 Topology Enters Mathematics  MacTutor Math History Archives
Linked essay describing the development of topology as a mathematical discipline from Euler through the early 20th century, including 17 references (books/articles).
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 Topology (Geometry and the Imagination)  Conway, Doyle, Gilman, Thurston; The Geometry Center
Topology is the theory of shapes that are allowed to stretch, compress, flex and bend, but without tearing or gluing. For example, a square is topologically equivalent to a circle, since a square can be continously deformed into a circle. As another example,
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 Topology (Graphics Archive, Special Topics)  The Geometry Center
Properties of objects that don't change when they are stretched or twisted (Klein bottle, Moebius band).
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 The Topology of Chaos: Alice in Stretch and Squeezeland  Robert Gilmore, Marc Lefranc
Web site around the book The Topology of Chaos: Alice in Stretch and Squeezeland, which is devoted to topological analysis, a relatively new technique for extracting from chaotic data the topological signatures that determine the stretching and squeezing
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 Toposes, Triples and Theories  Michael Barr and Charles Wells
A revised and corrected version of the original (1983) Grundlehren der math is available free for downloading. Formats: DVI, PDF, PostScript.
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 TopSecretMath.org  Donald Endriss
Stepbystep JavaScript tutorials for learning how to factor several different kinds of trinomials using the CAB method.
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 Tostaky.Biz  Jerome Verstrynge
JavaScript utilities formatted for the smaller screens of tablets and smartphones: timer, stopwatch, world clocks, and other timekeeping tools; and unit converters for area, force, length, torque, weight, and more.
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 Totally Free Math  Terry Wesner
A free downloadable 3rd edition elementary algebra textbook with accompanying ancillaries and no advertising.
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 Totally Tessellated  Bhushan, Kay, & Williams
A comprehensive introduction to tessellations and tilings  the basic underlying mathematics and examples of tessellations in real life. The highly illustrated, printerfriendly site includes history (tessellations in mathematics and science, decorative
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 To teach definitions in geometry or teach to define?  Michael de Villiers; Mathematics Education, Univ. of DurbanWestville, South Africa
This paper argues from a theoretical standpoint that students should be actively
engaged in the defining of geometric concepts like the quadrilaterals, and
presents some data relating to a teaching experiment aimed at developing
students' ability to
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 TotiPM  Jordi Lagares Roset, Prof. of Mathematics, Girona
Una página basicamente en Catalán, pero con referencias también en castellano e inglés. Páginas didácticas, problemas, software. A page primarily in Catalan but with Spanish and English language references. Lessons,
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 Touch3D
A commercial Macintosh program for 3Dmodeling, concept design, industrial design, quick prototyping, mockups, packaging, scale models, physical renderings, production preparation, and unfolding/unwrapping. Touch3D is a complete 3D modeling/unfolding
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 TouchMath: Multisensory Math Supplements  Innovative Learning Concepts, Inc.
The TouchMath Method is a multisensory approach to teaching basic number concepts, addition, subtraction, multiplication and division. TouchMath integrates digits 1 through 9 with a corresponding number of "touchpoints." Students physically touch each
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 Toupty.com: Jeux Éducatifs en Ligne
In French or English: free educational children's games, some involving simple mathematical concepts.
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Tour: M.C. Escher  Life and Work  National Gallery of Art, Washington, DC
A tour of four virtual rooms devoted to the art of M. C. Escher. For each graphic a larger picture with accompanying commentary is available by clicking on a small picture. The gallery has more than 400 works by Escher with many images available online.
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 Tournament of Towns  Math Net, University of Toronto
A worldwide problem solving competition in mathematics. The contest attracts students of all mathematical interests and abilities with its inclusive rules and creative problems  some as challenging as those of the International Mathematical Olympiad.
