Knot theory and fullerenes; "Perfect" fullerenes;
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 Geometry  Paul Bourke
Explorations and renderings of various surfaces and forms, including knots, surfaces, 3D shapes, curves, algorithms, tilings, plexagons, etc. Formulae for Quadrics (Surfaces of degree 2); Superellipse and superellipsoid; SuperToroid (3D); Plexagons; Hexagonal
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 helaman ferguson sculpture  Helaman Ferguson
A mathematician sculptor whose stone and bronze artworks include "Aperiodic Penrose," the Coons Siggraph award, "Esker Trefoil Torus," "Fibonacci Fountain," "Fibonacci Tetrahedron," "Figureeight Knot," "Eine Kleine Link Musik," "Torus with CrossCap,"
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 High School Projects (COMAP)  Consortium for Mathematics and Its Applications
Products developed in print, video, and multimedia formats, supporting the NCTM Standards, to bring mathematical modeling into high schools around the country, and present mathematics in contexts that are relevant to students. Curriculum: Mathematics:
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 Ideas, Concepts, and Definitions (MegaMath)  Nancy Casey; Los Alamos National Laboratory
A glossary and reference page to help students learn more about mathematics and find out what some of the special words mean. Topics: Doing What Mathematicians Do; Truth and Proof; Mathematical Objects and Their Properties; Modeling and Abstraction; Algorithms;
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 Impossible World  Vlad Alexeev
About impossible figures in art. These figures can be painted on paper but cannot be represented in space. There are many artworks by M.C. Escher, Jos de Mey, Sandro del Prete and many other artists. Also, you can view animations and read articles about
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 International String Figure Association (ISFA)
The ISFA site introduces "String figures" (designs formed from nothing more than a loop of string), with instructions on how to become a member of ISFA and information on email discussion groups and international gatherings, and links to related sites.
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 Jeffrey C. Lagarias
A member of the University of Michigan Department of Mathematics. List of publications, with many available for download in PostScript format; Lagarias' research interests include Number Theory, also Computational Complexity Theory, Cryptography, Discrete
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 Journal of Knot Theory and Its Ramifications (JKTR)  Kauffman, Lickorish, Wadati, Eds.
A forum for new developments in knot theory, particularly developments that create connections between knot theory and other aspects of mathematics and natural science.
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 Knot  Flaming Pear Software
The Knot program lets you create large 3D color animations and stills of abstract knots. You design the knot's form, color, motion, backgrounds and lighting, or design and render entire animations automatically. Makes standard QuickTime and TIFF files.
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 Knot Magic Not Magic
(MatheMUSEments!)  Ivars Peterson (Math Muse for Kids)
Sometimes what looks like an impressive knot isn't a knot at all. Magicians and escape artists are experts at tying phony knots. Though magicians like knots that can fool people, mathematicians are mostly interested in real knots, especially knots that
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 Knots (Geometry and the Imagination)  Conway, Doyle, Gilman, Thurston; The Geometry Center
A mathematical knot is a knotted loop (a knot that can be unknotted is called an unknot). Two knots are considered equivalent if it is possible to rearrange one to the form of the other, without cutting the loop and without allowing it to pass through
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 Knotted Walks  Ivars Peterson (MathTrek)
Given that it normally takes some effort to create a knot, the spontaneous formation of knots in ropes and strings can appear rather puzzling. Having no obvious explanation of the effect, frustrated users can't help but acknowledge this knotting phenomenon
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 Knot Theory  Robert Scharein
A branch of algebraic topology where one studies what is known as the placement problem, or the embedding of one topological space into another. The simplest form of knot theory involves the embedding of the unit circle into threedimensional space. For
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 Knot Theory  ThinkQuest 1997
A short course on knot theory, including tutorials on the basics, knot invariants, knot properties, and knot arithmetic; biographical information on historical and contemporary figures working with knot theory; applications of knot theory; a discussion
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 Laws of Form  Richard Shoup
Inspired by the book Laws of Form by George SpencerBrown, in which the author built a "calculus of distinctions." Read an interpretation of his laws of calling and crossing as a logical arithmetic; see a simple analysis of SpencerBrown's Counter; learn
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 Math Art Gallery  Dept. of Mathematics, University of Nijmegen, the Netherlands
Links to Singularity knots; Singularity knot animations; and Pictures generated by vort. Also a few 3D fractals; g=1, g=2, and g=3 surfaces plus source files for creating the pictures; source files; Interactive art in Minnesota, and All kinds of beautiful
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 The Mathematics and Origin of String Figures  Martin Probert
A mathematical analysis of string figures and their relation to knot theory (Cat's Cradle, Jacob's Ladder, etc.), comments on their history and origins, and original string figure designs by the author.
