 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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 Perspective Study  Hop David
David suggests a mapping from half of 3D space onto a plane, feeling that traditional perspective drawings are similar to the image projected by a pinhole camera. Perspective illustrations of arches, looking up or down at a skyscraper, peripheral vision,
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 Peter Ash's Thoughts on Math and Education  Peter Ash
Musings on doing and teaching mathematics, book reviews, and math problems both elementary and advanced from the creator of Cambridge Math Learning. Blog posts, which date back to August of 2007, include "Very Proper Fractions"; "Physical Models for NonEuclidean
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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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 Peter J. Lu  Department of Physics, Harvard University
Lu's mathematical and historical research has revealed new insights in medieval Islamic quasicrystalline tilings and the earliest machines, such as the one he suggests precisely interconverted the linear and rotational motion responsible for the distinctive
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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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 Peter Winton's Radical Home Page
Math topics include puzzles, a gallery of fractals, and Visual Basic programs to download (count the grains of rice on a chessboard, or graph different curves).
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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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 Philosophy of Science  David Banach
A syllabus and collected resources for a course in the philosophy of science, including excerpts from various books. Topics include ancient Greek science and mathematics: the Golden Section, Pythagoras, infinity and continuity, and Plato and Aristotle,
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 PhotoMath  Martha Jean Barrett; Kodak
A project where students created their own mathematical board games for use with younger or less advanced students, for grades 48. Working in teams, advanced students covered seven math categories: whole numbers, decimals, fractions, measurement, geometry,
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 Physicscatalyst
Study notes, videos, formula sheets, solved examples, solutions from India's National Council of Educational Research and Training (NCERT), and more for middle and high school maths.
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 Pieces 'n Creases: A Fun Guide to Origami  Herring, Long, Haeggquist, Jeremy; ThinkQuest Junior
Contents include the history of origami; uses and benefits; terms, symbols, and tips; origami and peace; poems about origami; activities, and resources for folding paper. An awardwinning entry from Vidor Middle School.
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 Plane Geometry by Shalosh B. Ekhad, XIV  Doron Zeilberger
A textbook entirely written in Maple, "by" Shalosh B. Ekhad, XIV (ca. 2050), "downloaded from the future" by Doron Zeilberger. Code provided, with illustrations and instructions.
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 Plane Geometry Web Pages  David Jaffe
Materials from a geometry course originally taught to future middle and high school teachers. Using definitions, theorems, proofs, and examples, the site introduces mappings; isometries and similarities; angles and trigonometry; congruence and similarity;
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 Plane Graphic Calculator  J. E. Lillge
A Java calculator that can plot graphs of mathematical functions. Intended primarily as an educational aid to understanding the geometric interpretation of mathematical functions, it also supports complex numbers, vectors, and parametrically defined functions.
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 Plane Isometries  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
A collection of basic facts and partial explanations on plane isometries. With accompanying Java applets for translation, reflection, rotation and glide reflection.
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 PlaneMath  InfoUse, in cooperation with NASA
Materials for elementary school students about math and aeronautics, designed to stimulate and motivate students with physical disabilities in grades 47 to pursue aeronauticsrelated careers via the development and delivery of accessible math education
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 Planetcalc  Anton Egoshin
More than a hundred free calculators on math topics ranging from area of a triangle by its coordinates to total squares (the number of squares in given rectangles). Categories of others include date and time, health, computers, engineering, finance, navigation,
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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 Planimeter  Paul Kunkel
The planimeter is a drafting instrument used to measure the area of a graphically represented planar region. The region being measured may have any irregular shape, making this instrument remarkably versatile.
