 When The Counting Gets Tough, The Tough Count On Mathematics  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
A discussion by William A. McWorter, Jr. of the application of the recursion formula for the Fibonacci sequence to counting and vector problems.
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 Where to Start?  Cut the Knot!, Alexander Bogomolny
A discussion of math education: the intent of the NCTM Standards, reflections on the history of constructivism, classroom practices (with a link to Marilyn Burns' Math Solutions page), and a simple applet for solving linear equations. An interactive column
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 Where Will the New Millennium Begin? (Math Chat)  Frank Morgan; Christian Science Monitor
Assuming the third millennium arrives on January 1, 2001, where on Earth should the celebration begin?
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 Which Countries Are Most Like Stars? (Math Chat)  Frank Morgan, MAA Online
Which countries in the world have a point such that the shortest line from
every other point in the country stays inside the country? (ignore mountains and valleys). Mathematicians call such countries starlike. Are there any countries such that the shortest
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 Which One Doesn't Belong?  Mary Bourassa
Also known as Imposter Sets, "Which One Doesn't Belong?" provides thoughtprovoking puzzles, each with many different, correct ways of identifying the exceptional shape, number, graph, or equation from the colorful 2 × 2 grid of similar ones.
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 Which One Is Older? (Math Chat)  Frank Morgan, MAA Online
Creative solutions to the challenge: how can two people determine which is older without revealing their ages? Math videos available from the Mathematical Sciences Research Institute via the MAA. "Mathematics in Arcadia," "Fermat's Last Theorem," as seen
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 Which Polygon Sides are Parallel?  NASA Lewis Learning Technologies Project
Which of these line segments are parallel? Two adjacent sides of a triangle; Two adjacent sides of a pentagon; Two opposite sides of a rectangle; Two radii of a circle. A diagram and a detailed answer are provided. From NASA's 9th Grade Math Proficiency
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 Which Problem Equals 25 Percent?  NASA Lewis Learning Technologies Project
Which problem has an answer of 25 percent? 1) 10 is what percent of 50? 2) 25 is what percent of 75? 3) 25 is what percent of 125? 4) 20 is what percent of 80? A detailed answer is provided. From NASA's 9th Grade Math Proficiency Test.
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 Whips and Dinosaur Tails  Ivars Peterson (MathTrek)
The loud crack of a deftly flicked bullwhip is a small sonic boom, generated when the whip’s thin, highly flexible tip exceeds the speed of sound. Sauropod dinosaurs of the family Diplodocidae have enormous tails that gradually narrow to thin, delicate
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 Whistler Alley Mathematics  Paul Kunkel
Kunkel's Geometer's Sketchpad lessons convey a conceptual understanding, usually without rigorous proof, with questions and suggestions for extensions: Buffon's Needle (an old probability exercise); Chinese Handcuffs (questions with applications for geometry,
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 White Group H2 Maths Tuition  Koh Y.S. Frederick
This Singaporean tutor offers examination advice and recommendations ("A level H2 maths question spotting thoughts"), a section for those "pursuing mathematics beyond the Singapore H2 9740 standard," and a "question locker" for students who "wish to challenge
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 White Narcissus  Ivars Peterson (MathTrek)
The elegant, swooping forms carved out of wood by sculptor Robert Longhurst often resemble gracefully curved soap films that span twisted loops of wire dipped into soapy water. Alhough these abstract sculptures bear an uncanny resemblance to mathematical
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 WhizGraph  a program for data analysis and graphic presentation on your Mac  Hans Timm
WhizGraph is a data analysis and graphic presentation shareware program for the Macintosh. It combines professional graphing and versatile layout options with clear data management and comfortable macro calculation. The website provides more specifications,
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 Whole Language Approach in Solving Word Problems (SMILE)  Barbara Thomas, Langston Hughes School
A lesson that uses the story of the Three Little Pigs to teach students to formulate addition and subtraction problems of whole numbers; relate everyday language to mathematics meaningfully; use problemsolving approaches to investigate and understand
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 Wholemovement  Bradford HansenSmith
Bradford HansenSmith presents the art and geometry of folding circles. As he explains, "Everything we know about geometry, mathematics, and all spatial arrangement and organization of matter is demonstrated by cutting into the wholeness of the sphere.
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 Whole number arithmetic  Martin Selditch
A tutorial that covers basic arithmetic with whole numbers. Exercises allow students to practice arithmetic skills.
