 Pascal's Fractals  Ivars Peterson (MathLand)
It's possible to convert Pascal's triangle into eyecatching geometric forms. For example, one can replace the odd coefficients with 1 and even coefficients with 0. Continuing the pattern for many rows reveals an everenlarging host of triangles, of varying
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 Pascal's Triangle from Top to Bottom  Matthew Hubbard and Tom Roby
A comprehensive resource for the study of Pascal's Triangle. The section "Applications" addresses questions such as "What types of questions are answered by the binomial coefficients?" and "What number greater than 1 shows up most often in Pascal's Triangle?"
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 Pascal's Triangle using Clock Arithmetic  Jay's Corner
Exploring Pascal's triangle when the modulus is a prime; when the modulus is a power of a prime; and when the modulus has at least two different prime divisors. From mod 2 to mod 12, illustrated. (See also Part II.)
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 Pascal Triangle Applet  Sergey Butkevich
An applet that graphically presents Pascal's triangle modulo an integer number p; i.e. it computes the binomial coefficients. It can draw triangles with up to 650 rows with a p value between 2 and 30,000 (though it's not very clear above 15,000). The
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 Passalgebra.com
Pass algebra with this online study guide. Practice with hundreds of problems, with answers worked out step by step. Examples of study guide and exercises provided. $27 for 1 year; stepbystep instruction for $2.50/problem.
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 Pass Calculus  Le Site PassCalculus.com
Calculus question solution service. Solutions offered via email, phone, or fax; quotes are free; payment by credit card. Sample solutions and FAQ online.
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 A Passion for Pi  Ivars Peterson (MathLand)
Some of you may be familiar with the sentence: How I want a drink, alcoholic of course, after the heavy lectures involving quantum mechanics! The number of letters in each word represents successive digits of pi: 3.14159265358979. How Simon Plouffe memorized
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 Pasta by Design  George L. Legendre
Photos of architect Legendre's 2011 book by the same title. Pasta by Design provides an illustrated taxonomy of over 90 forms of pasta, along with the mathematical formulae, descriptions of special attributes, and advice on specific cooking uses for each
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 Past Lectures  Gresham College
Dozens of video lectures by Robin Wilson, Gresham Professor of Geometry and former Visiting Professor in the History of Mathematics: "The Great Mathematicians," "Early Mathematics Day," "Lewis Carroll in Numberland," "Topics in the History of Financial
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 Path Puzzles  Erich's Puzzle Palace; Erich Friedman
Sixteen paththroughagrid puzzles; can you fill in the correct path? Answers provided.
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 Pathways to Science  Institute for Broadening Participation
Programs such as undergraduate summer research opportunities, graduate fellowships, postdoctoral positions, as well as resources and materials pertaining to recruitment, retention, mentoring, and funding of underrepresented groups on pathways to science,
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 Pattern  Drew, Wallace; Mathematics Across the Curriculum, Dartmouth College
An interdisciplinary course in textile design and elementary group theory. Syllabus, course pages (notes, figures, questions, group work and homework), final project and class artworks from a 1996 math and art crosscurricular class at Dartmouth College.
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 Pattern Recognition Student Projects, 1997  Godfried Toussaint, McGill University
A variety of student projects: papers presented on the Web, many with Java applets. Topics include: Skeletonization Algorithm of Hilditch; Alpha Shapes; Didier KMeans Algorithm; The MIT Reading Machine for the Blind; Distance Transforms; Midpoint Smoothing;
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 Patterns and Magic Squares  Recmath
This page looks at a particular subset of Magic Squares, those of order four which are 'continuous' (also known as pandiagonal, Nasik and Jaina). It explores the patterns possible when the numbers in these kinds of squares are
represented by a set of
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 Patterns of physical change  Phil Henshaw
Focuses on the use of tools such as derivative reconstruction (DR) to measure growth and changes in a system. Includes: a short paper "Is the basis of change evolutionary?"; a description of the theory of derivative reconstruction as a method of analyzing
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 Pat Thompson's Home Page  Patrick W. Thompson
Research on students' development of algebra and calculus ideas in grades 316, on the nature of multiplicative reasoning and its role in learning sophisticated mathematical ideas, and on teaching and learning statistical and probabilistic reasoning.
