 Tangencies of Circles and of Spheres: Radii Solutions  Eugene F. Dearing; Dearing Aviation
New methods of finding the radii of circles tangent to three given circles, (Apollonius' Problem), and the radii of spheres tangent to four given spheres, (Apollonius' Problem in three dimensions). Download the article in zipped format, or view it online.
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 TaniyamaShimura Conjecture Proved (Math Chat)  Frank Morgan, MAA Online
A proof of the full TaniyamaShimura conjecture, partly included in Wiles's 1994 proof of Fermat's Last Theorem, was announced last week [June, 1999] at a conference in Park City, Utah, by Christophe Breuil, Brian Conrad, Fred Diamond, and Richard Taylor,
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 A Taste for M&Ms  Ivars Peterson (MathLand)
The package of M&M's chocolate candies (plain) I had just opened contained 56 colorful, little oblate spheroids. It was obvious from a quick glance that certain colors were more common than others in this sample of M&M's. I counted up each color
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 Taxicab Angles and Trigonometry  Thompson, Dray
Taxicab geometry is essentially the study of an ideal city with all roads
running horizontal or vertical. The roads must be used to get from point A to point B; thus, the normal Euclidean distance function in the plane needs to be modified. Article abstract:
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 TCWORLD: Online Resource for Technology Coordinators
A monthly publication of articles on exceptional uses of technology in schools, software reviews, technology policies, computer setup tips and techniques, security methods, opinions on integration and access, purchasing tips, a newsletter, and more.
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 The Teacher as Facilitator  Classroom Compass
The spring 1994 issue of Classroom Compass, Working for Reform, looks at the idea of teacher as facilitator  a basic part of the reformed classroom. Two classroom activities (one for young children, Mud Slide, the other for later grades, Stream Works)
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 Teacher Education and Professional Development  Mathematics Education at the Math Forum
New ideas and pedagogy: articles, conference sessions, centers, and courses on the Web for preservice education, inservice education, and the college and university level.
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 Teacher Education Materials Project (TEMAT)  Horizon Research, Inc. (HRI)
A site for K12 professional development providers, with a conceptual framework "Designing Effective Professional Development" (short essays on: Understanding the Needs of the Target Audience; Deciding on the Purposes of the Professional Development;
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 Teacher Learning That Supports Student Learning  Linda DarlingHammond
"What do teachers need to know to teach all students according to today's standards? What kinds of preservice training and ongoing professional development will make teacher success more likely?" Article from Educational Leadership, February 1998, Volume
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 Teacher Quality and Student Achievement: A Review of State Policy Evidence  Linda DarlingHammond
From Education Policy Analysis Archives, Vol. 8, No. 1, January, 2000. Abstract: Using data from a 50state survey of policies, state case study analyses, the 199394 Schools and Staffing Surveys (SASS), and the National Assessment of Educational Progress
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 Teachers Becoming SelfDirected Learners: A Work in Progress  Horwitz, Hallam; Eisenhower National Clearinghouse
How the Annenberg Tuning Protocol is used by the PennMerck Collaborative for Science Education to foster a constructivist view of learning with reflective, internally motivated practitioners. The program involves a 13month graduate course designed to
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 Teachers Teaching With Technology (T3)
Professional development training in handheld technology for educators at each level. Sites worldwide in a host of different languages. The United States site includes: professional development institutes, courses, and seminars; resources for educators
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 Teaching and Learning Algebra pre19  The Royal Society and The Joint Mathematical Council (United Kingdom)
A policy document that addresses curriculum and teaching methods in algebra. The influences on pupils' experience of algebra within all aspects of the preuniversity education system were examined.
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 Teaching and Learning Geometry 1119  The Royal Society and The Joint Mathematical Council (United Kingdom)
A policy document that addresses the rationale for teaching geometry; its possible content; issues concerned with its effective teaching; and why this important subject, with such wide applications and a long history, remains one of the most difficult
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 Teaching and Learning (MAA)  Mathematical Association of America
Teaching and learning mathematics is what most MAA members do for most of their lives. This Teaching and Learning section provides useful and thoughtful articles about teaching mathematics. The Research Sampler is dedicated to spreading awareness of current
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 Teaching (Learning and Mathematics)  Hiebert, Wearne; Math Forum
In this 1992 article, "Links Between Teaching and Learning Place Value With Understanding in First Grade," James Hiebert and Diana Wearne, of the University of Delaware, describe an experiment they conducted in which they compared textbased instruction
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 Teaching & Learning Perspective: Constructivism  John Pais
Communicating Mathematics Using Heterogeneous Language and Reasoning. Mathematics is the science of patterns... Precisely how humans accomplish selforganization is still essentially unknown, but nevertheless has important consequences for structuring
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 Teaching Logic and Reasoning in an Illogical World  DIMACS Symposium
A July 1996 symposium: Participants, schedule, list of papers, and the papers themselves in html, ascii, or postscript. Sample papers: S. Maurer: Teaching reasoning, broadly and narrowly; C. Nelan: Student's attitude toward the relationship between language
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 Teaching Math to Young Children  Rick Garlikov
One of a series of webpages to help students understand math, and to help parents teach their children math  especially to help children have a good foundation. (These are not pages to teach the mere recipes or algorithms for solving problems.)
