 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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 On the Horizon (OTH)  School of Education, University of North Carolina (UNC)
OTH Online: the electronic version of the print publication, with the full text of prior volume years. Also the HORIZON mailing list, seminars and workshops, conferences, and presentations to explore and extend the educational community's thinking about
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 On the Square  Paul Kunkel
Given four arbitrary, unique points, A, B, C, and D, construct one line through each point such that the four lines form a square.
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 On the Teeth of Wheels (Computing Science)  Brian Hayes, American Scientist
A little history on the importance of gears in the history of computing and the importance of computing in the history of gears. "Designers of gear trains have not merely borrowed ideas from mathematics but have also developed some of those ideas on their
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 On This Day in Math  Pat Ballew
Mathematically significant events, births, deaths, and more, posted every calendar day. Ballew's blog reveals his thoughts on teaching math. His links and explanations written using The Geometer's Sketchpad include triangle medians; angle bisectors in
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 OOG: the Object Orientation Game  MCM Productions
MCM Productions' first publicly released software application. This 4in1 tiling puzzle game for the MSWindows environment allows players to test their problem solving ability with over 300 puzzles, including Tangrams, Pentominoes, Hexagons and Polyominoes.
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 .oO worksheeps  Felix Heckert
Generate worksheets of customized math exercises, complete with solutions: basic operations with integers, negatives, and fractions; binomial and quadratic formulas; partial roots; percent calculation; curve sketching; metric; derivations; antiderivatives;
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 Open Directory  Science: Math  Netscape
A comprehensive directory of math sites on the Web, listing links of mathematical interest by general topics, math topic, and site name.
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 Open Directory  Science:Math:Statistics  Netscape
A comprehensive directory of statistics sites on the Web, listing links of statistical interest by general topics, statistics topic, and site name.
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 OpenEnded Assessment in Math  Cooney, Thomas J.; Sanchez, Wendy B.; Leatham, Keith; and Mewborn, Denise S.
Over 450 openended, fieldtested assessment items, distributed more or less equally among elementary, middle school, and high school grade levels. The questions relate to five major content areas, based on the NCTM Standards: number and operation; probability
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 Open Logic Project
An opensource, collaborative textbook of logic and formal methods, starting at an intermediate level, aimed at a nonmathematical audience. Completely rigorous, the Open Logic Text text strives for modularity, configurability, adaptability, and integration
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 Open Middle  Johnson, Nanette; and Kaplinsky, Robert
"Open middle" problems, hints, and answers, all aligned to the Common Core State Standards (CCSS). Introduced by Dan Meyer, these kinds of math challenges have a "closed beginning," meaning that they all start with the same initial problem; a "closed
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 OPenn  University of Pennsylvania Libraries
Highresolution archival images of manuscripts from the University of Pennsylvania Libraries and other institutions, along with machinereadable descriptions and technical metadata. Digitized cultural heritage materials on mathematics include "Treatise
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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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 Open Problems (The Geometry Junkyard)  David Eppstein, Theory Group, ICS, UC Irvine
An extensive annotated list of links to material on open problems in geometry: antipodes; bounded degree triangulation; centers of maximum matchings; chromatic number of the plane; combinatorial complexity of spheres; covering points by rectangles; cube
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 Open Up Resources
Makers of a problembased math curriculum authored in collaboration with Illustrative Mathematics. Begun as as the stateled K12 OER Collaborative, the nonprofit Open Up Resources develops openlylicensed content available to districts via nocost licenses.
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 Opera Mathematica  Elsevier BV
François Viète's collected works, digitized by Elsevier, show how mathematicians used their books in the past: by writing directly on them as they worked through their questions. Viète, an innovator in the standardization of algebra,
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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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 Optique & Cabri  Charrier et Cortial
A collection of classic diagrams created using Cabri Géometre, reworked in Paint Shop Pro, and some have animated GIFs. Optique Géométrique (reflections and mirrors, refractions and diopters, thin lenses, optical instruments); Optique
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 Orbifold Pinball  Yevgeniy Dodis; The Geometry Center
A game in which you roll a ball on an unusual playing field. The game board is like ordinary pinball in that it features 'bumpers' off which the ball can bounce. But in this game, the board is 'curved' in such a way that a ball barely missing the bumper
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 The Orbifold Shop (Geometry and the Imagination)  Conway, Doyle, Gilman, Thurston; The Geometry Center
A symmetry project: the Orbifold Shop offers a free coupon for $2.00 worth of parts, installation included, to anyone acquiring a new orbifold. There are only a few kinds of features for twodimensional orbifolds, but they can be used in combinations:
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 Orbit Research
Developers and manufacturers of Orion Talking Scientific calculators the TI84 Plus and the TI36X, the iBill Talking Banknote Identifier, and other "products that enable an independent lifestyle for the physically challenged"  the visually impaired
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 Orbits and Gravitation  MacTutor Math History Archives
A hypertext essay covering Copernicus through Poincaré, LeviCivita, and Birkhoff, with References.
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 Order of Operations  Math Forum, Ask Dr. Math FAQ
What is the correct order of operations? Why use it? What is PEMDAS?
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 Order Of Operations (SMILE)  Bernice E. Holloway, Bellwood School District 88
A lesson designed to teach students to use grouping symbols and the standard order of operations to simplify numerical expressions; to use the order of operations to evaluate variable expressions; and to use the calculator and computer to solve numerical
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 O'Reilly  O'Reilly & Associates, Inc.
Computer books, software, and online publishing. Search the O'Reilly catalogue for concepts and keywords having to do with mathematics. Bookstores, conferences, software, how to order, contacts, affiliated companies.
