 Musical Multiples  MusicWorks 4 Learning
A multisensory approach to the times tables using manipulatives and music. Purchase the Musical Multiples CD, which contains 11 songs for the multiples of 212.
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 Music and Mathematics  Math Forum, Ask Dr. Math Common Question
A selection of answers to questions about music and mathematics, and pitches, tones, and musical scales, in particular
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 Music and Probability  Lorraine Fielding
A middle school's music project based on the Mozart Musical Dice Game, invented by Mozart around 1770, in which dice rolls generate twelvetone or diatonic minuets. Links to a web version of Mozart's game, using MIDI technology; and movie, audio files
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 Music by John Greschak  John Greschak
Platonic Dice: Dodecahedron, Platonic Dice: Hexahedron, Pentominoes, The Tower of Hanoi, and other music compositions based upon the mathematical properties of various objects. Listen with RealAudio or Midi.
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 The Music of José Oscar Marques
Listen to fractal music compositions in General MIDI file format, designed to show that recursive algorithms can be employed to create music of the same strange beauty as the richly decorated fractal picture on the site.
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 Music through the Curriculum  Phil Tulga
Developers of math programs such as "Math and Music," which teaches students how to "hear" math (what does a fraction sound like? how about a shape?); and "Math, Science and Sound," an assembly and family night program that connects thunder, volcanoes,
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 Nathan Selikoff
Works, publications, blog, and more from a "fine artist playing at the intersection of interactivity, math, and code." Works have included "Beautiful Chaos" (interactive software art), "Intersect"
(a public art installation), "Four Dimensions" (a realtime
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 NCTM San Diego Sessions on Humanistic Math  Mathematics Education at the Math Forum
A selection of presentations from the 74th Annual NCTM Meeting, April 1996, San Diego, CA.
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 Neural network music composition by prediction  Michael C. Mozer
Exploring the benefits of psychophysical constraints and multiscale processing. In algorithmic music composition, a simple technique involves selecting notes sequentially according to a transition table that specifies the probability of the next note
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 Oldani's Math and Music Website  Norbert Oldani
A description of the types of mathematics used for electronic music. The site includes other website links and a bibliography.
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 Online Math Applications  Leung, Jiang, Jiang, Chiu, Klopfer, Chiu; ThinkQuest Junior
Activities, examples, problems, and online quizzes about math applied to real world situations in investing (a stock market simulation game), music (classical MIDI files), history (biographies and anecdotes), science (astronomy, computers, 'math in the
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 Paul's Page of Pi  Paul A. Gusmorino 3rd
Most of the content of this site is focused on methods of calculating pi: Archimedes' method; Wallis' formula; Gregory, Leibniz, and Machin; Newton's fluxions; and Paul's 8192 digits. Also Pi Poems, Music of Pi, and Pi Links.
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 PianoMath Home Page: Improving Math Skills through Music  Peter Taussig, E. Paul Goldenberg
Essays and activities on links between music and mathematics. PianoMath is
a crossdisciplinary curriculum of musical classroom activities relating to
arithmetic, geometry, graphing, logic foundation, and prealgebra. It is
now being tested at an elementary
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 Play a Piano : An interactive Musical Java Activity  Paul Flavin
Play a Piano / Synthesizer / Oscilloscope: Play the piano using your mouse or computer's keyboard. Watch the wave forms as well as hear them. This virtual reality Java piano lets you play the piano and have a little fun while learning the relation between
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 Plus Magazine  Department of Applied Mathematics and Theoretical Physics, University of Cambridge
Plus (formerly PASSMaths) is a triannual online magazine for older pupils and the general public. It publishes articles explaining the diverse applications of mathematics used in solving problems in physics, chemistry, biology, engineering, and economics.
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 Prime Listening  Ivars Peterson (MathTrek)
Mathematician Chris K. Caldwell of the University of Tennessee in Martin has developed a scheme for listening to sequences of primes  to hear both simple patterns and perplexing irregularities found among those numbers. "Multimedia allows the use of
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 Prime Number Listening Guide  Chris Caldwell; Dept. of Mathematics & Computer Science, Univ. of Tennessee at Martin
A guide to an online program that you can use to create your own "primal sounds" if you can play midi files. Caldwell introduces a few ways to hear the primes and use them to hear both the simple patterns (there are some) and the perplexing irregularities
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 Printables: Student Handouts  The Learning Network
PDF format printable handouts. Browse by grade or subject; check out the featured handouts; or search for a topic of your choice. Other resources also available through the Lesson Planning Center links on the site.
