 1ucasvb's lab  Lucas Vieira
Diagrams and animations from a longtime contributor to Wikipedia's math and physics articles. Posts, which date back to February 2013 and feature graphics coded in POVRay and PHP, include "Experimenting with sound: the polygonal trigonometric functions
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 Aesthetics of the Prime Sequence  Turpel Armand
A brief introduction to prime numbers, with a primality testing applet, a page on primes and music, primes and nucleotide bases, primes graphics, idiot savants and primes, primesrelated software, related links, favorite books, and a special page of Lyapunov
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 Akustische Täuschungen/Acoustic illusions  Stefan Scheller
Endlos ansteigende Melodien: Der ShepardEffekt. Endlessly rising melodies: The Shepard effect. (Illustration: M. C. Escher: Treppauf, treppab  ascending, descending.) Besides the wellknown optical illusions there are acoustic ones, too. Perhaps the
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 American Pi  Lawrence Mark Lesser
Song lyrics by Lawrence Mark Lesser, approximately to the tune of Don McLean's "American Pie." Read a PDF of the Texas Mathematics Teacher article Slices of Pi: Rounding Up Ideas for Celebrating Pi Day, and see Lesser's "mathemusician" page for more lyrics
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 Annotated Bibliography of Software Resources (The Chaos Hypertextbook)  Glenn Elert
An extensive annotated list of software related to Elert's Chaos Hypertextbook. Major categories include: Chaos (Dynamical Systems); Iterated Function Systems (IFS); Lindenmayer Systems; Mandelbrot & Julia Sets; Music; Newton's Method; Terrain &
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 The Chaos Metalink  Industrial Street Productions
A site designed as an ongoing resource for all those interested in Chaos science and things fractal. This site is sponsored by Images of Chaos, an Artwork for Television and Industrial Street Productions as a service to the Chaos community. Featured Sites;
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 Circles of Dissonance  Ivars Peterson (MathTrek)
Much of today's music rests upon ancient tradition going back thousands of years to the time of the Greek mathematician and mystic Pythagoras. The Pythagoreans observed that tones an octave apart are pleasing to the ear. In modern terms,
one can say
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 Classroom Compass  Adams, Powell, Assoc. Editors; Southwest Educational Development Laboratory
A magazine published from 1994 to 2005, with ideas, activities, and resources for teachers interested in improving instruction in science and mathematics, and links to simple classroom activities with ideas about learning and instruction. Each issue presents
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 Connect with Music  Finn, Rudolph, O'Malley, Frankel, Ordway, and Langol
Thirty free interdisciplinary lesson plans that use multimedia, music, and technology to aid in the instruction of Language Arts, Mathematics, and Science at the middle school level. Lesson plans include comprehensive scoring rubrics, links to standards
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 Contradancing and Matrices  Ivars Peterson (MathLand)
Bernie Scanlon, a mathematics instructor at Bakersfield College in California, has been dancing nearly every weekend since 1990, even traveling to distant parts of the country to join in the fun. His passion is contradancing  a dance form unknown to
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 Culturally Situated Design Tools: Teaching Math through Culture  Ron Eglash
Java for creating your own Mangbetu design, cornrow curves, graffiti, bead looms, SimShoBan, Yupik star navigator, Yupik parka patterns, PreColumbian pyramids, and rhythm wheels  and learning the mathematics behind them. Organized into African, African
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 Curricula, Lessons, and Activities  ARTSEDGE
Annotated links on the Internet and additional offline resources highlighting lessons that interrelate the study of math with the arts. Organized into online curriculum, and related online resources of primary resources and indices.
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 Curriculum Development via Literary and Musical Forms  Joel K. Haack, Dept. of Mathematics, Univ. of Northern Iowa; the Math Forum
An article presented at the Humanistic Math session of the Joint Mathematics Meetings, January 1013, 1996, in Orlando, Florida. Haack's article discusses how the literary and musical forms can help develop a path through mathematical knowledge, envisioning
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 Dancing Chaos  Ivars Peterson (MathTrek)
Music, dance, and chaos... The image on the computer screen resembles a delicate, stylized butterfly with translucent wings held lazily askew. It's called the Lorenz attractor, named for meteorologist Edward N. Lorenz of MIT, who in 1963 discovered this
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 The Digit Connection  Lizzie
A tribute to the number pi through music, poetry, and fiction. (Meet Sailor Pi!) Also includes a brief history of pi with some ways to calculate it, a quote collection, and ways to celebrate the number  even if it's not Pi Day.
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 Discovering the Art of Mathematic  Fleron, Julian, et al.
