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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 -|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|- 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/ -|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|- 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 -|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|- CHECK OUT OUR WEB SITE: The Math Forum http://mathforum.org/ Ask Dr. Math http://mathforum.org/dr.math/ Problems of the Week http://mathforum.org/pow/ Mathematics Library http://mathforum.org/library/ Teacher2Teacher http://mathforum.org/t2t/ Discussion Groups http://mathforum.org/discussions/ Join the Math Forum http://mathforum.org/join.forum.html Send comments to the Math Forum Internet Newsletter editors _o \o_ __| \ / |__ o _ o/ \o/ __|- __/ \__/o \o | o/ o/__/ /\ /| | \ \ / \ / \ /o\ / \ / \ / | / \ / \ |

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