 Topological Space: Definition and Basic Theorems  Michal Wojcik
This page contains the definitions of the following concepts: topological space, open set, closed set, interior, closure. Contains the most basic theorems about these concepts together with an easytoread proof which is slightly informal in some places.
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 The Topological Zoo  The Geometry Center
For mathematicians and educators: a visual dictionary of surfaces and other mathematical objects, consisting primarily of movies, still images and interactive pictures. Can be used to complement classroom presentations, research papers and talks. Each
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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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 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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 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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 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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 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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 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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 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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 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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 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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 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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 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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 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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 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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 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 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 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 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 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 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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 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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 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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 Tricki  Gowers, Timothy; Sisask, Olof; and Frolkin, Alex
A wiki "repository of mathematical knowhow" that encompasses techniques ranging from the very general to those that concern particular subareas of mathematics. Browse problemsolving ideas by technique: for finding algorithms and algorithmic proofs,
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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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 Trig According to Euclid  Len Smiley, Deborah Smiley
Four figures proving trigonometric addition and subtraction formulas for cosine and sine. Free of Cartesian coordinates, the proofs are synthetic and use a common, minimal diagram from Euclidean geometry.
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 Trigonometric Functions and Calculus  Waner, Costenoble; Hofstra University
A text on the WWW for liberal arts and business majors. Contents (each with exercises): Modeling with the Sine Function; The Six Trigonometric Functions; Derivatives of Trigonometric Functions; Integrals of Trigonometric Functions.
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 Trigonometric Functions  Larry Gladney, Dept. of Physics, Univ. of Pennsylvania
From the Interactive Textbook of PFP 96. A review of the trigonometric functions, sine, cosine, and tangent, as the most frequently used functions seen in introductory physics.
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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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 Trigonometric Integrals  David Hart
An HTML version of a Maple worksheet used as an alternative to transparencies in a Calculus class lesson at Indiana University. How do you integrate the trigonometric functions? Includes discussion, formulae, diagrams, and exercises.
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 Trigonometry Formulas  Math Forum; Ask Dr. Math FAQ
Formulas for trig functions, bounds, identities, solving right and oblique triangles and inverse trig functions.
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 Trigonometry (Manipula Math)  International Educational Software (IES Inc.)
More than 20 Java applets designed to demonstrate principles of trigonometry, including sine, cosine, and tangent function boxes; graph of y=sin x, y=cos x,
y=sin ax, y=A sin (Bx+C), and y=sin x + cos x; Fourier series; sin t = a;
cos t=a; sin(A+B);
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 Trigonometry (S.O.S. Mathematics)  Dept. of Mathematical Sciences, Univ. of Texas at El Paso
An online course: learning units presented in worksheet format review the most important results, techniques and formulas in college and precollege trigonometry. Trigonometry: Angle Measures, Trigonometric Functions (magic identity, Addition Formulas,
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 Trigonometry  Technical Tutoring
Site provides an introduction to trigonometry, includes illustrative examples and exercises in basic trigonometry as well as a summary of the important basic trig identities and formulae.
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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 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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 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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 Truncated Octahedron Blocks  Hop David
A discussion of a threedimensional tessellation that may make a good bridge between the rectangular solid tessellation and the octa/tetrahedral tessellation.
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