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 Who Likes Homework
Tutors and homework helpers in math, chemistry, physics and more.
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 Who's Counting  John Allen Paulos
Columns by Prof. John Allen Paulos, the author of Innumeracy, Mathematician Reads a Newspaper, and other popular books. Humorous and enjoyable articles by a keen observer of the world around him whose mind has been sharpened by mathematical practice.
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 Who's Really Ahead?  Ivars Peterson (MathTrek)
The winding down of the current baseball season seems an appropriate time to take a look at a curious inconsistency that sometimes appears in team standings... Once in a while the team with the higher winning percentage may be at least onehalf a game
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 Who's Really No. 1?  Ivars Peterson (MathTrek)
It happens every fall. Fierce arguments erupt over which U.S. college football team is the best in the nation. As the season progresses, this frenzy of head scratching and navel gazing mounts until the climactic bowl games at the end of the year (more
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 Who Wants to Be a Mathematician  American Mathematical Society
In the game show "Who Wants to Be a Mathematician," high school students compete for cash and prizes by answering multiple choice mathematics questions. Read about past performances of the game; view videos of games played in Danvers, MA, at Danvers High
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 Who Wants to be a Millionaire? (Math Chat)  Frank Morgan, MAA Online
Answering the challenge: On ABC TV's "Who Wants to be a Millionaire," to maximize your expected winnings how sure should you be of your answer to the $500,000 question to answer? Somewhere from about 22.5% to about 46.5%, probably closer to the latter.
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 Who was Marin Mersenne?  Luther Welsh
It was not until the mid 20th century that Mersenne became known primarily for his Prime Number Conjecture. Historically, he was much better known for his correspondence with leading scientists of the day. Interested in optics, he also been called the
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 Why 2001 Won't Be 2001  Keith Devlin (Devlin's Angle)
"It's a good story... But how realistic is the behavior of HAL? We don't yet have computers capable of genuinely independent thought, nor do we have computers we can converse with using ordinary language. True, there have been admirable advances in systems
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 Why Calculus?  Helmer Aslaksen
A course the goal of which is to show why calculus has served as the principal quantitative language of science for more than three hundred years.
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 Why Does BacktoSchool Imply Back to Math?  Keith Devlin (Devlin's Angle)
...in a world where everyone can afford a pocket calculator and a great many people seem to be successful in life with little or no mathematical ability or knowledge of science, why do we place so much emphasis on math and science?
Whatever the answer,
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 Why Do Math?  The Society for Industrial and Applied Mathematics (SIAM)
A showcase for exciting mathematical and computational science topics at an introductory collegiate level. Short popular science articles that illustrate the innovative uses of math in yachting, cochlear implants, neuroscience, space travel, tomography,
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 The Why Files  University of Wisconsin
An electronic exploration of the issues of science, math, and technology that lurk behind the headlines of the day, presenting those topics in a clear, entertaining and accessible manner. Provides a bimonthly feature on the science of everyday life, archived
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 Why Isn't There a Nobel Prize in Mathematics?  Peter Ross
Ross writes that Garding and Hormander state, "The true answer to the question (of the title) is that, for natural reasons, the thought of a prize in mathematics never entered Nobel's mind." Nobel's final will of 1895 bequeathed $9,000,000 for a foundation
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 Why is the Area of a Circle Pi*r^2?  Eva Thury
An explanation of the formula for the area of a circle, based on "slicing" and rearranging the circle.
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 Why is the Mathematician So Messy? (Math Chat)  Frank Morgan, MAA Online
A physicist and a mathematician can clean a house in 6 hours; an engineer and the mathematician in 3 hours; and the physicist and the engineer in 1 hour and 12 minutes. How long would it take the physicist alone?
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 Why is the Product of Negative Numbers Positive? (Question Corner and Discussion Area)  University of Toronto Mathematics Network
A short essay and a description of a practical demonstration.