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 Paul Erdos: An Infinity of Problems  Ivars Peterson (MathLand)
Paul Erdos died of a heart attack on Sept. 20 [1996] at the age of 83. Considered by many as one of the great mathematicians of this century and certainly one of the most prolific ever, he will be missed. For more than 50 years, Erdos wandered the globe
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 Paul's Online Math Notes and Tutorials  Paul Dawkins, Lamar University
Online notes and tutorials on algebra, calculus, and differential equations. Also, PDFs, some reduced to fit onto one printed page, offering a review of algebra and trigonometry, a primer of complex numbers, listing common math errors, suggesting how
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 Paul's Page of Pi  Paul A. Gusmorino 3rd
Most of the content of this site is focused on methods of calculating pi: Archimedes' method; Wallis' formula; Gregory, Leibniz, and Machin; Newton's fluxions; and Paul's 8192 digits. Also Pi Poems, Music of Pi, and Pi Links.
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 paulus gerdes's Storefront  Paulus Gerdes
Purchase print editions or download Gerdes' titles, some also available in Portuguese, Dutch, and French: Drawings from Angola: Living Mathematics, Enjoy Puzzling with biLLies, Puzzle Fun with BiLLies, The Bisos Game: Puzzles and Diversions, Introducing
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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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 Payoff Calculator  www.payoffcalculator.info
Financial calculators for finding out how long payments will take to pay off a loan, mortgage, or car loan. These payoff calculators also estimate how much you can save by adding extra contributions to your payments.
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 PC Calc
Calculator program for Windows 2000/XP. Offers calculations, graphing, matrices, steps in solving equations, and more. Features listed and a free 30day demo is available on the site.
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 PCMI@MathForum  Suzanne Alejandre, Jim King
An overview and, in some cases, details of the working groups, schedules, and projects from each summer session: Research Program, Graduate Summer School, Undergraduate Program, Mathematics Education Research Program, Undergraduate Faculty Program, High
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 PCS Edventures  PCS Edventures!.com, Inc.
Education company with a product line ranging from handson learning labs in technologyrich subjects like engineering, science, math, robotics, IT, and electronics to administrative tools designed to help schools manage the enormous amounts of data required
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 Pédagogie Mathématiques  Académie de Rennes
De nombreux documents pédagogiques (du collège au BTS), des jeux ainsi que d'excellents exemples d'utilisation des T.I.C.E. (technologies de l'information et de communication pour l'enseignement) des maths.
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 PDEase2D  Macsyma Inc.
PDEase solves a range of nonlinear problems in heat transfer, solid mechanics, fluid mechanics, groundwater flow, electromagnetics, chemical reaction diffusion, and quantum mechanics. It simplifies finite element analysis with automatic gridding, automated
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 PDK Poster Project  Pamela Davis Kivelson
"Using Visual Means to Challenge Stereotypes." Posters for scientific literacy, humanizing the image of research science and scientists, and increasing the number of women and girls who choose to pursue and maintain careers in the physical sciences and
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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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 PearlQuiz  Web Pearls Inc.
A math quizauthoring system in three parts: an application platform that manages databases and computational engines; a server of HTML and JSP pages; and an author application for writing, editing, and publishing quizzes. Question types include true/false,
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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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 Pell's equation
 MacTutor Math History Archives
Linked essay on the indeterminate quadratic equation. With references and other related web sites.
