 MathsTools  Carlos Toro
Online apps for the Simplex algorithm, Runge Kutta methods, Fourier series, linear algebra, and more. Read the theory behind linear programming, numerical methods, Fourier analysis, special relativity, nonlinear programming, differential geometry, and
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 A Mechanism for Drawing Archimides Spiral  Liang Chen
A mechanism that can be used to draw Archimides Spiral, one of a group of curves that can be used for trisecting angles. The author's paper is available for downloading in postscript format.
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 Minimal Snow  Ivars Peterson (MathTrek)
For a truly cool experience, there's nothing like transforming a 12foot, 20ton block of manufactured snow into a giant sculpture. That's the premise underlying the Breckenridge snow sculpture championships in Colorado, held annually in January. This
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 Minimal Surfaces and Soap Bubbles  J. A. Sethian
Level Set Methods for Minimal Surfaces. A paper and movie about soap bubbles. Given a wire frame, how can one find a minimal surface that spans the frame? Motion under curvature provides an appealing way to find the surface. To illustrate the idea, what
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 A Minimal Winter's Tale  Ivars Peterson (MathTrek)
For the second year in a row, a team assembled by mathematician Stan Wagon of Macalester College in St. Paul, Minn., participated in the Breckenridge snow sculpture championships in Colorado. In its debut effort last year, the team carved a huge block
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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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 Motion of Fluid Interfaces  J. A. Sethian
A paper and movie about a rising bubble. Imagine an air bubble rising in water, a thermal of hot air rising on a cold day, or smoke rising out of smokestack. In each case, the interface between the two fluids will change dramatically as the fluids move.
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 Motion under Curvature  J. A. Sethian
A paper and movie of a curvature collapse. A famous theorem in differential geometry, proved less than ten years ago, says that any simple closed curve moving under its curvature collapses nicely to a circle and then disappears. That is, no matter how
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 Noise Removal from Images  J. A. Sethian
A paper and movie on noise removal. Level Set Methods exploit the fact that curves moving under their curvature smooth out and disappear. The idea is to view the pixel values as a topographic map; the intensity (somewhere between white and black) at each
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 On Deciding Whether a Surface is Parabolic or Hyperbolic [PDF]  Peter G. Doyle
An application of Rayleigh's method to the classical type problem for Riemann surfaces, which is really just the same random walk problem, only instead of walking around on an infinite graph the walker is diffusing around on a surface. The aim will be
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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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 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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 Random Walk on the Speiser Graph of a Riemann Surface [PDF]  Peter G. Doyle
A paper that appeared in the Bulletin of the American Mathematical society, which considers the problem of determining the conformal type of a covering surface of the Riemann sphere with punctures. To such a surface there corresponds a Speiser graph of
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 The R. Buckminster Fuller FAQ  Christopher J. Fearnley
The Frequently Asked Questions and Answers (FAQ) Resource on R. Buckminster
Fuller, based primarily on the history of the discussions, interests, and needs of the readers of the BITNET mailing list Geodesic and its USENET gateway bit.listserv.geodesic.
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 Ricci: A Mathematica package for doing tensor calculations in differential geometry  John M. Lee, Dept. of Mathematics, Univ. of Washington
Ricci has the following features and capabilities: manipulation of tensor expressions with and without indices; implicit use of the Einstein summation convention; correct manipulation of dummy indices; display of results in mathematical notation, with
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 Robotic Navigation with Constraints  J. A. Sethian
A paper and movie on robotic navigation. Finding the Shortest Path: The equation that describes the arrival time of this expanding front as it depends on the possible speed at any point and direction is the Eikonal equation. The fast marching method is
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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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 Sculpture Generator  Ivars Peterson (MathTrek)
"Judging what a sculpture will look like after it is finished can present many difficulties for an artist just beginning a piece... Computer scientist Carlo Séquin of the University of California, Berkeley, specializes in the
computerassisted
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 Selected Technical Papers by Title  UAB Graphics and AI Laboratory (GRAIL)
Papers from GRAIL, the University of Alabama at Birmingham Department of Computer and Information Sciences center for research in computer graphics and vision. Includes: The bisector of a point and a plane parametric curve; Computing point/curve and curve/curve
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 SG Symplectic Geometry (Front for the Mathematics ArXiv)  Univ. of California, Davis
Symplectic Geometry preprints, from the 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. Search by keyword or browse by topic.
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 Solving the Quintic by Iteration [PDF]  Peter Doyle, Curt McMullen
This paper, which appeared in Acta Mathematica, gives explicitly a new solution to the quintic polynomial, in which the transcendental inversion of the icosahedral map (due to Hermite and Kronecker) is replaced by a purely iterative algorithm. The algorithm
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 Solving the Quintic with Mathematica  Wolfram, Inc.
Solving the Quintic  The impossibility of solving general quintics in radicals, Tschirnhaus's transformation, Klein's approach to the quintic, Solutions based on series, Solutions based on differential equations, Equations of higher degree. Steps to
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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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 Sphere Formulas (Ask Dr. Math FAQ)  Math Forum
Formulas for finding the surface area and volume of a sphere, sphere sector, spherical cap, and segment, zone, and lune of a sphere.
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 Student Calculus Projects  David Arnold; Mathematics Dept., College of the Redwoods, CA
HTML or Scientific Notebook files. Topics: Equiangular Spiral; Semicubic Parabola; Nephroid; Astroid; Witch of Agnesi; Deltoid; Cassinian Oval; Equiangular Spiral; Quadratix; Ellipse; Conchoid of Nicomedes; Archimedes Spiral; Cardiod; Bernoulli's Lemniscate;
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 Theron J. Hitchman
Scholarship and teaching by a professor of mathematics at the University of Northern Iowa. Hitchman's research focuses on differential and metric geometry, dynamical systems, and Lie theory, with particular interest in discrete subgroups of semisimple
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 The Topological Zoo  The Geometry Center
For mathematicians and educators: a visual dictionary of surfaces and other mathematical objects, consisting primarily of movies, still images and interactive pictures. Can be used to complement classroom presentations, research papers and talks. Each
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 Tractrix Java Applet Class  PHD Computer Consultants Ltd
Download Tractrix.zip, a Java applet that makes the kind of pretty swirling patterns which Dutch mathematician Huygens originally named in 1692. Specify applet width and height, background and foreground color, coordinate pairs that will identify corners,
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 Unifpack (Web version 2.0)  Carlos O'Ryan Lira
A set of programs and C libraries for studying Riemann Surfaces with symmetry. Unifpack accepts a presentation of a finite group and calculates the Cayley graph of the group for that presentation. If the presentation is "admissible," Unifpack can calculate
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 Virtual Trips to Black Holes and Neutron Stars  Robert Nemiroff
A published paper understandable to undergraduates: "Visual Distortions Near a Black Hole and Neutron Star," Nemiroff, R. J. 1993, American Journal of Physics, 61, 619. Gravitational Principles and Mathematics; General Description of Visual Distortion
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 White Narcissus  Ivars Peterson (MathTrek)
The elegant, swooping forms carved out of wood by sculptor Robert Longhurst often resemble gracefully curved soap films that span twisted loops of wire dipped into soapy water. Alhough these abstract sculptures bear an uncanny resemblance to mathematical
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 Yahoo! Science: Mathematics  Yahoo! Inc.
All the best on the Web in math including Indices, alphabetically listed by category: Academic Papers; Algebra; Applied Mathematics; Books; Calculus; Chaos; Combinatorics; Complex Systems; Conferences; Education; Employment; Entropy; Equations; Ethnomathematics;
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