25 October 1999 Vol. 4, No. 43
THE MATH FORUM INTERNET NEWS
Exemplary/Promising Programs  Scientific Graphics  Hoffman, MSRI  Theory of Tieknots
EXEMPLARY, PROMISING MATHEMATICS PROGRAMS
U.S. Department of Education
http://www.ed.gov/PressReleases/101999/mathpanel.html
United States Assistant Education Secretary Kent McGuire
has announced the selection of 10 mathematics education
programs as "exemplary and promising." The K12 programs
chosen for their outstanding quality and demonstrated
effectiveness are:
Exemplary:
 College Preparatory Mathematics (CPM)
http://www.cpm.org/
 Cognitive Tutor Algebra
http://www.carnegielearning.com/
 Connected Mathematics
http://www.math.msu.edu/cmp/
 CorePlus Mathematics
http://www.wmich.edu/cpmp/
 Interactive Mathematics Program (IMP)
http://www.ithaca.edu/compass/
Promising:
 Everyday Mathematics
http://www.everydaylearning.com/
 MathLand
http://www.creativepublications.com/
 Middle School Mathematics through Application Project (MMAP)
http://www.irl.org/mmap/default.html
 Number Power (DSC)
http://www.devstu.org/
 The University of Chicago School Mathematics Project (UCSMP)
http://www.uchicago.edu/ssd/ucsmp/
For more, and to download information in PDF format, see the
Eisenhower National Clearinghouse:
http://www.enc.org/ed/exemplary/
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SCIENTIFIC GRAPHICS PROJECT  MSRI
David Hoffman; Mathematical Sciences Research Institute
http://www.msri.org/publications/sgp/SGP/indexc.html
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
 4Dimensional 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.
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THEORY OF TIEKNOTS  Yong Mao
http://www.tcm.phy.cam.ac.uk/~ym101/tie/aps97tie.html
The mathematical theory behind tying a necktie, with
illustrations of the Four in Hand, the Pratt Knot, the
HalfWindsor, and the FullWindsor, 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: http://www.tcm.phy.cam.ac.uk/~ym101/tie4/node1.html
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