 Tesseracts: Cubes Get Hyper (MatheMUSEments!)  Ivars Peterson (Math Muse for Kids)
Madeleine L'Engle, who wrote A Wrinkle in Time, used tesseract to mean a shortcut through space and time. In her story, spacetime wrinkles, or folds onto itself, creating new paths that allow characters to tesser, or travel from one end of the galaxy
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 Testing and Measurement: Articles and Research  Carolyn K., Hoagies' Gifted Education Page
Articles and reports on assessment and measurement, and also underachievement, in the context of the education of gifted children.
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 Tewodros Amdeberhan's Electronic Headquarters
Tewodros Amdeberhan studies combinatorics, number theory, special functions, partial differential equations, computer algebra, algorithmic proof theory, and harmonic analysis. His articles on these topics, as well as some unpublished musings, are available
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 TheMathPage: An Approach to Calculus  Lawrence Spector; Borough of Manhattan Community College, CUNY
An introduction to real numbers, including such topics as: continuous versus discrete; limits; continuous functions; the "limit" infinity (?); the derivative; the chain rule; velocity and rates of change; maximum and minimum values; derivatives of trigonometric
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 TheMathPage: Plane Geometry  Lawrence Spector; Borough of Manhattan Community College, CUNY
A complete course based on Book I of Euclid's Elements, culminating in the Pythagorean theorem. Includes questions for checking understanding, with solutions.
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 Theoretical and Numerical Approach to "Magic Angle" of Stone Skipping  Shinichiro Nagahiro and Yoshinori Hayakawa, Department of Physics, Tohoku University, Japan
As published in the American Physical Society's Physical Review Letters: Nagahiro and Hayakawa "... investigate the condition for the bounce of circular disks which obliquely impacts on the fluid surface. An experiment [C. Clanet, F. Hersen, and L. Bocquet,
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 Theory of Tieknots  Yong Mao
The mathematical theory behind tying a necktie, with illustrations of the Four in Hand, the Pratt Knot, the HalfWindsor, and the FullWindsor, and a classification of necktie knots with respect to size and shape. Tying a tie knot is equivalent to a persistent
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 These are Times that Try Mathematicians' Souls  David Brooks
Spurred by the Unabomber arrest, David Brooks, Science Editor, says it's time to stand on our desktops and shout to the world: "Say it out loud, I like math and I'm proud!" Previously published in The Telegraph (Nashua, NH).
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 A Thing In Common  Cut the Knot!, Alexander Bogomolny
Two applets, both of which use the Pythagorean theorem: a puzzle (Draw an {N/D} star polygon  a polygon whose N vertices are uniformly distributed on a circle, but each vertex is connected to its Dth neighbor. Regular polygons correspond to D = 1, and
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 Think & Derive  Chris Long
Monthly mathematical columns from May 1994 through April 1996 written for Central New Jersey Mensa's Forvm. Problems and puzzles, many with solutions.
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 Third International Mathematics and Science Study (TIMSS)  Math Forum
The Math Forum's page of resources on the TIMSS study. Initial findings, NCTM response, and more.
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 This Is Statistics  American Statistical Association
Why study statistics? For students as well as their parents, teachers, and counselors, the American Statistical Association (ASA) provides a host of motives: to make a difference, have fun, satisfy curiosity, and make money, among other reasons. "Which
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 Thomas Harriot's manuscripts  MacTutor Math History Archives
Linked essay: Thomas Harriot died in 1621. He had published no mathematical or astronomical works during his lifetime, but he left his papers in reasonably good order and set out his wishes in his will that they should be properly edited and published.
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 Those Amazing Flying Mathematicians  Keith Devlin (Devlin's Angle)
October is the month when those of us living in the United States see migrating birds moving south for the winter. How do they know which direction to fly?... Assuming that the average bird is not the mathematical equivalent of a college math major, how
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 The Three Jugs Problem  Cut the Knot!, Alexander Bogomolny
Two friends who have an eightquart jug of water wish to share it evenly. They also have two empty jars, one holding five quarts, the other three. How can they each measure exactly 4 quarts of water? ... The description of the 3 Jugs problem as a triple
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 Three Years Of Computing: Final Report on the Palindrome Quest  John Walker
"Pick a number. Reverse its digits and add the resulting number to the original number. If the result isn't a palindrome, repeat the process. Do all numbers in base 10 eventually become palindromes through this process? Nobody knows." The story of a
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 Tickling the Mind  Ivars Peterson (MathTrek)
... Different math teachers may use different styles and methods, and they may favor different topics. However, they all share the goal of building an appreciation of both the usefulness and the intellectual wonder of mathematics. Much of the current
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 Tilings and Geometric Ornament  Kaplan, Salesin
A project designed to explore the intersection between computer graphics, geometry, and ornamental design. Papers and illustrations on Escherization, Islamic Star Patterns, Parquet Deformations, Symmetrohedra, and Voronoi Diagrams.
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 Tiling with Polyominoes  Ivars Peterson (MathTrek)
"Mathematicians have proved that the general question of whether it's possible to cover the plane with identical copies of a given finite set of tiles is, in principle, computationally undecidable. In other words, there's no cookbook recipe or handbook
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 TiltAWhirl Chaos  Ivars Peterson (MathTrek)
The amusement park TiltAWhirl spins its passengers in one direction, then another... A rider never knows exactly what to expect next. Yet these complicated, surprising movements arise from a remarkably simple geometry. A passenger rides in one of seven
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 TIMSS Resource Center  Midcontinent Regional Educational Laboratory (McREL)
Articles, teleconferences, sites, and other materials about the Third International Mathematics and Science Study.