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 Pennies in a Tray  Ivars Peterson (MathLand)
What's the largest number of pennies that you can pack inside a circular tray to form a carpet of nonoverlapping coins? What about inside a square or triangular tray? What if you could expand or contract the size of all your pennies to fit a required
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 Penn State University Mathematics Department
Course home pages and instructional material; seminars, colloquia, and conferences; and subject area pages for Penn State research centers, with preprints and links to other resources on the Web: Algebra and Number Theory; Dynamical Systems; Mathematical
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 A Penny Surprise  Ivars Peterson (MathTrek)
Flipping a coin in the air, catching it, then determining whether it has come up heads or tails is to many people a prototypical random process. In some sense, however, coin tossing isn't really random at all. A mechanical gadget can flip a properly positioned
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 The Penrose Puzzle Room  World of Escher
Mathematically based Pentaplex Puzzles designed by Sir Roger Penrose, the wellknown English mathematician. The original 45 piece Gamebirds, 190 piece Perplexing Poultry  2 designs, 500 piece Jigsaw Puzzles  4 designs.
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 Penrose Tiling Generator  Stephen Collins
A software package for Windows NT, for generating rhombic Penrose tilings and investigating symmetrical topological chains within them.
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 Pens and Crystals (Math Chat)  Frank Morgan, MAA Online
Answering the challenge: How should you fence in two adjacent rectangular pens of given areas A, B with the least amount of fencing (including the fencing separating them)? Ms. Mattuck's 8th graders at the Richmond School use the Geometer's Sketchpad
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 Pentagonal Geometry and the Golden Ratio (The Geometry Junkyard)  David Eppstein, Theory Group, ICS, UC Irvine
An extensive annotated list of links to material on geometric problems defined on regular pentagons, involving pentagonal angles, or based on the golden ratio (the ratio of diagonal to side length in a regular pentagon).
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 The Pentagon Universe (Penrose tiles and more)  Kadon Enterprises, Inc.
Manipulatives based on Penrose tiles, golden triangles and other tilings based on the golden ratio.
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 Pentium Bug Revisited  Ivars Peterson (MathLand)
The incident that triggered a barrage of ridicule occurred in the fall of 1994, a few months after Intel had introduced its Pentium microprocessor. The furor started with an email message from Thomas R. Nicely, a mathematician at Lynchburg College in
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 Pentomino Relationships  Adrian Smith
The site describes how pentominoes (twelve pieces of wood, each a different shape and each made of five cubes) fit together into rectangles or cuboids, as well as the subsequent challenge of finding as many other solutions as possible from the one just
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 Perfect, Amicable and Sociable Numbers  David Moews
Definitions, descriptions, and discussions of perfect, amicable, and sociable numbers; aliquot sequences, related problems, and other definitions of divisibility, with a short bibliography.
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 A Perfect Collaboration  Ivars Peterson (MathLand)
Euclid and Euler seem an unlikely pairing. One was the most prominent mathematician of antiquity, best known for his treatise on geometry, the Elements. The other was the most prolific mathematician in history, the man whom his 18century contemporaries
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 Perfection  Greg Lobanov
This mobile game for iPhone and Android handheld devices presents convex and concave polygonal shapes for players to cut into the outlines indicated. Available directly from the iTunes app store and Google Play.
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 Perfect Numbers  MacTutor Math History Archives
Linked essay describing the work on perfect numbers from Pythagoras through Euclid, Nicomachus, the Arabs, Cataldi, Descartes, Mersenne, Fermat, Euler, Barlow, Catalan, Cole, and others; with other web sites and 20 references (books/articles).
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 Perfect Symmetry Number Theory  Derek Nalls
A fundamental, educational exposition of a nonstandard number theory based upon perfect symmetry (in contrast to broken symmetry) modelled throughout arithmetic, algebra, analytic geometry, analytic trigonometry and calculus.
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 Performance Evaluation  Keith Devlin (Devlin's Angle)
"Dear Professor G,..." A critique of current professorial evaluation schemes in the college/university setting.
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