 National Library of Virtual Manipulatives for Interactive Mathematics (NLVM)  Cannon et al., Principal Investigators; Utah State University
Java applets and other virtual manipulatives cover mathematics appropriate to grades K12, with a special emphasis on K8. Browse by grade band or by math topic: number and operations, algebra, geometry, measurement, and data analysis and probability.
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 Navworld  Joseph Portney
A center for the art and science of navigation, providing navigational "cerebrations," famous historical accounts, interviews and biographies. See Earthshapes, different ideas of what the earth would look like if it were one of 12 different shapes (physical
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 NCTM Standards (Standards 2000)  National Council of Teachers of Mathematics (NCTM)
NCTM's Principles and Standards for School Mathematics is the compilation of the lessons learned and experiences gained over the years since the 1989 Standards were released. The site features include: an online version of the Standards (including illustrations,
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 Ndimensional Cube Projection  Andrew Wallace
A Java applet based on the work of Jonathan Bowen that projects a twodimensional representation of a cube in any dimension from 2 to 15. The controls allow you to choose how the lines will be coloured, and how many dimensions to draw.
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 Neil J. A. Sloane
Neil Sloane's research ranges far and wide and includes coding theory, sphere packing, lattices and quadratic forms, packing lines, and planes, spherical codes and designs, quantizing, geometry, combinatorics, the design of experiments, integer sequences,
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 A New Polyhedral Surface  Davide P. Cervone; The Geometry Center
Main entry point for pages that describe the recently discovered tight polyhedral immersion of the surface of Euler characteristic 1 into threespace and demonstrate one way that mathematics can be presented by means of a networkbased multimedia hypertext
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 Noon Day Project  CIESE Collaborative Projects
Over 2,000 years ago, Eratosthenes made a remarkably accurate measurement of the earth's circumference. This project is a recreation of that experiment and invites the collaboration of students living at different latitudes to take measurements of shadows,
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 Not Just Sums  Emily Hillier, Not Just Sums
Teaching and learning resources from the U.K. Learn about the product range and educational philosophy, and try sample resources, a daily starter activity, and online games.
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 NRICH Maths, the Online Maths Club  Univ. of Cambridge, UK
A project that aims to establish a permanent national centre for curriculum enrichment to provide mathematical learning support for very able children of all ages. The learning and enjoyment of mathematics are promoted through an Internet Newsletter and
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 Numeracy Works  David Hartmann, Numeracy Works LLC
Numeracy Works is a commercial software company which sells Tabula, a new tool for math education. Use Tabula to create, construct, cut, tape, fold, and transform. Make fold patterns, tiling patterns, tessellations, and perspective drawings. Also on
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 Olimpiada Matemática Española  C. SánchezRubio
Convocatoria XXXV Olimpiada (Curso 1998/99); Comisión de la Olimpiada Matemática Española; Información para alumnos y profesores; Problemas de las últimas Olimpiadas (Fase nacional); Material para preparación;
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 ONLINE MATH: An Internet Mathematics Program  Larson, Neptune, Falvo; TDLC, a Division of Larson Texts, Inc.
ONLINE MATH is a mathematics tutorial instruction program available through the Internet. Designed to help students improve their math skills in a selfpaced environment, the program is mastery based, customizable, and includes readiness tests, cumulative
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 Online Math Education  Yordan Petrov Petrov
Math tutorials and quizzes, with some math history information as well. Includes a discussion forum. Available in English or Bulgarian.
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 On the Fourth Dimension  J. McManus
An essay explaining the concept of the fourth dimension, with links to related Web pages and suggestions for books that may be helpful.
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 Open Problems  Jeff Erickson
Open problems, mostly in geometry, including folding, combinatorial, and algorithmic problems. Contents include: Existence Problems: Does Object X exist?
