Math Forum Internet News

Volume 5, Number 9

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28 February 2000                                Vol. 5, No. 9

                 THE MATH FORUM INTERNET NEWS

Optical Illusions - SandlotScience | Fair Division Calculator
             Teaching and Learning about Decimals
             

               OPTICAL ILLUSIONS - SandlotScience 

                http://www.sandlotscience.com/
               http://www.lainet.com/~ausbourn/

Interactive Java applets and multimedia explorations of 
optical effects, with animations, art work, stories, and more. 
Contents include:
 
 - Impossible Objects, including columns, an endless
    staircase, animated stairs, Java triangle models, an
    interlaced tri-bar, an impossible hexnut, and more
 - Distortion illusions of "breathing" objects, a cafe
     wall, Fraze's Spiral, Poggendorf's Illusion, a twisted
     cord, and others 
 - Contrast and Color: illusions driven by the way we see
 - Typography: distortion and ambiguity
 - Games and Puzzles: Java-flavored diversions
 - Ambiguous Figures that appear as one thing, then
     another - don't miss the "3-in-1 Animation" of the
     Missing Corner Cube
 - After-Effect Illusions: what keeps our eyes going after
     we stop looking
 - Camouflage: the art of blending into a similar background
 - Moire Patterns: when two transparent patterns overlap
 - Giants of Illusions: examples from the work of Jerry 
     Andrus, M. C. Escher, and Sandro del Prete

The site also offers a selection of recommended books,
science toys, kits, and projects; PDF-formatted projects;
and links to more optical illusion Web sites.

            http://www.sandlotscience.com/links.htm
           http://www.lainet.com/~ausbourn/links.htm


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             FAIR DIVISION CALCULATOR - Francis Su

         http://www.math.hmc.edu/~su/fairdivision/calc/

An interactive Java applet designed to help you determine 
how to divide among n people: a desirable object (such as
a cake); an undesirable object (such as a set of chores);
or a set of indivisible objects (rooms, desirable) with
payments (rent, undesirable). 

See also Su's Fair Division page, with links to an 
explanation of "fair division," to exact vs. approximate 
algorithms, to Su's papers, and to other references on the 
subject.

       http://www.math.hmc.edu/~su/fairdivision/
                
                   
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             TEACHING AND LEARNING ABOUT DECIMALS
            Stacey, Chambers, Asp, Scott, Steinle
              University of Melbourne, Australia

  http://online.edfac.unimelb.edu.au/485129/DecProj/index.htm

A resource for teachers that explains the mathematical, 
psychological, and pedagogical ideas needed to teach students 
to work confidently with decimal numbers. 

Contents include: 

 - Background: main ideas, what learners find hard
 - Case Studies: video interviews and tests with six people 
    who demonstrate different, but common, wrong ideas
 - Teaching: survey of approaches, tests, ideas for lessons,
    educational software to download
 - Glossary: definitions and examples of technical terms
 

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