 The Brachistochrone  Paul Kunkel
An investigation of the problem: We are given two fixed points in a vertical plane. A particle starts from rest at one of the points and travels to the other under its own weight. Find the path that the particle must follow in order to reach its destination
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 The brachistochrone problem
 MacTutor Math History Archives
Linked essay on the brachistochrone problem, posed by Johann Bernoulli in Acta Eruditorum in June, 1696. With references and other related web sites.
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 Brahmagupta's Formula  Jim Wilson, Dept. of Mathematics Education, Univ. of Georgia
Problem: Develop a proof for Brahmagupta's Formula, which provides the area A of a cyclic quadrilateral (i.e., a simple quadrilateral inscribed in a circle) with sides of length a, b, c, and d as A = sqrt((sa)(sb)(sc)(sd)) where s is the semiperimeter
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 BrainBashers  Kevin N. Stone
A collection of logic, language and math puzzles, in a choice of easy/medium/hard. Rate the puzzles; show their answers. Logic puzzles include Einstein's Puzzle. Play games of strategy, such as "Four in a Row" (also known as "Connect Four") or games based
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 BrainBashers  Kevin Stone
Five math or logic challenges on a page, each with clickable hints and solutions. For games, visit http://www.brainbashersgames.com/.
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 Brain Boosters  Discovery Education
An archive of challenging puzzles, organized under: Categorization, Lateral Thinking, Logic, Number and Math Play, Reasoning, Spatial Awareness, Word and Letter Play.
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 Brainers  PedagoNet
More than 60 word problems and puzzles designed to develop logic and problemsolving skills. Submit your answers and suggestions to become part of the Wall of Fame. Site is in English, French, and Spanish.
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 Brain Food  Puzzles For the Brain To Gnaw On  Samuel Stoddard
Hundreds of online (CGI) puzzles, including logic puzzles, word problems, number puzzles, lateral thinking puzzles, scrambled equations, cryptograms, loginumber puzzles, discrete reasoning puzzles, mathematical reasoning puzzles, knight's dilemma, magic
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 Brainfreeze Puzzles  Riley, Philip; and Taalman, Laura
Free example puzzles and solving tips for colorful, handdesigned Sudoku variation puzzles with additional rules that challenge you to rethink your old Sudoku strategies and devise new ones. From the authors of the book, Color Sudoku.
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 Brainingcamp Educational Math Software  Dan Harris, President and CEO
Real math problems and simulations for 5th9th grade. Middle school math online software. Guided by NCTM and State mathematics standards. Video demo and free trial available.
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 Brainormous
Worksheet makers and math games available for demo or purchase: Zeus' Petals, Fourdoku, Multiflyer, Mathteroid, Gridiant, and more.
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 BrainPOP Math  BrainPOP, LLC
Short animated films that are simple and easy to understand on elementary mathematics, as well as health, science, and technology. Films often accompanied by quizzes.
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 BrainQuake  BrainQuake Inc.
Designers of arcade quality educational game apps that espouse embodied learning from which "you cannot fail to learn about mathematics." Use puzzlesolving skills to explore and practice basic arithmetic, integer partitions — even Diophantine equations
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 Brain Science & ICT in Mathematics Education  Dave Moursund
An exploration of three major topics from a math education point of view: Brain Science Craft & Science of Teaching & Learning (C&S of T&L) Information & Communications Technology (ICT). Read the author's thoughts on constructivism,
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 Brainwave  Wognum Art
Ten visual puzzles, to test your visual and reasoning skills. Most have to do with symmetry recognition. There is a "top 5% brain" award to those who earn ten "smart bulbs."
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 Brainy Figuring  Ivars Peterson (MathTrek)
In the May 7 Science, Dehaene and collaborators at the Massachusetts Institute of Technology present the first hard evidence that two quite different modes of brain activity underlie our inborn capacity for mathematics. Their study indicates that learning
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 Bray Proves Penrose Conjecture in General Relativity (Math Chat)  Frank Morgan, MAA Online
In 1979 R. Schoen and S.T. Yau proved that the total mass of a universe must be positive. Last year [1998] G. Huisken and T. Ilmanen proved that the total mass is at least as large as the largest constituent mass: M >_ m1. Finally this year [1999] H.
