 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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 Transformulas  Jedidiah Butler
Blog about transformational geometry, subtitled "picture = 100 formulas." Posts, which feature Butler's original GeoGebra applets and teaching notes, date back to March, 2014: "One Formula ... to Rule them All," "Circles Part 2: Angle Relationships,"
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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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 TREEFROG selfassessment system  Strickland, AlJumeili
An MSDOS and Windows program for checking math skills, based on mathematical rules. A student is presented with an expression (say integral of x cos x d x, or x2+3x+2 = 0) and told to convert it to another equivalent form (function of x + constant, x
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 Triangle: A TwoDimensional Quality Mesh Generator and Delaunay Triangulator  Jonathan Richard Shewchuk
Triangle generates exact Delaunay triangulations, constrained Delaunay triangulations, and quality conforming Delaunay triangulations. The latter can be generated with no small angles, and are thus suitable for finite element analysis. Instructions for
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 Triangle: A TwoDimensional Quality Mesh Generator and Delaunay Triangulator  Jonathan Richard Shewchuk, Carnegie Mellon University
A triangle that generates exact Delaunay triangulations, constrained Delaunay triangulations, and quality conforming Delaunay triangulations. The latter can be generated with no small angles, and are thus suitable for finite element analysis. Created
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 Triangle Calculator  Peter Chrenko
Select SideSideSide (SSS), SideAngleSide (SAS), AngleSideAngle (ASA), or SideSideAngle (SSA) congruence, then enter three known sidelengths or angles, and this JavaScript returns the triangle's remaining measurements. This calculator also uniquely
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 Triangle Centers  Clark Kimberling; Dept. of Mathematics, Univ. of Evansville, Evansville, IN
A listing, with description and illustration, of 20thcentury triangle centers (including: Schiffler Point, Exeter Point, Parry Point, congruent isoscelizers point, Yff Center of Congruence, isoperimetric point and equal detour point, AjimaMalfatti Points,
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 Triangle Congruence  Math Forum, Ask Dr. Math Common Question
A selection of answers to questions about triangle congruences, such as "Why can't the SSA Theorem be used to prove congruence?" and "When should we use Congruent Parts Congruent Triangles Congruent (CPCTC), and how does it prove anything?"
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 Triangle Formulas (Ask Dr. Math FAQ)  Math Forum
Formulas for finding the area, perimeter, etc. of an equilateral, isosceles, right, or scalene triangle.
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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: Proof  Michal Wojcik
A proof that the sum of the angles in a triangle is 180 degrees. This page is written in HTML with two graphical images.
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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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 Triangles and Simplices (The Geometry Junkyard)  David Eppstein, Theory Group, ICS, UC Irvine
An extensive annotated list of links to material on triangles and their higherdimensional generalizations (simplices), with a particular interest in partitioning regions into triangles, tetrahedra, or higher dimensional simplices, for various applications
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 Triangles, Circles, And Waves  Kenny Felder
The site provides an overview of trigonometry. The material is merely
a refresher; only useful to beginners in trigonometry when used as supplementary course material in a trigonometry class.
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 Triangles in Elliptic Geometry  Thomas Banchoff, The Geometry Center
An examination of some properties of triangles in elliptic geometry, which for this purpose are equivalent to geometry on a hemisphere. The aim is to construct a quadrilateral with two right angles having area equal to that of a given spherical triangle.
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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 Numbers
Triangular and square numbers, presented with numeric, algebraic, and geometric illustrations, proofs, and formulas.
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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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 Triangulation (SMILE)  Ann M. W. Brandon, Oak Forest High School
A lesson designed to teach students the basics of how to perform and calculate
triangulation. From the Practical and Applied Math section of a collection of almost 200 single concept lessons by the Science and Mathematics Initiative for Learning Enhancement.
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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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 A Tribute to Miro  Kathy Sederquist, Namaste Art Center
Students learn how contemporary artists work by doing a painting in the style of the Catalan artist Joan Miró. The basic lines in drawing, including vertical, horizontal, diagonal, and curved, are reviewed through experimentation.
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 Triceron Archive: Integral Calculus  Triceron.com
An enviroment for exchanging data, among others, theoretical and practical educational resources on integral calculus. Triceron carries a categorised directory of hyperlinks to www/ftp sites, usenet newsgroups, irc channels, freenet sites, usenet servers
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