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 Orig4mi  Jorge C. Lucero
Origami na ciência, tecnologia e design. Desde outubro, 2008, este profesor da Universidade de Brasília tem escrito neste blog artigos diversos sobre origami, inclusive abrigos dobráveis de bambu, origami com moléculas de DNA,
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 Origami Mathematics  Tom Hull
Information on origami and the mathematics of paper folding. With an origami math bibliography and pictures and tutorials in origami geometric construction, as well as links to other origami sites and events.
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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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 Origami (The Geometry Junkyard)  David Eppstein, Theory Group, ICS, UC Irvine
An extensive annotated list of links to material on the Japanese art of paper folding, obviously geometrical in nature. Some origami masters have looked at constructing geometric figures such as regular polyhedra from paper. In the other
direction, some
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 OrigamiUSA
Resources for origami enthusiasts and for those just learning the art of paper folding: Events (calendar, convention, and exhibit information); Resources (model index, links, email discussion list, folding groups directory, and lending library); Shopping
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 Original Lesson Plans  Mathematics  Thirteen/WNET New York
Original Webbased activities developed by Thirteen Ed Online Master Teachers. Each lesson consists of an overview with learning objectives, procedures for teachers, and "organizers" for students  handouts, bibliographies, and other materials. Math
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 Orlando Sessions: Math Education Reform  Math Forum
The 1996 Joint Mathematics Meetings in Orlando, Florida featured presentations on math education reform.
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 Orlando Sessions on Constructivism  The Math Forum
The 1996 AMS/MAA Joint Mathematics Meetings in Orlando, Florida featured presentations on constructivism. The goal: to disseminate innovative, successfully classtested pedagogical theoretical view of how mathematics is learned.
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 Orlando Sessions on PreService Teacher Ed  Math Forum
The 1996 Joint Mathematics Meetings in Orlando, Florida featured presentations on "Creating an Active Learning Environment  Preparing PreService
Teachers."
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 Orthocenter  Paul Kunkel
What is significant about the orthocenter of a triangle? Why does it even have a name? This investigation was prepared for a geometry teachers' workshop. It includes a lesson handout in Word format and was written for use in a computer lab with the Geometer's
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 Oscience.info  Subash Chandra
Introductions to limits and continuity, derivatives and antiderivatives, functions and graphs, matrices and determinants, properties of triangles, set theory, basic trigonometric formulae, and trigonometric functions and identities. See also Oscience's
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 ostermiller.org  Stephen Ostermiller
Converters, Calculators, and JavaScript include Multiplication Game, in which letters represent digits in a multiplication problem; Length, which converts between units of length and distance; Roman Numerals, which converts between Arabic and Roman numerals;
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 Other Maths  Jon Perry
Notes, applets, and proofs on a variety of open problems and conjectures: roots of x^p, highest power of 2 that divides ab + bc + ca, a prime product paradox, consecutive integers, (n + 1)!, Collatz, nsecting a line, the first lower digit, Fibonacci,
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 The Oughtred Society  Oughtred
An organization dedicated to the history and collection of slide rules. Meet William Oughtred, inventor of the modern slide rule; learn about the history and background of the Oughtred Society and its principles; join or renew membership; browse tables
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 Our Backpack Data: Making Conclusions from Graphs  William Thill
Students match different statistical questions from backpack data to an appropriate visual display. They choose graphs to answer the questions and make welljustified conclusions about each question. As an extension, students may create a new question,
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 Outposts, the Geometry Forum Newsletter Online  Sarah Seastone; The Math Forum
The newsletter of The Geometry Forum, published in 199495: Swarthmore College's electronic home for geometers of all kinds.
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 Overcoming Greatness: The Decline and Recovery of British Mathematics in the PostNewton Era  Robert Bruen; Harvard University
An historical essay on Newton and Leibniz, British Progress, European Progress, and the story of the overthrow of Newton's notation at Cambridge. Includes a bibliography.
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 Overthinking My Teaching  Christopher Danielson
Blog by a community college math teacher "interested in hard questions about teaching." Posts, which date back to July, 2009, have included "Wump hats," "An unnoticed rule for number language," "The end of word problems," "Cubeyness," "Cardinal and ordinal
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 An overview of Babylonian mathematics  MacTutor Math History Archives
Linked essay exploring the arithmetic and geometry of the Babylonians, who lived in Mesopotamia, a fertile plain between the Tigris and Euphrates rivers. The Babylonian civilization replaced the Sumerian civilisation and the Akkadian civilisation; this
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 An overview of Egyptian mathematics  MacTutor Math History Archives
Linked essay on the development of the Egyptian number systems, and the arithmetical methods they devised to work with their numerals. With references and other related web sites.
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 An Overview of IMP Years 1 and 2  Kim Mackey
An indepth review of the Interactive Mathematics Program (IMP) by a teacher. Contents include: Introduction: Why be concerned about IMP? Brief Synopsis of Year 1 and Year 2 of the IMP curriculum; A more indepth look at Year 2 IMP unit "Solve it!"; A
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 An overview of Indian mathematics  MacTutor Math History Archives
Linked essay on the contributions of Indian mathematics, in particular the number system invented by the Indians, on which much of mathematical development has rested. With references and other related web sites.
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 Overview of the History of Mathematics  MacTutor Math History Archives
Linked overview from the Babylonians through topics from the twentieth century, with additional sections on notation and communication, brilliant discoveries, how we view history, and a challenge, as well as a 700item general bibliography.
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 Owners of home computers join researchers in cracking problems and crunching data  Ivars Peterson  Science News Online
Owners of home computers have joined researchers in cracking problems and crunching data, searching for signs of intelligent extraterrestrial life, running large models of the world's climate, and carrying on a worldwide effort to identify recordbreaking
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