- 10 Lessons in Fractals, Complex Patterns, and Chaos - Jon Lee; Math Forum Teacher Exchange
From the Wright-Connection 8-week summer program, in which Dayton, Ohio, middle and high school math and science teachers participated in the real-world applications of math and science at Wright-Patterson 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 minute-long 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 n-ary 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 TI-85 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 n-space 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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- Conceptual Mathematics - Karl F. Kuhn
Lesson outlines for teachers, math challenges, and philosophical discussions on how math helps us understand sports, fair taxation, gender difference, and more. The author's musings on mathematics as a game cover Pascal's Triangle, primes, the golden
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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 es-tu 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 bee-line 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 7-12), graphics calculators in high school mathematics, computers in mathematics education, technology to support instruction, technology
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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 two-dimensional geometry - constructing the golden section: phi, Phi; Phi and the root-5 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 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 seed-heads; 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 101-300 and 301-500 (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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- Fr. Chris' Math Lab at the Cape - Christopher Crispin Thiel
Interactive Java tutorials, labs, and lessons for making angles; caroming billiard balls; investigating wavelengths of rainbows; constructing and measuring angles, triangles, and quadrilaterals; exploring ratios of terms in the Fibonacci-like sequences;
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- Fun With Mathematics! - Harry J. Smith
Mathematical recreations, curiosities, and software, from computing pi, tesseracts, and data encryption to golygons and quaternions - and much more.
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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 Independent Projects - Ruth Carver, Germantown Academy
Independent projects exploring topics in mathematics not part of the curriculum, by students in Ruth Carver's Spring Geometry Honors classes at Germantown Academy in Pennsylvania. Books, magazines, and the Internet were used for their research, with class
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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 and Fibonacci's Sequence - Chris and Scott
A discussion of proportion and phi, with a Fibonacci biography, information on the sequence, relations to art and architecture, a bibliography, and a section on biology (the Fibonacci sequence in nature).
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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 6-8 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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- Hands-on 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 high-level, general-purpose 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 jigsaw-puzzle 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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