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 Breaking Chocolate Bars  Cut the Knot!, Alexander Bogomolny
The chocolate bar puzzle has three parameters: two side lengths (m and n) and actual selection of lines along which to break the bar and its parts... An interactive column for MAA Online that uses a Java applet to simulate a puzzle or mathematical problem,
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 Breaking the Light Barrier  Michael H. Walker
Galleries of fractal images: Flarium 1, Inkblot 1, etc.
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 BreakTru Software  David Giordano
Math shareware and freeware downloads for the PC include Quick Conversion, which converts distance measures such as inches, feet, yards, rods, furlongs, miles, and leagues to and from metric units such as meters; Fractions n Decimals, which converts mixed
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 Break Your Record for 100 Math Tables  Keiya Kanno
Practice addition, subtraction, and multiplication in these 10 by 10 tables: downloadable Flash shareware software for Macintosh OS X / Windows 2000, XP. Time and score are recorded automatically, recording up to 8 different users.
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 Brendan McKay
Software includes nauty, a program for computing automorphism groups of graphs and digraphs, which can also produce a canonical labelling; and plantri, a program for generating planar triangulations. Also, skeptical treatment of claims made of miraculous
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 Brendt Wohlberg  University of Cape Town, South Africa
Fractal image compression resources: bibliography, publications.
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 Bret Victor
From the creator of Kill Math, Victor's "umbrella project for techniques that enable people to model and solve meaningful problems of quantity using concrete representations and intuitionguided exploration" in pursuit of a "widelyusable, insightgenerating
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 Bricks Activity  Suzanne Alejandre
A classroom activity (also called the Masonry Problem; a variation on polyominoes) aligned to the NCTM and California Standards, to be explored through manipulatives (dominoes). Students explore different possibilities of making brick walls with and without
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 The Bridges of Königsberg  Isaac Reed
This problem inspired the great Swiss mathematician Leonard Euler to create graph theory, which led to the development of topology.
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 The Bridges Organization: art and mathematics  George W. Hart, Webmaster
The Bridges Organization oversees an annual conference on connections between art and mathematics. The site's virtual museum shows sculpture, paintings, drawings, digital prints, textiles, origami and other paperfoldings created by mathematicians and
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 Bridge to Enter Advanced Mathematics (BEAM)
Creating pathways for underserved students from lowincome neighborhoods across New York City to become scientists, mathematicians, engineers, and computer scientists by providing them organizational help, academic counseling, academic help, mentorship,
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 Bridge to Higher Mathematics  Sam Vandervelde
Textbook for use with the proofs course taught at St. Lawrence University by Vandervelde, an Associate Professor of Mathematics who writes questions for the USA Math Olympiad. Bridge to Higher Mathematics incorporates "concept checks" and "mathematical
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 Bridging Math  Jennifer Bell
Blog by a K5 math coach in the Pacific Northwest. Posts, which date back to July, 2015, have included "#TMC15 Recap," "K12 Fraction Fun," "Choral Counting in Kindergarten," "#OML16 Recap," and "Number Talks and #ObserveMe." Elaborating on the name of
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 Bridging The Gap  Nicora Placa
Blog by a former elementary and middle school math teacher pursuing a Ph.D. in teaching and learning. Posts, which date back to April, 2013, have included "The subway ad that changed my life," "Transforming the Teaching Profession: It starts with RESPECT,"
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 Brief Course Materials for Various Courses  E. Lee Lady; University of Hawaii
A collection of short handouts: files are in PDF and DVI formats. Contents include: The Fundamental Theorem of Arithmetic, the division algorithm, solutions of linear congruences, solving the Chinese Remainder problem, an example of a continued fraction,
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 A Brief History of Algebra and Computing: An Eclectic Oxonian View  Jonathan P. Bowen; Oxford University Computing Laboratory, UK
Math history: Chapters on: The Origins of Algebra; Early English Algebra; Algebra and Analytical Engines; Boolean Algebra; Algebra and Computing; Recent Developments in the Algebra of Programs. References. Also available at http://www.museums.reading.ac.uk/vmoc/algebra/.
