 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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 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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 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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 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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 Triangle in Square Puzzles  Erich's Puzzle Palace; Erich Friedman
Eight puzzles involving cutting squares into triangles under certain constraints. Answers provided.
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 Triangle Puzzle  Evelyn Sander, Geometry Forum Archives, The Geometry Center
Pick an arbitrary point in the interior of an equilateral triangle. Now go halfway towards one of the three vertices (you get to pick which vertex). Now you are at a new point in the triangle. Again go halfway towards any vertex. Continue this process.
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 Triangles and Pyramids: Playing Math!  Hollis Easter
A "teachable" on the construction of freestanding pyramids made "by folding a single piece of paper, with only a single piece of tape to hold them together...." This blog post goes on to include photos of a net, diagrams, and "things to investigate":
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 Triangle with one 90degree Angle  NASA Lewis Learning Technologies Project
A triangle with one 90 degree angle is always: an equilateral triangle; an acute triangle; an obtuse triangle; or, a right triangle? A detailed answer is provided. From NASA's 9th Grade Math Proficiency Test.
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 triangular prism  Manjit Singh Atwal
Download lessons and worksheets about triangular prisms, including finding surface areas and volumes.
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 Tribute to Invariance  Cut the Knot!, Alexander Bogomolny
As a competitive activity, the Squares and Circles game is not very challenging in itself. That is to say, the outcome of the game does not depend on how the game proceeds. The challenge is to come up with this realization and establish its veracity.
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 Tricky Crossings  Ivars Peterson (MathLand)
Have you heard the one about an itinerant entertainer traveling with a wolf, a goat, and a basket of cabbages? The showman comes to a river and finds a small boat that holds only himself and one passenger. For obvious reasons, he can't leave the wolf
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 Trigonometry and Calculus Problem of the Week  Math Forum
Trigonometry and calculus problems from a variety of sources, including textbooks, math contests, NCTM books, puzzle books, and reallife situations, designed to reflect different levels of difficulty. From 1998 until 2002, the goal was to challenge students
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 TriMathlon: A Workout Beyond the School Curriculum  A. K. Peters, Ltd.
Companion site to the book TriMathlon: A Workout Beyond the School
Curriculum, by Judith and Paul Sally. Discuss math, the book, or the site with members of the Trimathlon community; explore the current "Periodic Puzzler"; or play one of the Shockwave
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 Trioker  Triominoes Puzzle  J. Marc Genevey
Le jeu de Trioker a été inventé par Monsieur Odier et étudié par luimême et son compère Mr Roussel dans leur ouvrage Surprenant Triangles. Il est composé de l'ensemble des 24 pièces triangulaires
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 Trisecting a Line Segment  Robert Styer
Several ways to trisect a line segment using compass and straightedge.
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 True Learning  Jinhee and Joseph Kim, TrueLearning LLC
Early learning curriculum, worksheets and lesson plans. The True Math activities provide an advanced foundation in math for your child with visually intuitive and engaging exercises. Free samples.
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 TSPBIB (Traveling Salesman Problem)  Pablo Moscato
A comprehensive listing of papers, source code, preprints, technical reports, etc., available on the Internet about the Traveling Salesman Problem (TSP) and some associated problems such as Fractal TSP Instances and VRP Instances, with links to software
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 TurkZeka  Yilmaz Ekici, TurkZeka.com
Clever puzzles, posted regularly, with quarterly puzzle competitions open to all with free login. In Turkish, English, and Japanese.
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 TutorNEXT  tutorNEXT, Inc.
Oneonone, individualized tutoring sessions in math and English. An enrichment program in math, and free printable math worksheets, are also available. Full listing of services on the site.
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 TutorTeddy.com
Online tutoring sessions across grades in arithmetic, algebra, statistics, probability, calculus, geometry, and trigonometry. The TutorTeddy.com site also freely offers more than a hundred chalkboard video lectures and worked problems.
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 TutorVista  TutorVista.com
Interactive lessons, worksheets, and homework help for math students grades 312 from this online education company.
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 TuvaLabs  Tuvalabs LLC
Common Corealigned math learning units based on "topics, news stories, and significant events occurring in student's life outside school," such as sports and nutrition.
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 The TwoHeaded Quarter by Joseph Ganem  Chartley Publishing, LLC
A companion site to The TwoHeaded Quarter, written by a physicist scrutinizing daytoday financial decisions, such as "How far should you drive to buy cheaper gas?" and "Is money saved when you buy on sale?" and "How far should you drive to save money?"
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 Two Trains  Math Forum, a Classic Problem from the Ask Dr. Math FAQ
Two trains leave different cities heading toward each other at different speeds. When and where do they meet?
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 UC Berkeley Mathematics Department
Department info; a collection of the Berkeley [Ph.D.] preliminary exams; undergraduate study hints and survival guide; Notherian Ring (women in mathematics at Berkeley  includes WWW sites of interest to women mathematicians or grad students); Center
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 The Ultimate Online Review Book  ThinkQuest 1997
Previous New York State Regents Exams available to help you study for standardized tests. Tests and answer keys from the early 1990s are organized into Sequential Math 1, Sequential Math 2, Sequential Math 3.
