 The 'PhiNest'  Gary Meisner
This source for the golden section, golden mean, divine proportion, Fibonacci Series, and phi discusses phi "for neo'phi'tes"; credit cards; energy; geometry; history; life; the human hand; the human face; the human body; human beauty; development; the
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 Photos by Paul Halmos  Mathematical Association of America (MAA)
Snapshots taken by Paul R. Halmos of notable contemporaries, academics, and other intellectuals of the 20th century. Search or browse the tagged collection of pictures, each of which includes a brief note about the subjects photographed in Halmos' own
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 The Pixel Calculator  METIP (Mathematics Experiences Through Image Processing) Project
The Pixel Calculator is intended primarily for use by students of ages 1217 in a variety of enrichment activities involving mathematics and digital image processing. It provides a good introduction for students to digital images by allowing students
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 Planet Perplex  Stefan Van den Bergh
Collection of optical illusions, impossible objects, visual puzzles, and hidden images.
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 The Platonic Solids Information Site  Dan Radin
Information, computer graphics, a computeranimated video, teaching tools, and links pertaining to the threedimensional geometry of the polyhedron in its many forms. Radin focuses particularly on the five Platonic solidsthe tetrahedron, the cube, the
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 Platonic Solids  Paul Bourke
Definitions, formulas, and illustrations of the threedimensional regular polyhedra: tetrahedron, octahedron, hexahedron (cube), icosahedron, dodecahedron, including the solids as drawn in Kepler's Mysterium Cosmographicum, and as represented in stone
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 Platonic Solids  Rüdiger Appel
Dwnload GIF animations, with shadow effects, of the five Platonic solids. Also available in German.
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 Play a Piano : An interactive Musical Java Activity  Paul Flavin
Play a Piano / Synthesizer / Oscilloscope: Play the piano using your mouse or computer's keyboard. Watch the wave forms as well as hear them. This virtual reality Java piano lets you play the piano and have a little fun while learning the relation between
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 Plotting Functions of a Complex Variable  George Abdo, Paul Godfrey
Graphs of functions of a complex variable, compared with graphs of functions of a real variable (the Introduction includes a review). Includes Conformal Maps requiring Möbius and SchwartzChristoffel Transformations. Full color images show conformal
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 Polaroid Geometry Scavenger Hunt  Math Forum
This activity presented by Ruth Carver at the Math Forum's 1996 Summer Institute, "Constructing Mathematics on the Internet," displays pictures of items found on this a hunt for a list of geometric items (tessellations, symmetry, concentric circles, shapes,
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 Poles and Zeros of a Causal LTI System  Manfred Thole
A Java applet that shows the domain of a system whose transfer function has two poles and two zeros. Poles and zeros can be dragged with the mouse. The amplitude response and the phase response are shown along the side. Plot: H(s) may take a while.
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 Polyedergarten  U. Mikloweit
Photographs of paper models of uniform polyhedra, prisms and compounds. Versions of the site also exist in German and French.
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 Polyhedra  Albert P. Carpenter
Photos of paper models of discontinuous "nolids," or zerovolume polyhedra. Inspired in part by the work of Allan Holden and his book Shapes, Space and Symmetry, Carpenter's images include antinanotubular polyhedra; carbon based nanostructures (polyhedra
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 Polyhedra Collection  V. Bulatov
Galleries of polyhedra shown using JPEG pictures and 3D objects in VRML2.0 format. Uniform polyhedra; Duals; Compounds; Johnson's solids; 59 stellations of icosahedron; 270 stellations of deformed dodecahedron; symmetric stellations of rhombic triacontahedron:
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 Polyhedra  Rolf Asmund
A gallery of regular polyhedra, snub uniform polyhedra, deltahedra (polyhedra consisting only of equilateral triangles), and polychora; with animations, still graphics, and some taxonomic data (vertices, edges, faces, polygons, radii, and more). Mobius
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 Polynomiography  Bahman Kalantari
Polynomiography is the "art and science of visualization in approximation of zeros of polynomials. This visualization is via fractal and nonfractal images created based on the mathematical convergence properties of iteration functions." The galleries
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 Polyominoes  Slavik Jablan
A plane topological disk (i.e. a plane region without "holes") consisting of n edgetoedge adjacent squares is called a polyomino. This site offers a shape description: in every border square cell of a polyomino we could introduce twosided mirrors perpendicular
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 Portraits of Albert Einstein  Robert Bruen
Numerous blackandwhite photographs of Einstein, provided by Robert Bruen.
