 10 Lessons in Fractals, Complex Patterns, and Chaos  Jon Lee; Math Forum Teacher Exchange
From the WrightConnection 8week summer program, in which Dayton, Ohio, middle and high school math and science teachers participated in the realworld applications of math and science at WrightPatterson Air Force Base. The lessons, which emphasize
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 5 Numbers  Simon Singh and Marcus du Sautoy, BBC Radio 4
Web pages and Real Audio Music downloads of fifteen minutelong radio broadcasts that take a "quirky look" at zero, pi, the golden ratio, i, and infinity. "Hear about the stark reality behind the imaginary number, try a slice of pi, find out about the
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 8 is Great: Math Games
Addition, multiplication, and division practice at the elementary level. Tips and tricks offered for 9 and 11 times tables, factoring a quadratic expression, and generating the Fibonacci sequence. Also includes a sudoku puzzle.
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 Alex Vinokur's Home Page  Alex Vinokur
Links to resources of interest to computer scientists: Huffman Coding (an nary Huffman Template Algorithm, Arbitrary Huffman trees), Fibonacci numbers (computing very large Fibonacci numbers, computing Fibonacci numbers on a Turing Machine, the connection
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 Algorithms  National University of Ireland
Web interfaces that provide steps for moving the disks of the Towers of Hanoi, calculate the Euclidean greatest common divisor (GCD) algorithm using recursion, and compute maximum profit from the knapsack problem using dynamic programming. Also, generate
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 Andy Norton's Web Page  Dept. of Mathematics Education, Univ. of Georgia
Illustrated essays and explorations of algebra and geometry using various technology, including TI85 calculators, CBL's and computer software such as Geometer's Sketchpad (with sketches to download), Algebra Expressor, and Excel, by a grad student in
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 Center for Technology and Teacher Education  Curry School of Education, University of Virginia
An interdisciplinary group that develops materials to prepare teachers to use technology to enhance and extend students' learning of mathematics. This site offers activities using graphing calculators, The Geometer's Sketchpad, Microsoft Excel, the ExploreMath.com
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 chaotic nspace network  Jon Camp and Benjamin Martin
Fractals: an introduction, gallery of images, and evaluation of software for fractal creation, with links to download. Other mathematics resources include a brief introduction to the Fibonacci sequence.
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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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 Design Ideas  Julie Coghill
A series of articles that discuss quilt design using proportion, asymmetry, and Pythagorean triples.
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 Des Trucs et des Maths  Philippe Picart
Sur le nombre pi; le nombre d'or; le Rubik's cube; des ressources à télécharger; et "des trucs de maths divers," comme un JavaScript qui répond à la question "Quel jour de la semaine estu né?" Avec un coins des
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 Easier Fibonacci puzzles  Ron Knott
Puzzles that are simply related to the Fibonacci numbers....; Brick Wall patterns; Making a beeline with Fibonacci numbers; Chairs in a row; Stepping Stones; Fibonacci numbers for a change!; Telephone Trees ; Leonardo's Leaps; Fix or Flip; Two heads
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 Ed Dickey's Home Page  Ed Dickey
Syllabi for courses on teaching in middle/high school (mathematics), teaching mathematics with manipulatives (grades 712), graphics calculators in high school mathematics, computers in mathematics education, technology to support instruction, technology
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 Elementary Math Enrichment  Beth Schaubroeck
Free mathematics enrichment materials for accelerated 4th and 5th graders. The 70 lessons, grouped into 12 different units, include solutions and teacher guides: Ancient Mathematics (Mayan math, in base 20; and Egyptian math, which lacks zero), Baseball
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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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 Examples of Essays  Jim Wilson; Dept. of Mathematics Education, Univ. of Georgia
Extended Concurrencies of the Triangle, J. Wilson; Parabolas Inscribed in a Triangle, G. Giddings; Polygonal Spirals, L. Shook and M. Callinan; Roots 2 and 5, J. Wilson; Those Amazing Palindromes, Shareef Bacchus; Tangrams, Greg Huberty; Phi: That Golden
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 The Famous Wonders of the Mind / Les Merveilles de l'Esprit  Nan Zhu, Yifei Zhu  ThinkQuest '99
Math and science stories teach students some famous tricks and formulae through history, games, and short essays on the golden section, the Fibonacci sequence, Pascal's triangle, logarithms, the Bridges of Konisberg, the binary system, etc. In English
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 Fascinating Flat Facts about Phi  Ron Knott
Phi and twodimensional geometry  constructing the golden section: phi, Phi; Phi and the root5 rectangle; the shape of a piece of paper; Phi and the pentagon triangles; Penrose tilings; a rectangle/triangle dissection problem; the Golden Spiral; trigonometry
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 Fibonacci at Random  Ivars Peterson  Science News Online
In a book completed in 1202, mathematician Leonardo of Pisa (also known as Fibonacci) posed the following problem: How many pairs of rabbits will be produced in a year, beginning with a single pair, if every month each pair bears a new pair that becomes
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 Fibonacci  James Grant
Pages about Fibonacci the mathematician, the sequence that bears his name and its relationship to the Golden Ratio, as well as how the Fibonacci numbers occur in nature.