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 TIMSS United States: International Mathematics and Science Study  U.S. TIMSS National Research Center, Michigan State University
The Third International Mathematics and Science Study represents the most extensive investigation of mathematics and science education ever conducted. Approximately 50 countries participated in this comparative survey of education focusing upon 9yearold
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 Title III MSS Final Performance Report  Dana Lee Ling
Dana Lee Ling is a mathematics and science software specialist at the College of MicronesiaFSM. Articles document the College's attempts to increase the success of prealgebra and algebra students through "conceptual" and technologybased approaches.
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 Too Much to be a Coincidence? (Math Chat)  Frank Morgan, MAA Online
Answer to the Challenge: In the September ACBL Bridge Bulletin, Noreen Wurdemann of the Bahamas reports that the two bridge hands below were dealt out at her club. She says that she is "100% certain there was no hankypanky." What is the probability of
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 Topological Groups, Lie Groups  Dave Rusin; The Mathematical Atlas
A short article designed to provide an introduction to Lie groups, an important special branch of group theory. They have algebraic structure and yet are also subsets of space, and so have a geometry; moreover, portions of them look just like Euclidean
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 Topological Knot Theory Information & Research  Claremont High School, Claremont, CA
Files and data related to the knot theory work developed by students at Claremont High School. A TeX file contains source code for the Paper "Tabulating Alternating Knots Through 14 Crossings," by B.Arnold, C.Candy, K.Erdener, J.Fan, J.Hoste, R.J.Muir,
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 Topology Atlas  Shakhmatov and Watson; York University, Toronto, Ontario, Canada
A multipurpose center for electronic distribution of information related to topology, the mathematical study of surfaces, sometimes called "rubber sheet geometry" because topologists consider geometric figures as though they were drawn on infinitely
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 Topology  Dave Rusin; The Mathematical Atlas
A short article designed to provide an introduction to general topology, the study of sets on which one has a notion of "closeness"  enough to decide which
functions defined on it are continuous. Thus it is a kind of generalized geometry (we are still
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 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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 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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 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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 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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 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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 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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 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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 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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 Tricky Dice  Ivars Peterson (MathTrek)
The game involves four specially numbered dice. You let your opponent pick any one of the four dice. You choose one of the remaining three dice. Each player tosses his or her die, and the higher number wins the throw. Amazingly, in a game involving 10
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 Tricky Tables (MatheMUSEments!)  Ivars Peterson (Math Muse for Kids)
The shape of a billiard table has a lot to do with the types of shots you can make in a game of billiards. Which of the odd tables pictured do you think would be your best bet for hitting another ball? Suppose you have a circular table, or a rectangular
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 The Trigonometric Functions  MacTutor Math History Archives
Linked essay sketching trigonometry from its beginnings out of the early correspondence between astronomy and mathematics through the 18th century, with 17 references (books/articles).
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 Triogram Models  Hansen, Kooperberg, Sardy
An electronic version of a paper that introduces the Triogram method for function estimation using piecewise linear, bivariate splines based on an adaptively constructed triangulation. Java applets are included and a PostScript version of the entire paper
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 Trisecting an Angle  MacTutor Math History Archives
Linked essay tracing the history of the classical Greek problem of trisecting an
arbitrary angle using for the construction only ruler and compass (which is
impossible)  but, failing that, finding some other method.
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 Trisecting the Angle  Steven Dutch; University of Wisconsin  Green Bay
Why is trisecting an angle with a straightedge and compass impossible? Discussion includes several other proofs of impossibility (the largest prime number, the square root of 2, repeating patterns in the plane) and some alternate methods of trisection
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 Triumph of the Nerds: A History of the Computer  Robert X. Cringely; PBS Online
A companion Web site for the Public Broadcasting System television special hosted by Robert Cringely, "Triumph of the Nerds: The Rise of Accidental Empires." Learn how youthful amateurs, hippies, and selfproclaimed "nerds" accidentally changed the world.
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 Troublesome Weather Trends  Ivars Peterson (MathTrek)
In the February Bulletin of the American Meteorological Society, Statistician Kevin J. Coakley of the National Institute of Standards and Technology in
Boulder, Colo. argues that ... daily temperatures don’t vary randomly. They generally tend to rise
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 Trouble with WildCard Poker  Ivars Peterson (MathLand)
Poker originated in the Louisiana territory around the year 1800. Ever since, this addictive card game has occupied the time and teased the minds of generations of gamblers. It has also attracted the attention of mathematicians and statisticians. The
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 Truel in the Sun  Ivars Peterson (MathTrek)
Brilliant sunshine bakes a huddled row of ramshackle, weatherbeaten buildings lining a dusty thoroughfare. Two gunfighters slam out of a decrepit saloon and stalk toward their posts at either end of the street. Facing each other, they prepare to draw
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 TSM4: 'Using the Internet for Mathematics'  Oundle School, Peterborough, UK
A oneday conference for teachers held 11 May 1998 at Oundle School, Peterborough, UK. Technology for Secondary and College Mathematics (TSM) is a teacher training initiative based at Oundle School. Online Workshops: "How to download text and images off
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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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 Turbulence, Chaos and Disordered Systems
A research group at the Eindhoven University of Technology in the Netherlands investigating turbulence, selforganization, chaos, and complexity in fluids. Descriptions of projects and full text of related thesis projects.
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