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 The Published Data of Robert Munafo  Robert Munafo
Mathematical data includes MuEncy, The Encyclopedia of the Mandelbrot Set (History, Exploring, Area, Algorithms, Naming, etc), properties of specific numbers, such as 2.68542 . . . and 143, and very large numbers and ways to write them. Programs include
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 Pythagoras: Music and Space  J. BoydBrent
A brief introduction to Pythagoras' observations on the relation between music and number. Graphics show music intervals expressed as mathematical ratios. Pythagoras observed that when the blacksmith struck his anvil, different notes were produced according
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 Rachel W. Hall's Research Page  Rachel Wells Hall
Rachel W. Hall in the Department of Math and Computer Science, Saint Joseph's University, Philadelphia, PA, offers links to her articles on mathematics and music in PDF format, including: Geometrical Music Theory; A Course in Multicultural Mathematics;
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 Rhythms and Ratios  Peter Appelbaum
Rhythmic patterns are used to help the student act as apprentice mathematician and citizen mathematician (reading the newspaper, responsible consumerism, etc.). Rhythmic Ratios observations and introductions include the Basic Pattern Idea; Something to
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 The Ridiculously Enhanced Pi Page  The Exploratorium, San Francisco, CA
Pi Day celebrations, Pi music, links, beads, and pie. A certified 98% contentfree page.
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 Schoolhouse Rock
Schoolhouse Rock is one of many artifacts from the 1970s that still is in existence today. In the mid70s, ABC TV aired these short cartoons, which taught a generation about government, history, grammar, science, and math. The lyrics of all the songs
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 ScottBeall.com  Scott Beall
Professional development programs for mathematics teaching and interdisciplinary curricula, emphasizing the integration of music and mathematics. With examples from his recent publication Functional Melodies  Finding Mathematical Relationships in Music
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 Seeing and Learning Astronomy and Cosmology Through the Lens of Music  Sloan Edward Williams III  YaleNew Haven Teachers Institute
Exploring music, astronomy and cosmology, starting with the historical roots; the Pythagoreans in particular contributed profoundly to the development of Western Music by discovering two facts: first, that the sound caused by the
string depends on the
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 A Song About Pi  Ivars Peterson (MathTrek)
A short biography of Irving Kaplansky, Director Emeritus of the Mathematical Sciences Research Institute (MSRI) in Berkeley, CA, and his analysis of the structure of complex songs.
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 The STEM Collaborative  Maryland Public Television, Arkansas Educational Television Network, Alabama Public Television, and Kentucky Educational Television
The four online adventures Scale City, ProportionLand, Math by Design (architecture), and Rock 'n Roll Road Trip (music) engage students to use geometry, algebra, and proportional reasoning for skateboard ramps, cooking, amusement park roller coasters
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 Third Apex to Fractovia  Juan Luis Martínez
Several galleries, each with up to 18 fractal images, and discussions on fractals as art. Also an uptodate list of freeware fractal generators, screen savers, and fractal music software, with links and reviews.
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 Tides and Tide Prediction  Tony Phillips; Dept. of Mathematics, SUNYStony Brook
General information about tides and tide prediction: Priming/Lagging: a calculus with calculators exercise demonstrating the priming and lagging of the tides at Stony Brook. Samples of current tide predictions from the National Ocean Service. TideSounds:
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 Topical Index of Internet Resources (The Chaos Hypertextbook)  Glenn Elert
An extensive list of links to sites related to Elert's Chaos Hypertextbook. Major categories include: Chaos (Dynamical Systems); Dimension; FAQs; Feigenbaum Constants (Bifurcation Diagrams); Fractals; Image Compression; Iterated Function Systems (IFS);
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 TotiPM  Jordi Lagares Roset, Prof. of Mathematics, Girona
Una página basicamente en Catalán, pero con referencias también en castellano e inglés. Páginas didácticas, problemas, software. A page primarily in Catalan but with Spanish and English language references. Lessons,
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 Toying with Reality: Java Applets and VRML  Paul Flavin
Virtual Reality: Modeling with Math, and a little Java. Applets to manipulate: The Pythagorean Theorem; Equation Grapher: "You type, I Graph"; Graphing Vector Calculator; Java 3d Visualizer; Virtual Rubik's Cube; Raytracing applet; Java Calculator; Play
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 Vi Hart  Vi Hart
Blog, videos of math "doodling," instructions for slicing food mathematically, and more from the selfdescribed recreational mathemusician who considers math a hobby, with "special interests in symmetry, polyhedra, and surreal complexity. This usually
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 What Is Mathematics?  John M. Lawler, Dept. of Linguistics, Univ. of Michigan
Listings of links on Godel, Escher, and Bach, and other material related to Hofstadter's book by that name, from a math appreciation course.
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 www.caseymongoven.com  Casey Mongoven
In his music, Casey Mongoven works with Fibonacci numbers, related sequences, and the golden ratio. The site includes scores, writings, WAVs, and MP3s among other files available for download. In English and German.
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 Zap Headquarters  Sue and Bob Durante
Sue and Bob Durante offer a wide variety of Math Programs for school assemblies, math nights, workshops and more. Blending magic with Math and teaching many bits of magical fun that use math and will get students to use math outside of the classroom.
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