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 Fibonacci Numbers and Nature  Ron Knott
Fibonacci and his original problem about rabbits that gave the series its name; the family trees of bees; the golden ratio and the Fibonacci series; the Fibonacci Spiral and sea shell shapes; branching plants; flower petal and seedheads; and the leaf
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 Fibonacci Numbers and the Pascal Triangle  Radoslav Jovanovic
Brief articles about Pascal's triangle, Fibonacci numbers, Lucas numbers, and the golden section, including the relations between Fibonacci numbers and Pascal's triangle, and Fibonacci numbers and the golden section. In English, German, or Serbian.
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 The Fibonacci Numbers  David Schweizer; Math Department, College of the Holy Cross
A directory of material related to the Fibonacci numbers. Math material  the Fibonacci numbers' appearance in the Mandelbrot set; the first 500 Fibonacci numbers in blocks of 100; factorizations; Web resources.
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 The Fibonacci Numbers, Pineapples, Sunflowers, and the Golden Mean  Don Cohen (The Mathman)
Mathematics from a Pineapple: Infinite sequences, limit of a sequence, ratios, fractions, and decimals. Also Looking at a Regular Pentagon. Sample problems with some answers from Chapter 7 of Don Cohen's worksheet book.
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 The Fibonacci numbers  Ron Knott
The Fibonacci series; The first 100 Fibonacci numbers, completely factorised .. and, if you want more ... Fibonacci numbers 101300 and 301500 (not factorised).
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 A Fibonacci Primer (SMILE)  Larry Freeman, Kenwood Academy
A lesson designed to challenge teachers and students to discover and prove some
interesting properties of the Fibonacci sequence and its unexpected relation to the geometry of the regular pentagon and the theory of limits. From the Recreational and
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 Fibonacci Rabbit Sequence  Ron Knott
One way to look at Fibonacci's Rabbits problem gives an infinitely long sequence of 1s and 0s, the Fibonacci Rabbit sequence: 1 0 1 1 0 1 0 1 1 0 1 1 0 ..., also called the Golden string or Golden sequence since it is a close relative of the number Phi,
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 Gardner's Web  David Cox
A newsletter containing articles written by students, interesting Web links, and taxing puzzles.
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 Geometry Online  Cynthia Lanius
Geometry activities from a geometry class at Milby High School in Houston, Texas. Topics include: History of Geometry (contributions of Egyptians, Babylonians, and Greeks, with links to biographies of major contributors to geometry); Hidden Polygons (locate
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 Geometry Web Page  Ephraim Fithian; Kutztown University
Sixteen geometry activities: Tangrams; Golden Ratio; Geoboard; Polygons; Symmetry; Constructions; Polyominoes and Polyiamonds; Star Polygons; Special Points in Polygons; Polygon Tessellations; Kaleidoscope Tessellations; Escher Tessellations; Space Cubes;
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 The Golden Mean  Michael L. Wright; Michael's Crazy Enterprises, Inc. (MCE)
"The Golden Mean (or Golden Section), represented by the Greek letter phi, is one of those mysterious natural numbers, like e or pi, that seem to arise out of the basic structure of our cosmos. Unlike those abstract numbers, however, phi appears clearly
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 The Golden Mean  Rashomon (K. Wiedman)
The Golden Mean or Golden Section was derived by the ancient Greeks. Like pi, the number 1.618... is an irrational number. Both the ancient Greeks and the ancient Egyptians used the Golden Mean when designing their buildings and monuments. Links to pages
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 The Golden Ratio  Andi, Mel, and Shuj
An introduction to the golden ratio, also known as phi: its connection to the Fibonacci sequence, related constructions (star, line segment, rectangle, and spiral), and connections to biology, history, and aesthetics. Site also includes a glossary and
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 The Golden Ratio  Blacker, Polanski, Schwach; The Geometry Center
Introduction to the Golden Ratio and Fibonacci Sequence. Instead of simply supplying definitions and asking the student to engage in mindless practice, students work through several activities to discover the applications of the Golden Ratio and Fibonacci
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 The Golden Ratio  John Kyrk
Animations for building the golden rectangle from the Fibonacci series; clockwise and counterclockwise spirals; how the proportions of the human body display the golden ratio.
