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  Selected Sites   (see also All Sites in this category)

  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. 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 - 34 items found, showing 1 to 34

  1. Algebra (MathPages) - Kevin Brown
    More than 50 "informal notes" by Kevin Brown on algebra. Kummer's Objection; irreducibility criteria, multiple linear regression, string algebra, characteristic polynomial of a matrix, iterated means, sums of powers, polynomials from Pascal's Triangle, ...more>>

  2. Algebra Through Problem Solving - Hillman, Alexanderson
    A non-traditional Algebra text (high school and early college levels) placed on the Web by the Science Education Team at Los Alamos National Laboratory. Browse it on the Web or download a PDF version. Chapter headings include: The Pascal Triangle; The ...more>>

  3. AMOF: The Amazing Mathematical Object Factory - Frank Ruskey
    Combinatorial objects are everywhere. How many ways are there to make change for $1 using unlimited numbers of coins of all denominations? Each way is a combinatorial object. AMOF is part encyclopedia and part calculator, a teaching tool that generates ...more>>

  4. Combinatorial Figures - Robert M. Dickau; Math Forum
    Mathematica pictures that are interesting for elementary combinatorics. Catalan number diagrams; permutation diagrams; derangements; shortest-path diagrams; Stirling numbers of the first and second kind; Bell numbers, harmonic numbers and the book-stacking ...more>>

  5. 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>>

  6. 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>>

  7. 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>>

  8. 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>>

  9. 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>>

  10. 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>>

  11. 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>>

  12. Fibonacci's Chinese Calendar - Ivars Peterson (MathTrek)
    In a book completed in 1202, mathematician Leonardo of Pisa (Fibonacci) posed the 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 productive from the second ...more>>

  13. 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>>

  14. 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>>

  15. helaman ferguson sculpture - Helaman Ferguson
    A mathematician sculptor whose stone and bronze artworks include "Aperiodic Penrose," the Coons Siggraph award, "Esker Trefoil Torus," "Fibonacci Fountain," "Fibonacci Tetrahedron," "Figureeight Knot," "Eine Kleine Link Musik," "Torus with Cross-Cap," ...more>>

  16. 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>>

  17. 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>>

  18. 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>>

  19. The Mathematical Works of Rajesh Ram - Rajesh Ram
    A collection of formulas and identities: Fibonacci, Pell, square and triangular numbers, and sums of cubes and other powers, with an identity related to Ramanujan's Number. ...more>>

  20. Mathematics Journals (AMS) - American Mathematical Society
    A list of mathematics journals with articles on the Web and a list of Web sites for printed journals, with tables of contents of issues, abstracts of papers, actual papers, information about submissions and subscriptions, etc. See also the Annual Listing ...more>>

  21. The Mathematics of the Fibonacci Series - Ron Knott
    Patterns in the Fibonacci Numbers (Cycles, Factors); The Fibonacci Numbers in Pascal's Triangle (Why do the Diagonals sum to Fibonacci numbers? Another arrangement of Pascal's Triangle; Fibonacci's Rabbit Generations and Pascal's Triangle); The Fibonacci ...more>>

  22. MiniWebtool - Kevin Liu
    Online math tools include an average calculator, base converter, base-n calculator, binary calculator, binary converter, binary to decimal converter, binary to hex converter, binary to octal converter, bitwise calculator, compound interest calculator, ...more>>

  23. New Mathematical Constant Discovered - Keith Devlin (Devlin's Angle)
    Descendent of Two Thirteenth Century Rabbits: A recent mathematical result by Divakar Viswanath, a young computer scientist at the Mathematical Sciences Research Institute (MSRI) in Berkeley, California, has put the Fibonacci numbers back in the news ...more>>

  24. Number Theory (MathPages) - Kevin Brown
    More than 100 "informal notes" by Kevin Brown on number theory: linear recurring sequences, Zeisel numbers, Wilsonian primes, arithmetic progression, sublime numbers, square triangular numbers, and many more. ...more>>

  25. On the Teeth of Wheels (Computing Science) - Brian Hayes, American Scientist
    A little history on the importance of gears in the history of computing and the importance of computing in the history of gears. "Designers of gear trains have not merely borrowed ideas from mathematics but have also developed some of those ideas on their ...more>>

  26. Pascal's Triangle - Math Forum, Ask Dr. Math FAQ
    What is Pascal's Triangle? How do you construct it? What is it good for? ...more>>

  27. The Power of One - Robert Matthews, The New Scientist
    Benford's law demands that around 30 per cent of the numbers in a given data set will start with a 1, 18 per cent with a 2, right down to just 4.6 per cent starting with a 9. This essay provides a mathematical history behind the counterintuitive law, ...more>>

  28. The Remarkable Number 1/89 - Robert Miner
    An overview of the Fibonacci series, interesting facts about it, and a sketch of the proof of why the decimal expansion of the fraction 1/89 contains all the Fibonacci numbers expressed as a sequence of decimal fractions, a fact discovered by Cody Birsner. ...more>>

  29. Title III MSS Final Performance Report - Dana Lee Ling
    Dana Lee Ling is a mathematics and science software specialist at the College of Micronesia-FSM. Articles document the College's attempts to increase the success of pre-algebra and algebra students through "conceptual" and technology-based approaches. ...more>>

  30. Using the Fibonacci numbers to represent integers - Ron Knott
    We use base 10 for written numbers, and computers use base 2, but what about using the Fibonacci numbers as the column headers? or base Phi (1.618034...) instead of base 10? There are some interesting infinite series that relate to these - each with a ...more>>

  31. Using the Internet: Mathematics - Douglas Butler; Pearson Publishing (U.K.)
    A 55-page looseleaf book compiled to save teachers time finding excellent resources on the WWW and to provide a curriculum-based bank of ideas. Support activities do not demand that students have free access to the Web. The pack is divided into ten main ...more>>

  32. The Vibonacci Numbers (Computing Science) - Brian Hayes, American Scientist
    A new mathematical constant, from a branch of the Fibonacci number family in which, instead of always adding two terms to produce the next term, you either add or subtract, depending on the flip of a coin at each stage in the calculation. Hayes writes, ...more>>

  33. When The Counting Gets Tough, The Tough Count On Mathematics - Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
    A discussion by William A. McWorter, Jr. of the application of the recursion formula for the Fibonacci sequence to counting and vector problems. ...more>>

  34. YoeServ Math Help - Yoe Corporation
    Pages that include solutions to problems one might encounter when trying to write a computer program or solve some other problem: Finding out how many digits are in a number; Calculating Z-scores by integration; The rules of logarithms; Explicit formula ...more>>


 
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