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 POVRay  Persistence of Vision Raytracer Pty. Ltd
The Persistence of Vision RayTracer creates threedimensional, photorealistic images using a rendering technique called raytracing, which calculates an image of a scene by simulating the way rays of light travel in the real world. Download the latest
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 Powers of Ten  Bruce Bryson
A series of images based on the book Powers of Ten, by Philip and Phyllis Morrison and the Office of Charles and Ray Eames. Each picture's subject is ten times wider or narrower than the next. Images range from quarks at 1016 meters to groups of galaxies
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 Primordial Soup Kitchen  David Griffeath, Dept. of Mathematics, Univ. of Wisconsin
Research on the selforganization of random cellular automata. Griffeath produces colorful computer graphics that illustrate the ability of local parallel update rules to generate spatial structure from disordered initial states. His Welcome offers access
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 Problem Pictures  Richard Phillips
A CDROM of 184 attractive, unusual, or puzzling color photographs accompanied by activities for mathematics teaching. Images may defy explanation, motivate investigation, or inspire the viewer to answer a question. Other pictures may be the starting
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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 Projects of R. W. Gray  Robert W. Gray
Geometric coffee tables, an introduction to polyhedra and the jitterbug (a dynamic polyhedron) that draws on the golden ratio, a collection of notes with respect to R. Buckminster Fuller's work, photos of a dome frame Gray built with students at Oswego
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 Pulchritudinous Primes
Visualizing the distribution of prime numbers: graphical investigations in 2D, 3D, Prime Island, The Ulam Spiral Phenomenon, Triangle Numbers on the Ulam Spiral. With an introduction, Why Primes?
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 Puzzle Zapper  Alexandre Owen Muñiz
Original mathematical puzzles, some available in lasercut acrylic for sale: polyomino common superforms, pentomino coloring problems, miscellaneous polyomino explorations, flexible polyforms, square grid puzzles, visualizing sequences of numbers, Lissajous
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 Pythagorean Theorem  Over 20 Proofs  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
A general exposition of the Pythagorean theorem, with proofs from Euclid to Garfield  and more. Also links to other sites on the Web with proofs.
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 Quilt Block Patterns  Hester ButlerEhle
Links to a variety of quilt block patterns (fourpatch, fivepatch, ninepatch, and more). Several are suitable for replication using pattern blocks.
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 Raccordo tangenziale tra superfici toriche  isawi
In Italian: "Ricerca riguardante la messa appunto di un procedimento di costruzioni geometriche capace di determinare delle superfici inviluppanti tre quadriche di rotazioni assegnate ( sfere, ellissoidi, parabolidi o iperbolici). I risultati raggiunti
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 Raw  DensityDesign Lab
The "missing link between spreadsheets and vector graphics," this open web app's interface lets you create custom vectorbased visualizations on top of the DataDriven Documents JavaScript (D3.js) library. Starting with delimiterseparated values in plaintext
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 Recreational Mathematics Topics  Steven Dutch; University of Wisconsin  Green Bay
Contents: Symmetry, Crystals, Polyhedra and Tilings: an extensive, illustrated collection including reflectional and rotational symmetry; repeating patterns in two and three dimensions; building crystal forms with unit cells; regular, Archimedean, radial,
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 Recursion in Space  21 Isometric Models  Ernest V. Miliauskas
Mathematical constructions, subassemblies or subsets of an infinite set, presented in a slide show that demonstrates the author's interest in symmetric threedimensional forms. From chalk talks in advanced spacial studies given at Ryerson University
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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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 Redecorator Fractal Wallpaper Manager  Seraline P/L, Sydney, Australia.
