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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. -|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|- 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 -|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|- 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 -|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|- CHECK OUT OUR WEB SITE: The Math Forum http://mathforum.org/ Ask Dr. Math http://mathforum.org/dr.math/ Problem of the Week http://mathforum.org/geopow/ Internet Resources http://mathforum.org/~steve/ 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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