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 Why It Is Important to Learn Algebra  EdSource
This PDF document is a parent/student guide explaining why Algebra I is a required subject, how it helps prepare students for the future, how Algebra I fits into the student's high school math program, and what parents can do to support their student's
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 Why It's Hard to Fold a Triangle in Half (Math Chat)  Frank Morgan, MAA Online
For a circular piece of paper, the lines along which you can fold it "in half" (with half the area on each side) are precisely the lines through the center. What other shapes work the same way? This works for lots of shapes, such as rectangles, parallelograms,
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 Why major in Mathematics?  Department of Mathematics, University of Georgia
Seven reasons to pursue, or applications of, the major in mathematics: because you like it, because professional schools realize it develops analytical skills and the ability to work in a problem solving environment, because employers highly value those
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 Why Not Geometry?  Cut the Knot!, Alexander Bogomolny
An exploration of the validity of teaching algebra at the middleschool level, testing, mathematics ewducation reform, the goal of education, and a suggestion that geometry might be a more important starting point.
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 Why Study Math? How to Study Math  Math Forum, Ask Dr. Math FAQ
Why do we need to learn math? When are we ever going to use it in real life? Math study tips.
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 Why Teach Mathematics?  Harold Brochmann
A series of articles addressing the questions Why do we have to learn this stuff? Why do we teach mathematics? Is the mathematics we teach relevant? Why is teaching mathematics so difficult?
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 Width, Diameter, and Geometric Inequalities (The Geometry Junkyard)  David Eppstein, Theory Group, ICS, UC Irvine
An extensive annotated list of links to material on width, diameter, and geometric inequalities.
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 Wild About Math!  Sol Lederman
Math posts, which date back to October, 2007, have included "10 ways to get wild about Math," "How to square large numbers quickly (part 1)," "26 tips for using learning styles to help your kids with Math," "The algebra of crossmultiplication," "Flexagon
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 Wilder's Fourth Grade Math and Science  Jim Wilder
Wilder's blog, which dates back to July of 2008, has included posts such as "Pumpkin Investigation/Family Math Night," "Spuds, Velocity, & Central Tendency," "predict the pattern," "codes and the tricky elevens," and "thinking about patterns." Wilder
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 Wildlife Trade: Buyer Beware  Shelly Peretz, Thornridge High School, Dolton, IL
Collecting and analyzing consumer values, attitudes, and beliefs regarding wildlife trade and endangered species: a project that demonstrates the feasibility of integrating learning strategies, math, social studies and science within a traditional high
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 Wiles' proof of Fermat's Last Theorem  Paul Hewitt; University of Toledo
An overview, following Glenn Stevens' article in Modular Forms and Fermat's Last Theorem (SpringerVerlag, 1997). Notes from a series of three 1998 lectures.
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 Wiles, Ribet, ShimuraTaniyamaWeil and Fermat's Last Theorem  Dept. of Mathematics and Statistics, The University at Albany
An archive of FLT material from conferences, lecture, meetings, newsgroups, and Web sites. Much of the material that seeded this archive was copied from the former gopher archive pertaining to "Fermat's Last Theorem"at emath.ams.org.
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 William Lowell Putnam Mathematical Competition  The Mathematical Association of America (MAA)
The examination tests originality as well as technical competence. Questions cut across the bounds of various disciplines, and selfcontained questions that do not fit into any of the usual categories may be included. Announcement of winners, description
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 William's Home Page  William Gibbs
A collection of activities that use simple materials to help students explore mathematical concepts. Topics include: shapes and patterns made from paper circles; geometrical activities with magic paper; window patterns from geometrical shapes; where there
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 Will it rot my students' brains if they use Mathematica?  Theodore W. Gray and Jerry Glynn
Excerpts from the introduction to The Beginner's Guide to Mathematica V4. Jerry: "I have young students who reach for their calculators to get the answer to 5×6. My response, when I see that, is to explain that such behavior is socially unacceptable,
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 Will the real continuous function please stand up?  Keith Devlin (Devlin's Angle)
A description and a more rigorous CauchyWeierstrass definition that "forms the bedrock of modern real analysis and any standard 'rigorous' treatment of calculus," with a discussion of how the formal definition involves a major shift in conceptual model
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 Wilson A. 'Snowflake' Bentley (18651931)  Tobias C. Brown
An American farmer who spent most of his life producing photomicrographs of snowflakes at his Jericho, Vermont farm. The site includes a Snow Crystal Display with a sequence of 26 images.
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 Wilson's Inversive Geometry with CabriJava  Wilson Stothers, University of Glasgow
An introduction to inversive geometry, with explanations and illustrations using
CabriJava. Many of the results and ideas are Greek, largely due to Apollonius of Perga. The approach is from the Klein viewpoint, using a group of transformations of a
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