Math Forum Internet News

Volume 2, Number 30

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 28 July 1997                                Vol. 2, No. 30

               THE MATH FORUM INTERNET NEWS

Oriental Carpets | Geometry Ctr Student Projects | Neg X Neg


                    SYMMETRY AND PATTERN:
                 THE ART OF ORIENTAL CARPETS

        http://mathforum.org/geometry/rugs/

 A joint project of The Textile Museum and The Math Forum 

        Highlights include:

        - About Symmetry and Pattern
            An illustrated introduction to the
            mathematical aspects of this exhibit.

        - Rug Gallery
            Images of 28 carpets, each accompanied
            by comments from the author.

        - About Oriental Carpets
            Social, historical, and technical
            information about Islamic art.

        - Educational Resources
            Including student activities and
            suggestions for further reading.


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            GEOMETRY CENTER STUDENT PROJECTS

            http://www.geom.umn.edu/~demo5337/

Student Projects from Math 5337: Computational Methods in 
Elementary Geometry (Technology in the Geometry Classroom).
These materials were developed at the Geometry Center by 
pre- and in-service teachers of high-school geometry. The
projects for teachers and students (primarily grades 7-12) 
offer a wide of topics in geometry:

  - Symmetry
  - The Golden Ratio
  - Classification of patterns
  - Concurrency points in a triangle
  - The Pythagorean theorem
  - Geometry in Art
  - Charlotte and the World Wide Web
  - The Geometer's Sketchpad



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         EXPLAINING NEGATIVE X NEGATIVE = POSITIVE

        A discussion from amte, the mailing list of
     the Association of Mathematics Teacher Educators.

   http://mathforum.org/epigone/amte/twaxkhingror

"I think it seems quite arbitrary to many ordinary people 
 that a product of two negative numbers should be positive -
 they don't see the sense in it. Indeed, I have seen volumes 
 written by people we would likely call cranks who argue that 
 we mathematicians got it wrong when we defined multiplication 
 that way, and that it has caused untold trouble.... suppose
 we take a geometric approach to numbers..."
                                  - Ladnor Geissinger

"I give three 'reasons' to my students, each of which I hope
 will provide them with an opportunity to reflect upon an 
 aspect of mathematics. 1) Sometimes mathematical definitions 
 are designed to maintain the system..." 
                                  - Randolph Philipp

"...my favorite is one I saw years ago at a math conference, 
 which uses the idea of a hot air balloon.... we talk about 
 this as a very simple example of mathematical modeling - 
 and how sometimes it may not be a very perfect fit but is 
 good for helping us develop a sense of what is going on, 
 and how we can stretch our model only so far to make sense."
                                  - Marjorie (Marj) Enneking

"I like Morris Kline's way of explaining that neg times neg 
 is positive. (Mathematics: A Cultural Approach. 1962. 
 Addison-Wesley. page 67-68). There he says: 'The operations 
 with negative numbers and with negative and positive numbers
 together are easy to understand if one keeps in mind the 
 physical significance of these operations...' The difference 
 between his explanation and a straight profit/debt model 
 (which fails in the case of multiplying and dividing) is 
 that Kline has introduced TIME...."
                                  - Genevieve Boulet


        For more approaches, see the Dr. Math FAQ:

 http://mathforum.org/dr.math/faq/faq.negxneg.html


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