A wallpaper manager, or randomizer, and image creator for Windows 95/98/NT/2000. Redecorator can change your desktop wallpaper as often as you like, creating seamless tiles and fractals.
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 ReInventing FourthGrade Mathematics  Jack J. Lopez; Kodak
A series of four related activities through which students acquired a firm, active knowledge of some of the basic terminology of Euclidean geometry, learning the vocabulary for describing various geometric shapes and transformations. Students photographed
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 Research Papers  The Geometry Center
Scientific papers written at the Geometry Center that use the unique aspects of hypertext to present information in a nonlinear fashion. Many include movies or interactive pictures. A Tight Polyhedral Immersion of the Real Projective Plane with one Handle
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 Research  Peter Alfeld; University of Utah
Researchrelated materials: An interactive applet that lets you explore the BernsteinBézier form of a bivariate polynomial; recent papers, complete bibliography, recent talks, computer graphics (illustrating various mathematical concepts: US Global Positioning
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 Rivendell Educational Archive  Leigh Denault
An educational archive of materials in botany, history, math, science, drama, literature, philosophy, and art. Math resources include mathematician biographies, a fractal image gallery, and a bibliography.
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 Room 8 Geometry Book  Ms. Woods' First Grade
Shape drawings by firstgraders: Prelude; Shapes  Triangles, Circles, Ovals, Squares, Rectangles, Diamonds, Pentagons, Hexagons, Octagons, Other Shapes; Forms  Cubes, Rectangular Prisms, Pyramids, Spheres, Cylinders, Cones; Concepts  Corners, Angles,
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 Rouse Ball's Fallacy  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
A famous fallacy by Rouse Ball now implemented in Java. A proof that an obtuse angle is right. How can that be?
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 R. S. Schaeffer  Randy S. Schaeffer, Math & Computer Science, Kutztown University of Pennsylvania
Schaeffer teaches a course called "Methods of Teaching Secondary Mathematics." Download the lessons created by his students that call on Geometer's Sketchpad, graphing calculators, and Microsoft Excel. Lesson topics address parallel lines, box and whisker
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 S3Triplett als 3DWelt und als Animation  Stefan Scheller
Ein S3Triplett (drei orthogonale Projektionen) wartet mit überraschenden Effekten auf. Besonders interessant wird das Triplett, wenn es als VRMLAnimation betrachtet wird (VRMLPlug In vorausgesetzt). A GIFanimation shows a S3triplet. When watched
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 The Sands of Time  Troy Jones
The author uses ridges in piles of salt to model geometric concepts. This page features an article (PDF format), PowerPoint presentation, Geometer's Sketchpad file, and textbook reference for a classroom exploration of such concepts.
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 Sangaku  Hiroshi Kotera
Click on the map of Japan to see photographs of sangaku  Euclidean geometry theorems rendered as colored drawings on wooden tablets, and hung in shrines or temples  dating to the Edo period (16031867). Also, learn how to use counting rods, called
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 sciencetotouch  Jürgen RichterGebert
Projects for interactively visualizing science, from one of the coauthors of the Cinderella geometry software package: iOrnament, a drawing and explanation app for the 17 crystallographic wallpaper groups; ixquadrat, a museum exhibit of symmetry, Escher,
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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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 Scott Kim, Puzzle Master
A puzzle and graphic design creator, Scott Kim offers links to his online puzzles, a gallery of inversions (or ambigrams, words or names written so they read in more than one waysome read upside down, some flip in a mirror, some read as two different
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 Seattle Fractals Digital Art  Doug Harrington
A fractal art site featuring highresolution digital fractal art prints for sale, and fractal art Windows 95/98/NT/2000 screensavers.
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 Self Portrait at Age 13: Albrecht Durer 1484  Ralph Martel
A paper illustrated by a PowerPoint slide show to demonstrate how Albrecht Durer used geometry in his art work from the age of thirteen. This paper by Martel is one of a series that he is writing on mathematics and art. Suzanne Alejandre wrote a teaching
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 Seventeen Kinds of Wallpaper Patterns  Mathematics Museum (Japan)
Examples of the 17 wallpaper groups in Japanese culture. Also available in Japanese.
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