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 Tournament Scheduling  Math Forum, Ask Dr. Math Common Question
A selection of answers to questions about scheduling tournaments, from "Can you help me construct a schedule for a round robin style junior hockey tournament with two divisions using only four fields?" to "What are the odds of one person predicting the
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 A Tour of Fractions  Math Forum
The Web often seems more like a maze than an organized set of resources. To help you find what you need, the Math Forum presents a 'tour' of fractions, offering links to lessons, activities, and materials, questions and answers from Ask Dr. Math, and
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 A Tour of Measurement  Math Forum
A central resource for people teaching and learning about measurement. For teachers there are links to lessons and materials, questions and answers from Ask Dr. Math, and recommended software, grouped by level (elementary, middle school, high school).
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 Toward a Fairer Expansion Draft  Ivars Peterson (MathLand)
When new teams are brought into an established league, the team owners usually take turns picking players from a pool of available talent. The conventional method for such drafts, however, often produces unfair results. For example, if one of two owners
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 The Tower of Hanoi  Andrew Cumming
Interactive version of the famous logic puzzle, in html and VRML versions, with a separate page about solving it.
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 Tower of Hanoi  Math Forum, a Classic Problem from the Ask Dr. Math FAQ
There are three posts. Disks of different sizes are placed on the lefthand post, arranged by size with the smallest on top. You are to transfer all the disks to the righthand post in the fewest possible moves, without ever placing a larger disk on a smaller
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 Tower of Hanoi on the Web  Miroslav Kolar
The legend: A group of Eastern monks are the keepers of three towers on which sit 64 golden rings. Originally all 64 rings were stacked on one tower with each ring smaller than the one beneath. The monks are to move the rings from this first tower to
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 Tower of Hanoi (SMILE)  Paul Eubanks, Washington High School
A lesson for grades 612 designed to teach students to discover a pattern and to evaluate an exponential expression. From the Patterns and Logic section of a collection of almost 200 single concept lessons by the Science and Mathematics Initiative for
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 Toying with Reality: Java Applets and VRML  Paul Flavin
Virtual Reality: Modeling with Math, and a little Java. Applets to manipulate: The Pythagorean Theorem; Equation Grapher: "You type, I Graph"; Graphing Vector Calculator; Java 3d Visualizer; Virtual Rubik's Cube; Raytracing applet; Java Calculator; Play
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 Toys from Trash  Arvind Gupta
Stepbystep photographic instructions for building elegantly simple, colorful "Math Magic" doityourself manipulatives: Abacus, Flexagon, Triangle Grid, Flat Flexagon, Slipper Insets, Folding Pentagon, Tangram, Paper Octagon, Cylinder and Cone, Area
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 Trachtenberg Basic Multiplication Tutorial  Moshe Berlin
TracMath is a freely downloadable tutorial (MS Windows) for the basic system of Trachtenberg Multiplication. This system teaches a set of algorithms that perform the same function as the times tables. When students ask "How does it work?" you can use
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 Trachtenberg Speed Math  Alpha Centauri Software
Software that teaches Jakow Trachtenberg's speed system of basic mathematics that he invented while imprisoned by Hitler during WWII. For Windows only. Demo version available.
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 Trachtenberg Speed System  Math Forum, Ask Dr. Math FAQ
An introduction to Trachtenberg's system of performing highspeed multiplication, division, addition, subtraction, and square root, all in one's head, with references.
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 Tracking  Education Week on the Web
Should schools  as the engine of democracy  provide relatively similar curricula for all students? Or should they instead sort students by skill levels and prepare them for their different roles as adults? A discussion of the pros and cons of tracking,
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 Tractrix Java Applet Class  PHD Computer Consultants Ltd
Download Tractrix.zip, a Java applet that makes the kind of pretty swirling patterns which Dutch mathematician Huygens originally named in 1692. Specify applet width and height, background and foreground color, coordinate pairs that will identify corners,
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 Traditional Schooling: Articles and Research  Carolyn K., Hoagies' Gifted Education Page
Articles and reports on traditional schooling issues: Academic Acceleration; Advocacy; Bullies; Curriculum Adjustments; Early (or late) Kindergarten; Educational Theories; Grouping; Individualized Education Profiles (IEPs); Mentors; Success Stories; Testing
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 Traffic Jam Activity  Suzanne Alejandre
A classroom activity (also called Hop, Skip, Jump) aligned to the NCTM and California Standards, to be explored through large movement experience, manipulatives, and an interactive Java applet. Students then revisit the activity, look for patterns, and
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 Traffic Jam  Math Forum
Equal numbers of people face each other with one open slot between them. Everybody faces the open slot. If there are 6 people there will be 7 slots, 6 of
which must always have people in them. People must attempt to exchange places without turning around.
