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  1. 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, golden number, golden section) and golden string. Includes: geometric applications of the golden ratio; Fibonacci puzzles; the Fibonacci rabbit binary sequence; the golden section in art, architecture, and music; using Fibonacci bases to represent integers; Fibonacci Forgeries (or "Fibonacci Fibs"); Lucas Numbers; a list of Fibonacci and Phi Formulae; references; and ways to use Fibonacci numbers to calculate the golden ratio. more>>

  2. The Fibonacci Series - Matt Anderson, Jeffrey Frazier, and Kris Popendorf; ThinkQuest 1999
    The Fibonacci Series is deceptively simple, but its ramifications and applications are many. Learn more about the Fibonacci Series itself: an introduction, the rabbit problem, Binet's formula, the successor formula (given only one term in the Fibonacci series, determine the term that directly follows it), binomial form, Fibonacci spiral. See how the Fibonacci Series relates to the golden ratio: the golden rectangle, the golden ratio, the golden spiral. Explore applications of the Fibonacci series: Fibonacci ratios, Binet revisited, one over eighty-nine (examining the decimal expansion of 1/89), apartment buildings (an explanation of why the number of combinations for each set of a certain group of apartment buildings is a Fibonacci number), nature, Leonardo da Vinci. Learn about the lives of Fibonacci and other important mathematicians: Leonardo Fibonacci, Édouard Lucas, Jacques Binet, Jordanus Nemorarius. A quiz is available for each of the four main sections of the site; an index organizes all of the site's Shockwave Flash demonstrations; and the authors also provide further reading, a bibliography, and documentation on the site's development. Much of the site's content is available in streaming Real Audio narration. more>>

  3. Golden Ratio, Fibonacci Sequence - Math Forum, Ask Dr. Math FAQ
    About the Golden Ratio (or Golden Section or Golden Mean), the Golden Rectangle, and the Fibonacci Sequence. more>>

  All Sites - 90 items found, showing 1 to 50

  1. 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 ...more>>

  2. 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 ...more>>

  3. 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. ...more>>

  4. 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 ...more>>

  5. 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 ...more>>

  6. 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 ...more>>

  7. 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 ...more>>

  8. 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. ...more>>

  9. 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 ...more>>

  10. Design Ideas - Julie Coghill
    A series of articles that discuss quilt design using proportion, asymmetry, and Pythagorean triples. ...more>>

  11. 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 ...more>>

  12. 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 ...more>>

  13. 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 ...more>>

  14. 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 ...more>>

  15. 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. ...more>>

  16. 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 ...more>>

  17. 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 ...more>>

  18. 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 ...more>>

  19. 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 ...more>>

  20. 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. ...more>>

  21. 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 ...more>>

  22. 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. ...more>>

  23. 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. ...more>>

  24. 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. ...more>>

  25. 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). ...more>>

  26. 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 ...more>>

  27. 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, ...more>>

  28. Gardner's Web - David Cox
    A newsletter containing articles written by students, interesting Web links, and taxing puzzles. ...more>>

  29. 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 ...more>>

  30. 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; ...more>>

  31. 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 ...more>>

  32. 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 ...more>>

  33. 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 ...more>>

  34. 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 ...more>>

  35. 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. ...more>>

  36. 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. ...more>>

  37. 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 ...more>>

  38. 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 ...more>>

  39. 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 ...more>>

  40. 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. ...more>>

  41. 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 ...more>>

  42. 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, ...more>>

  43. 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 ...more>>

  44. 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 ...more>>

  45. 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. ...more>>

  46. 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 ...more>>

  47. 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 ...more>>

  48. 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 ...more>>

  49. 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 ...more>>

  50. 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 ...more>>

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