Resources to help mathematics faculty teach the subject to liberal arts and humanities undergraduates by actively involving them in authentic mathematical experiences that "provide meaningful cognitive and metacognitive gains, and nurture healthy and
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 Drums That Sound Alike  Ivars Peterson (MathLand)
Peterson writes that physicists and mathematicians have long recognized that the shape of the boundary enclosing a membrane plays a crucial role in determining the membrane's spectrum of normalmode vibrations. He outlines the progress made on Mark Kac's
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 Encyclopaedia of Tuning  Joseph L. Monzo
A dictionary of terminology, often involving math, that is used by musicians and mathematicians to discuss tuning theory.
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 The Equal Tempered Scale and Some Peculiarities of Piano Tuning  Jim Campbell
An article on tuning applications from the Precision Strobe Tuners site. The Phenomena of Sound and the Harmonic Series, with information about Fourier analysis; Beats; The Physics of Ringing Strings; The Evolution of the Equal Tempered Scale; Piano Tuning;
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 An essay on patterns in musical composition, transformation, mathematical groups and the nature of musical substance  Bill Hammel
An article on music composition and history, with a discussion of the organizing principles of various musical scales as they affect musical composition and links to related sites.
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 Fibonacci Numbers and the Golden Section  Ron Knott
Information about the Fibonacci series, including a brief biography of Fibonacci, the numerical properties of the series, and the ways it is manifested in nature. Fibonacci numbers are closely related to the golden ratio (also known as the golden mean,
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 Foundation for Advancements in Science and Education
Since its inception, the mission of this independent nonprofit public charity has "evolved continuously, encompassing challenging new issues and exploring innovative applications of information technology." In particular, FASE sells The Eddie Files,
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 Fractal Music  G. Forrest Cook
Audio excerpts from a compilation of fractal music put together by the author.
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 Fractal Music: Research, Publications, and Compositions by Harlan Brothers  Harlan J. Brothers
In 2003, Benoit Mandelbrot suggested to Harlan Brothers that he undertake a rigorous treatment of the subject of fractal music. Here is an overview of Brothers’ subsequent research, including papers, definitions, and examples.
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 From Polychords to Polya: Adventures in Musical Combinatorics  Mike Keith
A book that explores the various connections between the basic musical building blocks  chords, scales, and rhythms  and the area of mathematics known as combinatorics, which is concerned with counting and classifying configurations of objects. Questions
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 The Golden Section In Art, Architecture and Music  Ron Knott
An introduction with illustrations and references to some applications and occurrences of the Fibonacci series and the Golden Ratio in architecture, art and music. The constant Phi has been used to design architecture, from the Parthenon in Athens to
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 Gsystems  Vladimir Ladma
A paper presenting an algebraic theory of musical chord structures that seeks to provide a simple algorithm for generating these structures.
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 Java Set Theory Machine  Jay Tomlin
Musical set theory encompasses the notion of defining sets of pitches and organizing music around those sets and their various manipulations. The site offers a Java applet that allows you to manipulate pitch class sets: play them, rotate and invert them,
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 K12 Teaching Materials (Mathematics Archives)  University of Tennessee, Knoxville (UTK)
An extensive list of Internet sites with significant collections of materials that can be used in the teaching of mathematics at the K12 level. Organized into categories: lesson plans, schools, software and other K12 Internet math sites.
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 Leonardo OnLine  International Society for the Arts, Sciences and Technology (ISAST)
A journal founded in 1968 in Paris by kinetic artist and astronautical pioneer Frank Malina. Today, it covers the application of contemporary science and technology to the arts and music. This site includes an art gallery with texts by the artists, excerpts
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 Liz's Research Interests  Liz Bradley, Department of Computer Science, University of Colorado
Artificial intelligence projects include Chaography, a pair of tools that use mathematics to generate choreographic variations: Chaographer, which uses a chaotic mapping to generate variations on a musical piece; and MotionMind, which uses machine learning
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 lofi paranoid ambient fractal music  Dave Sag
Selfsimilarity is the essence of fractal geometry: this is selfsimilar music, where each part has the same structure as the whole. Download an example in Real Audio, Shockwave, or aiff format. Another version of this page, What do I mean by 'fractal
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 The Map is Not the Territory  Malke Rosenfeld
Blog by a traditional percussive dancer (Appalachian style flatfooting and clogging and Canadian step dancing) who "teaches the math that directly relates to the process of making rhythm and patterns with the feet." Posts about the mathematics of percussive
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 Math and a Music Education  Ivars Peterson (Mathland)
Peterson discusses explorations into math and music by Pythagoras, Johannes Kepler, Galileo Galilei, Leonhard Euler, Johann Sebastian Bach, Frederic Chopin, and twentiethcentury composers, and cites a Nature journal article about a study suggesting that
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 Math Community of Interest  TeacherVision; The Learning Network
Lesson plans by grade level, lesson features, printable worksheets, online student activities, references and research aids, teaching tips, and parental advice.