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 Traffic Signs  Richard C. Moeur
Graphics of the most commonly used traffic signs in the United States, useful for challenging students to find symmetrical signs (in addition to polygons).
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 Transformational Geometry  Leslie Howe
Java applets to illustrate translation, rotation, glide reflection, etc. Directions for tessellations by hand and using dot paper. Links to sites of artists that illustrate these ideas.
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 Transformations and Tessellations  Lynda Kozicz Leahey
A unit introducing the concepts of transformations and tessellations. Students will explore the attributes of transformations: reflections, translations, rotations and dilations by using pattern blocks, algebraic notation and computer design. They will
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 Transformations  David A. Reid
A transformation is a onetoone mapping on a set of points. The most common transformations map the points of the plane onto themselves, in a way which keeps all lengths the same. These transformations are called isometries. Another common sort of transformation
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 Transmath  A CBL Mathematics Tutor  Joanna Brown
Transmath is a computerbased (Windows platform) mathematics tutor designed to strengthen and consolidate the basic mathematical knowledge of students commencing numerate degrees. Module exercises, featuring animations, come with constructive interactive
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 Transparent Media  Transparent Media, Inc.
Commercial software company offering shareware software for fraction exploration, as well as other free downloads and commercial products.
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 Transversal of a Latin Square  Jay's Corner
A transversal in a Latin Square is a collection of positions, one from each row and one from each column, so that the colors that are in these positions are all different. This page shows an example of a transversal in a 4x4 Latin square
See also Transversals
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 The Traveling Salesman Problem (TSP)  Vasek Chvátal
The problem: given a finite number of cities and the cost of travel between each pair of them, find the cheapest way of visiting them all and returning to your starting point. This site includes a link to TSPLIB, Gerhard Reinelt's library of some hundred
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 Traveling Salesman's Sketchpad  Selim Tezel
The Traveling Salesman's Sketchpad lets you investigate the Euclidean Traveling Salesman Problem (TSP) using an interface inspired by The Geometer's Sketchpad®. The Traveling Salesman's Sketchpad facilitates algorithm and data visualization, conjecture
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 The Travelling Monkey  Ivars Peterson (MathLand)
One of the classic problems of planning ahead concerns a traveling salesman who must visit customers in a number of cities scattered across the country and then return home. The problem is to find the shortest possible route visiting each city only once.
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 Travelling Salesman's Problem  Gunno Törnberg
Algorithms to solve the travelling salesman's problem (a travelling salesman is to visit a number of cities; how to plan the trip so every city is visited once and just once and the whole trip is as short as possible?) Links to Java applets; the shell
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 The Travelling Salesman's Problem  Manu Konchady
A trucking or delivery company is focused on optimum delivery cost. This can be achieved by using a system which determines the best highway route for each load. An optimum highway route can be displayed on a map. A route with 16 nodes is used to test
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 Travel Triangles (SMILE)  Sarah Barrett, Mars Hill School
A middle and high school geometry lesson designed to teach students to review and demonstrate an understanding of the three kinds of angles (by degrees). From the Geometry and Measurement section of a collection of almost 200 single concept lessons by
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 The Treb Challenge  GlobalSpec, Inc.
Custom build a trebuchet for three challenges: distance, accuracy, and power. Between launches, continue modifying the catapultlike seige engine's projectile weight, launch angle, gravity, wind, counterweight mass and height. After each challenge, the
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 TreeAge Software, Inc.
Producer of decision analysis software. Product information, interactive demos and trial download, FAQ and technical support, ordering, and registration.
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 TREEFROG Mathematical Software  John Moores University, Liverpool, UK
Modular software for Windows, intended to be used along with traditional teaching methods, to provide instant feedback at each stage. It covers basic order of operations; manipulation of fractions; transposition of formulae and the quadratic equation;
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