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 The Ultimate Puzzle Site  van Gassel, Heijmans, van Veldhoven
A site in English and Dutch by three Dutch students. Contents include: Various Basic Puzzles and Riddles (no mathematics); Harder Puzzles and Riddles (no mathematics); Mathematical and Logicdeductional Puzzles with solutions; BrainTeasers; and Complex
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 Uncle Bob's Puzzles  Robert & Claire Mead, Haverhill, NH, USA
Math and logic problems (no solutions); if you have questions, want a hint, or want to submit a solution you're invited to email the author. Asterisks indicate greater difficulty: Blind Cowboy; A Game of Catch; The Next Three; Grandpa's Birthday; Square
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 Undergraduate Research Project in Random Tilings  Propp, Wilson
This project investigates different regions of random tilings of nxn squares with 1x2 dominoes: square, hexagon, fortress, dungeon, and Aztec diamond (the set of lattice squares completely inside a square tilted 45 degrees, discovering that the dominoes
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 Understanding Algebra  James Brennan, Boise State University
In addition to "stuff to play with" on the web (a Graphing Applet (for exploring slope and intercepts of straight lines), a Prime Factorization Machine, a Prime Number List, a Quadratic Equation Solver, and a Quadratic Function Plotter), this book's full
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 Understanding Mathematics: A study guide  Peter Alfeld, University of Utah
A resource and source of encouragement, with questions and Alfeld's comments (Are you frustrated working through heaps of meaningless problems that are all alike? Does the thought "I can look it up if I have to" occur to you frequently? Do you feel that
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 Understanding 'Rate' Word Problems  Rick Garlikov
A conceptual explanation of doing various kinds of math "rate" problems (e.g., "distance/speed/time" problems, problems involving combining work done by different agents working at different rates of speed, quantity/proportion problems, etc.).
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 Understanding Temperatures  NASA Lewis Learning Technologies Project
These were the low temperatures recorded for January 15 in these cities: Minneapolis:  6 degrees; Cleveland: 5 degrees; Fargo: 11 degrees; Chicago: 2 degrees; Milwaukee: 3 degrees; Detroit: 1 degree. Which city had the low temperature closest to 0
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 UniformMotion Problems: Just Playing With Cars (SMILE)  David Drymiller, Morgan Park High School
A lesson that uses batteryoperated cars to teach students to solve uniform motion word problems using rate X time = distance; and gives them practice in measuring in the metric and English systems. From the Practical and Applied Math section of a collection
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 Unit Measurement Conversion  NASA Lewis Learning Technologies Project
Which statement is NOT correct? 96 cups = 6 gallons; 9 days = 216 hours; 84 ounces = 7 pounds; 2 miles = 10,560 feet. A detailed answer is provided. From NASA's 9th Grade Math Proficiency Test.
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 Units of Measurement  NASA Lewis Learning Technologies Project
Which object is matched with its appropriate unit of measurement? Milligrams for the weight of a textbook; Kilometers for the length of a sailboat; Grams for the weight of a needle; Kiloliters for the capacity of a reservoir. A detailed answer is provided.
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 University of South Carolina High School Math Contests  David Sumner
Problems from the University of South Carolina (USC) High School Math Contests, since 1994. Walk step by step through illustrated solutions to each problem using the "next step" button. The delivery of questions is designed for competitive timing. Also,
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 Unlucky in Cards (Math Chat)  Frank Morgan, MAA Online
In his Contract Bridge syndicated column Phillip Alder says that the odds against getting a "Yarborough  a hand with no card higher than a nine" are 1827 to 1, and that the odds against two players getting a Yarborough on the same deal are about 182
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 Unsolved Problems in Function Theory  Alexandre Eremenko
Files available in PDF format: Some constants studied by Littlewood; Meromorphic functions satisfying certain differential equations (E. Hille); Does every universe contain a place where you can stay at rest? (Lee Rubel); Holomorphic curves with few inflection
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 Unsolved Problems in Number Theory, Logic, and Cryptography  Tim Roberts
This site "concentrates only on problems which are easily understandable to the amateur.... explainable on a single screen (perhaps 200 words), using simple terminology." Read brief descriptions of open problems such as the Chromatic Number, the Collatz
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 USA Map Jigsaw Puzzle  Jill Britton
Students are challenged to move each of the contiguous 48 states into the correct position on the map. Note the number of colors necessary for separation of the states.
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 USA Mathematical Talent Search (USAMTS)  The Art of Problem Solving Foundation
The USA Mathematical Talent Search (USAMTS) is a free mathematics competition open to all United States high school students that emphasizes problem solving and mathematical writing. Funded by the National Security Agency, USAMTS was initiated by George
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 USAMO/APMO/IMO/Putnam Archive  Kiran S. Kedlaya
Questions from some recent math competitions, in LaTeX or postscript format: the USA Mathematical Olympiad (USAMO) for high school students [19891999]; the Asian Pacific Mathematical Olympiad (APMO), a regional olympiad among countries on the Pacific
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 Usenet FAQ Archive : Recreation : Puzzles  Netmeg Internet
Problems and puzzles, with solutions, from the rec.puzzles archives, in the categories: analysis, arithmetic, combinatorics, competition, decision, geometry, group, induction, instructions, language, logic, physics, pickover, probability, real life, references,
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 Using Algebra and Discrete Mathematics to Investigate Population Changes in a Trout Pond (iMath Investigations)  Illuminations; National Council of Teachers of Mathematics (NCTM)
An online, interactive, multimedia math investigation that illustrates the use of iteration, recursion, and algebra to model and analyze a changing fish population. Graphs, equations, tables, and technological tools are used to investigate the effect
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 USolvIT  Paul Igodt and Frank De Clerck
In Dutch or English: USolvIT is a database containing thousands of mathematics/physics/statistics problems as an assessment tool. Part of the content is freely accessible via the web. A major part is for use by teachers in course contexts.
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