Combinatorial Problems: How complex is Object X? Algorithmic Problems: How fast can Problem X be
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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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 Optimization Technology Center  Argonne National Laboratory and Northwestern University
A research center dedicated to optimization problems. The "optimization tree," with descriptions of the different subfields of numerical optimization; interactive demonstrations and case studies, including the diet problem and minimum surface area; linear
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 Oranges Project Page  Debbie Lewis; The Levering School, Philadelphia, PA
An eighth grade project. Students use measurement to investigate the proportional relationship between the edible part of an orange and the peel or inedible part of a orange. They investigate different types of oranges such as navel, blood, and clementines
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 Origami Page  Joseph Wu
Origami is the art of paper folding. The word is Japanese, literally meaning "to fold" (oru) "paper" (kami). Links to photo galleries, information on origami, files and diagrams, other origami home pages, and areas related to origami (A paper on Molecular
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 Panagiotis Stefanides
Geometry presented at national conferences in Greece. Contents include: Quantization of Circle Duality; Logos Pyr Chronos; 'Buena Fortuna' (artwork); Geometric Mean Ratio (T) by Ruler and Compass; Quadrature Master Theorem; Corollary (Circle Circumference
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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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 Paul Trow's Math Page  Paul Trow
Trow's interactive web pages and perl software let you graph the LotkaVoltera equations and see interconnected predator and prey populations plotted over time; model the trajectory of a cannonball for different muzzle velocities and angles of elevation,
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 Pavilion of Polyhedreality  George W. Hart
A page of images of polyhedra from the author of Multidimensional Analysis and the Encyclopedia of Polyhedra. Constructions from wood, paper, paper clips, pencils, food and forks. The is also an extensive linked list of other Web pages related to polyhedra
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 PAX Puzzle  PAX Puzzle
Wooden puzzles, rope puzzles, puzzles boxes, and board games for sale. Recommendations and gift sets available.
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 PCTM Online Puzzle of the Week  Judy Brown; Pennsylvania Council of Teachers of Mathematics
Weekly illustrated math puzzle online competition from 199697, with an archive of past puzzles. Since 1997 this project has moved to the Math Forum to become its Middle School Problem of the Week.
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 Peanut Software for Windows  Rick Parris
Abstracts and links for downloading free mathematics software: Wingeom (highprecision geometric constructions); Winplot (generalpurpose plotting utility); Winstats (scatter plots, curve fitting, histograms, statistical data, and standard theoretical
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 Pedagogy Articles  Schiller
Translations of papers by G.W. Leibniz on the catenary (or funicular curve) and by Gauss on the Fundamental Theorem of Algebra.
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 Peek: Ndimensional polytope visualization by crosssection and projection  Gordon Kindlmann
A program to explore higher dimensional objects interactively through the use of crosssections and projections. The goal is for the user to gain some intuition about higherdimensional geometry. Projective views and 3dimensional crosssections of hypercubes.
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 Perspective Images  H. B. Meyer
The computation of image points of perspective images by the use of similar triangles ("numerical perspective") is shown. By inversion of the corresponding mapping equations the determination of proportions of various distances in the real scene becomes
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 Peter Doyle  Mathematics, Univ. of California at San Diego
Advanced tutorials, proofs and papers, mostly statistics, probability, geometry, and graph theory, but with examples from other mathematics areas as well. Don't miss Dr. Doyle's Flip Flops.
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 peterlu.org  Peter Lu
Publications and research into medieval Islamic geometry (e.g., decagonal and quasicrystalline tilings in its architecture), softmatter and colloid physics, highperformance imaging, ancient Chinese technology (e.g., first use of diamond, early precision
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 Petran Mathematics  Petro Greffrath
From South Africa: grade 11 and 12 math problems, tests, and answers. Teachers may register their students (R360/year for 110 students; the Petran academic year starts 1st February and ends 31st January the following year). Includes access to an EnglishAfrikaans
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 Pi Squared over Six  Clive Tooth
"This value, (pi^2)/6, seems to crop up quite often in mathematics. I think that most of these occurrences can be traced back to the fact that it is the sum of the reciprocals of the squares of the positive integers...." See the first 500 decimal places
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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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 Platonic Spheres (Dr. Neubert's Website)  KarlDietrich Neubert
A systematic approach to generating the Platonic bodies, using Java applets. A major aspect is the inclusion of Descartes' concept of angular deficit as a measure of curvature. An extension of Platonic bodies to Platonic spheres.