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 Play Ball (SMILE)  Roslyn N. Matthews, South Shore High School
A baseball lesson designed to teach students to compute batting and earned run averages; given general dimensions of the playing field and some equipment, change the units to the metric system; find the diagonal distance from 3rd base to 1st base; and
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 Play With Your Math  Kelly, JOEY; and Yu, Xi
Biweekly math problems that "require you to try, fail, and adjust many times before finding a solution." Each short, provocative question comes illustrated and ready to print out in large type on 33" × 40" dimensions: Space Race, Star Polygons,
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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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 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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 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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 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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 Potent Problems  Institute for Studies in Educational Mathematics
A database of problems that deepen understanding of mathematics through multiple answers, approaches to an answer, interpretations, extensions, perspectives on a mathematical idea, layers of complexity, or algorithms. Potent problem content topics include
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 Power Math: Online Math Problem Solving
Algebra, geometry, and arithmetic formulas for grades up to 9th.
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 PowerMath: the Virtual Reality Mathematics Teacher  Alexandre Menezes, PowerClassroom Software, LLC
Modular, studentcentered instruction software for Windows, based on visualization of mathematical ideas. Available in licenses from one to unlimited users. Demo CD available. Pricing and topics listed on web site.
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 Praktick  Praktick Learning private Ltd.
Autoscoring practice problems aligned to the UK's Central Board of Secondary Education (CBSE) Standards, from prekindergarten to grade seven. Questions adjust dynamically based on performance, while a timer counts up response time; incorrect answers
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 PreAlgebra Problem of the Week  Math Forum
Math problems for students learning algebraic reasoning, identifying and applying patterns, ratio and proportion, and geometric ideas such as similarity. The goal is to challenge students with nonroutine problems and encourage them to put their solutions
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 The Precalculus Page
Lesson plans and staff development activities with a problemsolving approach to precalculus, with materials on logarithms, the binomial theorem, and the law of sines, and problems (without answers) on algebra, exponential and logarithmic functions, other
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 Printable Math Worksheets  Homework for Kids
Practice worksheets, most with randomly generated problems, on the following topics: learning numbers, addition and subtraction, multiplication and division, fractions, decimals, time, measurements, perimeter, area and volume, integers, set theory, equations,
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 Printable Math Worksheets  TestDesigner.com
Free printable math worksheets, with answer keys, on number concepts, measurement, geometry, algebra, and statistics. Customize your own tests by selecting from the growing database of questions  or create your own.
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 Printables: Student Handouts  The Learning Network
PDF format printable handouts. Browse by grade or subject; check out the featured handouts; or search for a topic of your choice. Other resources also available through the Lesson Planning Center links on the site.
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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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 Proactive Play  Punitha Jayaraman
Articles on cognitive development research into, and activities to improve, spatial skills. Posts, which date back to October, 2012, have included "Hari Builds with Construction Set," "Piaget and van Hiele: Compare, Contrast and My Thoughts ...," "Hari's
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 Problem Corner  Les Reid; Southwest Missouri State University (SMSU)
High School, Advanced, and Challenge problems, updated monthly (approximately). High School: solutions are not solicited, although feedback (generalizations, suggestions for future problems, etc.) is appreciated. Each month, the solution to the previous
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 Problem of the Week  Dr. Annalisa Crannell; Franklin & Marshall College
Puzzles to solve in number theory, geometry, probability, cryptography, and the like. See problems from 2006, 2005, 2004, 2003, 2002, 2001, 2000, 1999, 1998, and 1997.
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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  Richard Mann
A new word problem, math challenge, or other puzzle posted each week since November, 2008, by a Saint Ann's School teacher, with student acknowledgements to follow.
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 Problem Problems  Michael Pershan
Blog by a New York City math teacher trying "to better understand the connections between problem solving, learning, and teaching." Posts, which date back to May, 2015, have included "Getting Stuck on a Geometry Problem," "Minimalistic Hints Are Still
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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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 Productive Struggle
Group blog, with most contributions by secondary math and science teachers, that aims to "push teachers to learn in the same way that we push our students to learn" and "work together to make our struggles productive." Posts, which date back to March,
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 Professional Development Center (PDC)  Key Curriculum Press
Professional development opportunities from summer institutes to weekend workshops for teachers across the United States, with scheduled 1day, 3day, and 7day courses, as well as opportunities for custom offerings specific to district needs. In particular,
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