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 Golden Rectangle and Golden Ratio  Jim Loy
An introduction to the ratio involved in the Golden Rectangle, with a link to The Most Pleasing Rectangle Web Poll.
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 The Golden Rectangle (SMILE)  Edwina R. Justice, Gunsaulus Academy
A lesson for grades 68 designed to teach students to measure using metric units;
to calculate averages; to compare and round decimals; to use calculators; to examine the relation between the Fibonacci Sequence and the Golden Ratio; and to relate mathematics
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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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 The Golden Section Ratio: Phi  Ron Knott
Contents: What is the Golden Ratio (or Phi)?  A simple definition of Phi, A bit of history; Phi to 2000 decimal places; Phi and the Fibonacci numbers  Another definition of Phi, A formula for Phi using a continued fraction, Rational Approximations
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 The Golden Section, Related to Music and Natural Sciences  Martin Morgenstern
An extended bibliography related to the golden section in music, mathematics, architecture, biology, etc. Articles and books are listed, and linked to Amazon.com or other sources for purchase where possible.
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 The Great Golden Pyramid  Tony Smith
The largest of the Giza pyramids is usually called the Great Pyramid. It can also be called the Great Golden Pyramid, because its geometry is that of the Golden Mean. Pictures and diagrams of the interior and exterior architecture, with explanations of
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 Handson Math: Activities for the Elementary Classroom  Janine Parker
Lesson plans for children in grades one through six about topology, number patterns, and geometry. Handouts for each lesson may be downloaded in PostScript form or as GIF files, and a zipped DOS program to display Platonic solids, Archimedean solids,
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 How Divine Is My Proportion? (SMILE)  Edwina R. Justice, Gunsaulus Scholastic Academy
A lesson for grade 8 that relates the ratio of successive numbers in the Fibonacci Sequence to the "divine proportion" and compares approximate golden rectangles to human body proportions. From the Arithmetic section of a collection of almost 200 single
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 Icon Odds and Ends  Dept. of Computer Science, Univ. of Arizona
Icon is a highlevel, generalpurpose programming language with a large repertoire of features for processing data structures and character strings; an imperative, procedural language with a syntax reminiscent of C and Pascal, but with semantics at a
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 Integer Sequences and Arrays  Clark Kimberling; Dept. of Mathematics, Univ. of Evansville, Evansville, IN
Certain seemingly simple sequences of integers baffle the best mathematicians. Other sequences, less baffling, exhibit patterns  or absence of patterns  whose appeal shines beyond whatever applications these sequence might find outside mathematics.
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 An Introduction to Continued Fractions  Ron Knott
Continued fractions are just another way of writing fractions. They have some interesting links with a jigsawpuzzle problem of splitting a rectangle up into squares and also with one of the oldest algorithms known to mathematicians  Euclid's Algorithm
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 Investigating Patterns: Number Patterns Fun with Curves & Topology  Jill Britton
Annotated list of links within various number pattern, curve, and topology topics. Linked items feature activities for students. Topics include: prime numbers/magic squares, clock or modular arithmetic, the golden ratio, Fibonacci numbers, binary numbers/Pascal's
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 La Biblio
Una biblioteca de textos electrónicos. Los índices adjuntos permiten navegar por una gran diversidad de temas, todos ellos relacionados con el mundo de las Matemáticas a un nivel de bachillerato o superior. De una
recopilación
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 A Little Math about the Golden Mean  Rashomon (K. Wiedman)
The Fibonacci Series and the Golden Mean are intimately connected. The Fibonacci Series is a series of numbers in which each number is the sum of the two previous numbers... The ratio of each term to the previous term in the Fibonacci Series is equal
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 The Magical Maze: The Natural World and the Mathematical Mind  Prof. Ian Stewart; Mathematics Dept., University of Warwick, UK
At every step in a mathematical investigation you are faced with choices: some choices lead in fruitful directions, most do not. So mathematics is a maze  a logical maze, a mental maze which attempts to parallel the maze of cause and effect that we observe
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