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 Plexagon  Pleated Hexagon  Paul Bourke, Ron Evans
Plexagon is a new modular geometry based on the radial pleating of polygonal plates, and their joining or cobracing into 3D modules. This engineering approach can form a very practical basis for modular greenhouses (using recycled plastic sheeting) and
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 Point Plots and Space Curves  Theo Gray
Download a Mathematica notebook that defines the functions PointParamPlot3D, SpaceCurve, and PointSpaceCurve. These functions let you make discrete point plots in two and three dimensions. The SpaceCurve and PointSpaceCurve functions let you make threedimensional
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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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 Polygons, Polyhedra, Polytopes  Russell Towle
Polytope is the general term of the sequence, point, segment, polygon,
polyhedron, ... . Towle offers several pages devoted to the theory of polytopes, from polygons to star polytopes in 4space, including Mathematica notebooks with constructions.
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 Polymath Love  Gary Smith
Free and lowcost Macintosh software for middle school mathematics: over
200 programs written by a classroom teacher. Program descriptions and some free programs are available to download from the Web, or order the CDROM for $100 U.S., which includes
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 Polytopes and Polyhedra  Dave Rusin; The Mathematical Atlas
A short article designed to provide an introduction to geometric objects made from straight pieces: polygons, polyhedra, and generalizations. Applications and related fields and subfields; textbooks, reference works, and tutorials; software and tables;
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 Polytopes, Zonohedra, Zonotiles, Mathematica notebooks  Russell Towle
Some of the author's endeavors in geometry, including studies of zonohedra, polyhedra, spacefillings, polytopes in higher space, and the discovery of new types of polyhedra and spacefillers. Mathematica notebooks are provided which create these kinds
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 The postIMO97 web page  Olimpíada Matemática Argentina
Problems and results from the math olympics held in Argentina in July, 1997. Available in English and Spanish, with problems also in French, Russian, German, and a host of other languages.
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 PRISMNEO: Programming Remediation and Intervention for Students in Mathematics  Near North School District, Ontario, Canada
Handson Geometer's Sketchpad manipulativesplus "some things that cannot be done by hand!" The GSP files, as well as some QuickTime movies, are organized into Grade 7, Grade 8, and Grade 9 under the following topics: area, central tendency, equations,
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 Problem of the Week  Purdue University
A panel in the Mathematics Department publishes a challenging problem once a week and invites college and precollege students, faculty, and staff to submit solutions. Solutions are due within two weeks from the date of publication and should be sent
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 Problem of the Week  U.S. Military Academy
A current collegelevel Problem of the Week, with links to past problems and solutions, a project of the Pi Mu Episilon chapter of the United States Military Academy. MathCad or Word are needed to view past problems and solutions.
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 Problems of the Week  Math Forum @ Drexel
Our goal with the Problems of the Week is to engage students in nonroutine, constructedresponse mathematics investigations that integrate writing with problem solving in the math classroom. In addition to the Current PoWs and the Problems of the Week
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 Problem Solving in Mathematics  Jim Wilson; Univ. of Georgia
Problems in algebra, geometry, conversion, cryptarithm, "mean," trigonometry, and a mixture of all, many with comments and solutions, from a course given in the Dept. of Mathematics Education at the University of Georgia. The site also provides links
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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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 ProjectBased Instruction in Mathematics for the Liberal Arts  M. B. Ulmer; University of South Carolina at Spartanburg
Information and activities/projects for a complete projectbased postalgebra course for liberal arts majors, also suitable for use with high school courses following algebra. Activities are in PDF format.
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