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 Teaching with Electronic Technology  Michael L. Hall
A collection of Web sites reflecting a variety of uses for computing and related forms of electronic technology in teaching, arranged to proceed from more general and theoretical resources to instructive examples of specific applications of technology
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 Teaching with Original Historical Sources in Mathematics  Laubenbacher, Pengelley; Dept. of Mathematical Sciences, New Mexico State Univ.
Excerpts, many in .dvi or postscript formats, and links to extensive information from a book on teaching mathematics with original historical sources: courses, books, and materials available at the undergraduate and high school levels, work with school
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 TeachingWorks
Establishing a "professional system for the training of teachers" through "a common curriculum for professional training that focuses on highleverage practices and on the subjectmatter knowledge needed for teaching; performance assessments of teachers'
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 TeAchnology  Teachnology, Inc.
A portal for information about current and past practice in the field of education. Read math teaching "Ideas That Worked"; and tutorials ranging from teacher retirement planning and "What to Consider When Writing a Lesson Plan" to "How to Deal With Disruptive
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 Technical Reports index  University of Cambridge Computer Laboratory
Technical reports by the University of Cambridge Computer Laboratory, some dating back to 1974, and all those published since January, 2002. Titles include "Decimalisation table attacks for [ATM] PIN cracking"; "Turing Switches  Turing machines for alloptical
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 Technische Universität München School of Education
Research, publications, teaching portfolios, and more about the Technische Universität München (TUM) School of Education, which trains teachers for vocational schools and upper secondary schools (Gymnasien) in Germany. See, in particular, the
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 Technologies: Past and Future  Cut the Knot!, Alexander Bogomolny, with Don Greenwell
A discussion of the similarities in browsing through books and surfing the Internet, the serendipitous discoveries that can be made, fallacious geometric and other puzzles, and an interesting integer matrix, with recommendations of books to read and sites
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 Technology for All Americans Project  International Technology Education Association (ITEA)
An effort to increase the technological literacy of all Americans, to develop a clear vision of what it means to be technologically literate, how this can be achieved at a national level, and why it is important for the nation. Read the Executive Summary:
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 Technology in Math Education  Mathematics Education at the Math Forum
Teaching and technology: case studies and critical issues; calculators; computers; conferences, forums, and panel discussions; pedagogy and curriculum development; software for mathematics education; text recommendations.
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 Technology in the IMP Classroom  Alper, Fendel, Fraser, Resek
The Interactive Mathematics Program (IMP) has developed a new fouryear high school curriculum which is organized around units lasting from 5 to 8 weeks. Each unit centers on a rich problem, and students develop new concepts and skills by solving that
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 Ted Spence's Home Page
Research into the classification of combinatorial designs. Recent work has entailed the classification of all Hadamard matrices of order 28. Links include: a List of Publications; 2designs; Hadamard matrices Twographs; Steiner S(2,4,25); Regular graphs
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 Teen Math Whizzes Go Euclid One Better  Gautam Nair, The Wall Street Journal
The scholarly journal Mathematics Teacher has churned out some 7,500 articles published over the past nine decades. This month, Volume 90, issue No. 1 will feature a first: a formal math treatise by two high school students. A reproduction of an article
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 Tell A Number Trick (Magic of Numbers)  Paul Chika Emekwulu
A number trick, with an algebraic investigation and an explanation. From Novelty Books and Articles OnLine.
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 Templates for Linear Algebra Problems  Bai, Day, Demmel, Dongarra, Gu, Ruhe, and van de Vorst
The solution of linear systems of equations and eigenvalue problems lies at the
heart of most calculations in scientific computing. This paper discusses some recent developments designed to help the user on advancedarchitecture computers, focusing on
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 Temple Circles  Ivars Peterson (MathTrek)
One tradition that flourished 200 years ago in Japan, during its period of isolation from the western world, involved Euclidean geometry. Scholars and others would inscribe geometric problems on wooden tablets, then hang the tablets under the eaves of
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 Terry McConnell's Home Page  Terry McConnell, Mathematics Department, Syracuse University
Download PDFs of tests given in McConnell's introductory calculus, Math 295. "Stuff" ranges from a remark on average velocity and an expository paper showing the details of how to derive the second order correction to the period of a plane pendulum using
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 The Tesseract  Cut the Knot!, Alexander Bogomolny, with Don Greenwell
A hypercube is a multidimensional analogue of a 3dimensional cube in that each coordinate of a point in a hypercube is restricted to the same 1dimensional (line) segment. The Tesseract is a 4dimensional hypercube. With an applet designed to demonstrate
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 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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 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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