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 Mathematics by Somos  Michael Somos
A mathematician at Cleveland State University and the originator of Somos Polynomials and the Somos Sequence. Brief discussions of these objects, as well as rational triangles and Pythagorean triples, may be found on this site along with links to resources
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 Mathematics in John Robinson's Symbolic Sculpture  University of Wales, Bangor
Art and mathematics are combined in this site, which explores Borromean Rings, The Möbius Band, Bernard Morin and the Brehm Model, The Projective Plane, Fibre Bundles, Knots and Links, Torus Knots, and Fractals through the work of sculptor John Robinson.
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 Math WWW VL: Software  Dept. of Mathematics, Florida State University
Links to software sites for collegelevel mathematics.
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 Notation for some Knots (Geometry and the Imagination)  Conway, Doyle, Gilman, Thurston; The Geometry Center
It is hard mathematically to completely codify all possible knots. Given two knots, it is difficult to tell whether they are the same. It is harder still to tell for sure that they are different. Many simple knots can be arranged in a form described
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 Papers  Chaim GoodmanStrauss, Dept. of Mathematics, Univ. of Arkansas
On Composite Twisted Unknots; Matching Rules and Substitution Tilings; Aperiodic Hierarchical Tilings; Bounding the Results of Arithmetic Operations on Random Variables with Unknown Dependency; A Small Set of Planar Aperiodic Tiles; A Pair of Aperiodic
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 The Problem of Knot Classification  Charilaos Aneziris
Contents: Denoting Regular Knot projections; When is a notation drawable?; Equal Drawability; Identifying Equivalent Knot Projections; Ordering Knot Notations; Connected Sums; Comparing Regular Knot Projections; NF=14 Results; Calculating the Alexander
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 Profile (John H. Conway): Not Just Fun and Games  Mark Alpert, Scientific American
A short biography of the Englishborn Princeton University mathematician and a discussion of some of his major mathematical contributions. ...over the past three decades Conway has made some of his greatest contributions to mathematical theory by analyzing
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 Strings on Your Fingers  Michael P. Garofalo, Red Bluff, California
Links to a host of Web sites, including Web and print bibliographies, with suggestions for where to learn more about string figures and Internet links.
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 Theory of Tieknots  Yong Mao
The mathematical theory behind tying a necktie, with illustrations of the Four in Hand, the Pratt Knot, the HalfWindsor, and the FullWindsor, and a classification of necktie knots with respect to size and shape. Tying a tie knot is equivalent to a persistent
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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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 Topological Knot Theory Information & Research  Claremont High School, Claremont, CA
Files and data related to the knot theory work developed by students at Claremont High School. A TeX file contains source code for the Paper "Tabulating Alternating Knots Through 14 Crossings," by B.Arnold, C.Candy, K.Erdener, J.Fan, J.Hoste, R.J.Muir,
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 Tying Down a Random Walk  Ivars Peterson (MathTrek)
For many men, the ordeal of fashioning a neat tie knot is fading into the distant past. It seems ironic that two physicists have now put necktie knots back on center stage. Thomas M. A. Fink and Yong Mao of the Cavendish Laboratory in Cambridge, England,
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 Unicursal curves and knot diagrams (Geometry and the Imagination)  Conway, Doyle, Gilman, Thurston; The Geometry Center
A unicursal curve in the plane is a curve that you get when you put down your pencil, and draw until you get back to the starting point. As you draw, your pencil mark can intersect itself, but you're not supposed to have any triple intersections. You
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 Untangling the Mathematics of Knots (MegaMath)  Nancy Casey; Los Alamos National Laboratory
Fundamentals of knot theory for a wide range of levels  a variety of activities for exploring knots made from pieces of rope. Students can make and verify observations about knots, classify them, combine them, and find ways to determine if two knots
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 Vagn Lundsgaard Hansen
A personal home page with links to: a mathematical story "I am the greatest," solving and proving/explaining the isoperimetric problem for quadrilaterals; Mathematics and the Public  some experiences with the popularization of mathematics; and Mathematics
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 What is the best way to lace your shoes?  Burkard Polster, Nature
"The two most popular ways to lace shoes have historically been to use 'crisscross' or 'straight' lacing  but are these the most efficient? Here we demonstrate mathematically that the shortest lacing is neither of these, but instead is a rarely used
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 Writings from the MegaMath Project (MegaMath)  Casey, Fellows, Koblitz; Los Alamos National Laboratory
Documents containing classroom materials and discussions of mathematics pedagogy. The Los Alamos workbook; Lessons for math teachers; An hour in the classroom; Literacy lessons and mathematics learning; Computer science in elementary school; Combinatorially
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