Math Forum Internet News

Volume 3, Number 50

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14 December 1998                                   Vol. 3, No. 50

                 THE MATH FORUM INTERNET NEWS

Fibonacci & Golden Section - Knott | Geometry in Motion | Dragonfly


    FIBONACCI NUMBERS AND THE GOLDEN SECTION - Ron Knott

http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fib.html

All about the Fibonacci series and the Golden Section, 
written for students and teachers at a variety of levels,
with a brief biography of Fibonacci, the numerical 
properties of the series, and ways it is manifested
in nature. 

The Fibonacci numbers are closely related to the golden ratio, 
also known as the golden mean, golden number, or the golden
section; and the golden string (Fibonacci Rabbit Sequence). 
Ron Knott's pages include:

- The Fibonacci Numbers and the Golden Section in Nature 
- The Mathematical World of Fibonacci and Phi
- The Golden String
- Fibonacci Puzzles (easier and harder)
- Fibonacci - the Man and His Times 

- More Applications of Fibonacci Numbers and Phi:

    The Golden Section In Art, Architecture and Music 
    Fibonacci Bases and Other Ways of Representing Integers 
    The Fibonacci Numbers in a Formula for Pi
    Fibonacci Forgeries 
    The Lucas Numbers

Ron also provides a list of links and references for 
still more information: 

http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibrefs.html
       

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               GEOMETRY IN MOTION - Daniel Scher

               http://members.xoom.com/dpscher/
  
This site offers direct interaction with geometric diagrams, 
using JavaSketchpad applets to illustrate and explore a range
of mathematical applications. Contents include:

 A variety of curve-drawing devices:

   - Bent Straw               - Limacon
   - Concentric Circles       - Pantograph of Sylvester
   - Congruent Triangles      - Sliding Triangle
   - Expanding Circle         - Taut String
   - Falling Ladder           - Van Schooten's Ellipse
   - Folded Circle            - Van Schooten's Hyperbola
   - Hanging String           - Van Schooten's Parabola
   - Intersecting Circles

 Other activities:

   - Constant Perimeter and Area Rectangles 
   - The Burning Tent Problem 
   - A Quadrilateral Puzzler 
   - An Even Split 
   - Maximizing Area     
   - A Tangent Teaser
   - A Vector Approach to Simultaneous Equations 
 
 Copies of Scher's articles, which can be read in PDF format:

   - Lifting the Curtain: The Evolution of the Geometer's 
     Sketchpad 
   - Demystifying e^i(pi) 
   - Dynamic Geometry Visualizations in Linear Algebra 
   - Problem Solving and Proof in the Age of Dynamic Geometry 
   - A Triangle Divided: Investigating Equal Areas 
   - The Building on Strengths Colloquium 

Scher's book for grades 10-12, Exploring Conic Sections 
with The Geometer's Sketchpad, providing add-on modules on 
ellipses, hyperbolas, and parabolas, is available from 
Key Curriculum Press:

   http://www.keypress.com/product_info/modules.html#conic
        

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                      DRAGONFLY WEB PAGES

             http://miavx1.muohio.edu/~Dragonfly/

Dragonfly is an inquiry-driven, science-oriented magazine 
published bimonthly during the school year, inspiring 
children to join with their peers and with scientists in 
national and international investigations. Dragonfly also 
publishes poetry, autobiographies, natural history essays, 
humor, artwork, and other creative expressions by children 
and scientists. 

Such interdisciplinary explorations as "Small and Tall" 
(watch Danielle grow from age 5 to age 17 in 5 seconds) 
link math and science. 

Topics cover houses, navigation, space, earth sounds,
using tools, hide and seek, webs of life, animal talk,
ice and snow, skeletons, flight, and trees and seeds.
Future issues, to which you are invited to contribute, will
feature plants, time, water, life cycles, the year 2000, 
games, family, and the planet.

Project Dragonfly is a collaborative effort of Miami 
University (Oxford, Ohio) and the National Science Teachers 
Association (NSTA), with funding from the National Science
Foundation. 
    

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