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 A Brief History of Cosmology  MacTutor Math History Archives
A hypertext essay describing the course of cosmology from its beginnings in early Babylonian society through the present, with References.
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 A Brief History of Mathematics  British Broadcasting, United Kingdom
Ten episodes of maths history by Marcus du Sautoy, first broadcast on the BBC in 2010, each themed around a particular mathematician or group of mathematicians.
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 A Brief History of Mathematics  Marcus du Sautoy, BBC Radio 4
Audio biographies of famous mathematicians: Newton and Leibniz, Euler, Fourier, Galois, Gauss, Riemann, Cantor, Poincaré, Hardy and Ramanujan, and Bourbaki. Each clip, originally aired on BBC Radio 4, runs about fifteen minutes long.
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 A Brief History of Mechanical Calculators  James Redin
An essay on the historical evolution of calculating machines, from the abacus to Babbage's differential machine to today's computers. Contents include: the abacus; the Antikythera calculator; Napier's Bones; Leonardo da Vinci's design; Schickard’s machine;
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 Brighten's Fractals Page  Brighten Godfrey
Investigate "Just Another Fractal Generator," a Java applet to make Iterated Function System (IFS) fractals based on triangles, or view a gallery of images created using the program.
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 BrighterDiscovery.com  KW Studios, Inc.
Products for children to "reach their full potential while having fun doing it." Browse by age (from 012 months to 8+ years) or product type, including Activity Toys, Alphabet & Numbers, Blocks & Building Sets, Games, Puzzles & Logic, and
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 Brightest Moon for Thousands of Millennia? (Math Chat)  Frank Morgan, MAA Online
Answer to the challenge: Was there any validity to the claim that the full moon of December 22, 1999 was the brightest that we shall see for millions of years? (Factors that coincided.) New challenge: Eric Brahinsky saw in an article on "New molecule
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 Bright Ideas Software
Bright Ideas Software was formed in 2001 with the goal of producing high quality educational software for the college and university market, with particular focus on graphical visualization tools for the physical sciences. We are located in Southeast
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 Brilliant
Weekly Olympiadstyle challenges that offer "rigorous, competitive, whimsical, and edifying" problem sets in math and physics. Register to explore the Brilliant Techniques Trainer's practice exercises; answer correctly to earn points redeemable for lanyards,
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 A Brilliant Madness: The story of Nobel Prize winning mathematician John Nash  PBS
"The story of a mathematical genius whose career was cut short by a descent into madness." Read a synopsis of the documentary, the film's transcript, primary sources such as John Nash's dissertation, his Nobel autobiography, and more. Based on the documentary,
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 Bring The Internet Into Your Classroom  NASA Quest Project
Links to an Internet Video Series designed to help teachers, administrators and community members introduce the Internet into K12 classrooms; grant information; which schools are online; and the universe of other NASA and Education Online Resources.
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 British Combinatorial Committee  Peter Cameron, Chair
A body that works for the support of combinatorial and discrete mathematics in the United Kingdom. Conferences in 2000 and 2001; Bulletin and information; News Items; links to related sites.
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 The British Society for the History of Mathematics (BSHM)
The British Society for the History of Mathematics promotes research into the history of mathematics and its use at all levels of mathematics education through meetings, a newsletter, and by other means. The BSHM takes in all periods and civilisations,
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 British Weights and Measures Association  Mr. Vivian Linacre, Edinburgh, UK
Views and aims; press releases; the association's publications and some articles from them; a list of patrons and officers; subscription details; an invitation to help; and contact information. "The British Weights and Measures Association opposes wanton
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 BrokenAirplane.com  Phil Wagner
Blog of "tips and ideas that you can use in your classroom immediately, and suggestions to help you, no matter your teaching or technology experience." Posts, which date back to June, 2010, have included "Math Project  Slope Art," "SAM Animation Is the
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 A Broken Calculator  Cut the Knot!, Alexander Bogomolny
Thoughts on the controversial question of using calculators in the classroom, and the author's belief that even a broken calculator may have its uses: the elementary mathematics curriculum may emphasize any or all of the paperandpencil, mental, or technologybased
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 Brownian Motion  Charlie Geyer
An applet that draws onedimensional Brownian motion, with source code and a link to statistical Java applets by others.
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