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Volume 4, Number 43

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25 October 1999                                 Vol. 4, No. 43


Exemplary/Promising Programs | Scientific Graphics - Hoffman, MSRI |
Theory of Tieknots EXEMPLARY, PROMISING MATHEMATICS PROGRAMS U.S. Department of Education United States Assistant Education Secretary Kent McGuire has announced the selection of 10 mathematics education programs as "exemplary and promising." The K-12 programs chosen for their outstanding quality and demonstrated effectiveness are: Exemplary: - College Preparatory Mathematics (CPM) - Cognitive Tutor Algebra - Connected Mathematics - Core-Plus Mathematics - Interactive Mathematics Program (IMP) Promising: - Everyday Mathematics - MathLand - Middle School Mathematics through Application Project (MMAP) - Number Power (DSC) - The University of Chicago School Mathematics Project (UCSMP) For more, and to download information in PDF format, see the Eisenhower National Clearinghouse: -|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|- SCIENTIFIC GRAPHICS PROJECT - MSRI David Hoffman; Mathematical Sciences Research Institute A graphical geometry catalogue of: - Minimal Surfaces: Gauss map, Weierstrass formula, conformal mapping, stereographic projection, and an extensive minimal surfaces index - CMC (Constant Mean Curvature) surfaces, which have the same mean curvature everywhere on the surface - Level Surfaces: level sets approximating minimal curvature of selected level surfaces, skeletal graphs surfaces, approximated by level surfaces, and level surface examples - 4-Dimensional Euclidean Space (R4): Clifford torus - The Complex Plane (C2): complex function visualizer The site includes descriptions of the software used to create the images and movies; versions of the applications for Silicon Graphics workstations are publicly available via anonymous ftp. The staff of this MSRI site includes: David A. Hoffman, Project Director; James T. Hoffman, Senior Scientific Programmer; John McCuan, NSF Postdoctoral Fellow; and Michael Callahan, Graduate Research Assistant. -|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|- THEORY OF TIEKNOTS - Yong Mao The mathematical theory behind tying a necktie, with illustrations of the Four in Hand, the Pratt Knot, the Half-Windsor, and the Full-Windsor, and a classification of necktie knots with respect to size and shape. Tying a tie knot is equivalent to a persistent random walk on a triangular lattice. Using this model, the number of all possible knots in each class (set by the number of total and centre moves, respectively) is calculated. The optimal knot in each class is determined by the aesthetic conditions of symmetry and balance. Of the 85 tie knots found, the model predicts the four knots in widespread use and introduces nine new ones. The full text of the tie article is available for browsing at: -|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|- CHECK OUT OUR WEB SITE: The Math Forum Ask Dr. Math Problems of the Week Mathematics Library Teacher2Teacher Discussion Groups Join the Math Forum Send comments to the Math Forum Internet Newsletter editors _o \o_ __| \ / |__ o _ o/ \o/ __|- __/ \__/o \o | o/ o/__/ /\ /| | \ \ / \ / \ /o\ / \ / \ / | / \ / \

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