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 Math Dance  Karl Schaffer and Erik Stern
The Dr. Schaffer & Mr. Stern Dance Ensemble has performed and conducted workshops on math dance in hundreds of schools and conferences since 1987. From that work, CoArtistic Directors Karl Schaffer and Erik Stern wrote MathDance, a 132page book with
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 Mathematical Connections  Whittle, Luoma; Dept. of Learning Support, Augusta State University
"Exploring the Interplay Between Mathematics and the Humanities." A forum for exploring the interplay between mathematics and the humanities, including, but not limited to, the relationship between mathematics and the arts, anthropology, history, literature,
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 Mathematical Modeling  Thomas E. Kelley, Dept. of Mathematical Sciences, Metropolitan State College of Denver
Description of course projects that emphasize learning mathematics through work on openended problems that have no "one correct solution," requiring the construction of a proposed mathematical model and designed to motivate students' learning of mathematics
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 Mathematics and Music  Michael Beer
An essay in PDF format providing a short overview of the relationship between mathematics and music. Topics include: Tone and tuning: the Pythagorean perception of music; Mathematical music: Fibonacci numbers and the golden section in musical compositions;
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 Mathematics in Art and Architecture  Helmer Aslaksen
An interdisciplinary course on mathematics in art and architecture, including the pyramids, Dürer and da Vinci, kaleidoscopes, the Golden Ratio and the Platonic solids, symmetry and patterns, music, Vitruvius, mazes and labyrinths, the origin of
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 Mathie x Pensive  Gregory Taylor
Musings on mathematics, teaching, and more by an Ottawa (Canada) high school math teacher who majored in computer science and graduated from the mathematics program at the University of Waterloo before receiving his B. Ed from Queen's University. Posts,
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 Math Pages  Kevin Brown
A collection of over 600 brief articles covering a huge variety of mathematical topics. Contents include: Number Theory; Combinatorics; Geometry; Algebra; Calculus and Differential Equations; Probability and Statistics; Set Theory and Foundations; History
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 Math Songs Wiki  Fridemar Pache
Listen to Bext, an animated proposition and proof of the Binomial Expansion Theorem sung by computer voice. With karaokestyle singalong text. Requires Flash. Also available from http://www.seedwiki.com/wiki/math_songs_wiki/.
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 Math That Makes You Go Wow  A MultiDisciplinary Exploration of NonOrientable Surfaces  Boittin, Callahan, Goldberg, Remes
A Web course intended for inclusion as a short segment in a late middle school or early high school math course and designed to convey the beauty and fascination of such mathematical objects as the sphere, the torus, the Klein bottle, the Mobius band,
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 Math Unplugged  Sara Jordan
A series of cassettes, CDs, and books offering a musical callandresponse approach to learning math. Multiplicaton and Division Unplugged drills students' counting skills by 2's, 3's 4's, etc. during the choruses, to strengthen their knowledge of the
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 Medieval Harmony  Ivars Peterson (MathTrek)
Harmonic numbers. The history of mathematics contains many gems of mathematical reasoning and thought. At a Mathematical Sciences Research Institute meeting last October, number theorist Hendrik W. Lenstra Jr. of the University of California at Berkeley
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 More than Magic Squares  Ivars Peterson (MathLand)
Peterson writes about magic squares, quoting Benjamin Franklin's interest in them. In addition to giving a few examples, Peterson also mentions Victor E. Hill IV's musing about whether the discoverer of the magic square actually set out to find an example
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 Mozart's Musikalisches Würfelspiel: A Musical Dice Game for Composing a Minuet  John Chuang
During his life, Mozart wrote the measures and instructions for a musical
composition dice game that cuts and pastes prewritten measures of music together to create a minuet. Compose a minuet online in one of three ways: CGI generates all random numbers,
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 Mudd Math Fun Facts  Francis E. Su; Mathematics Dept., Harvey Mudd College
A site developed as a resource for professors wishing to enrich their courses with mathematical 'fun facts': more than 100 5minute math tidbits that can be used at the beginning of class to get students interested in mathematics. They are best used in
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 Musemath  Bob O'Rourke
Videos on the mathematics and physics of the Western Traditional Music Scale.
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