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9 August 2004 Vol. 9, No. 32 THE MATH FORUM INTERNET NEWS Alison Miller | Problems of the Week | Tool Fest An Amazing, Space Filling, Non-Regular Tetrahedron CONGRATULATIONS, ALISON! http://mathforum.org/announce/congrats_alison.html Alison Miller returned from Athens, Greece, with a gold medal from the 45th International Mathematical Olympiad (IMO). In helping the team from the United States finish second among the 85 participating countries -- its best medal count and highest placing in a decade -- the homeschooled teen from Niskayuna, New York, became the first ever female gold medal winner for a team from the USA. Alison credits her participation in the Math Forum's Geometry Problem of the Week service as her first experience with expository writing in mathematics. \|/ PROBLEM OF THE WEEK - THE MATH FORUM http://mathforum.org/pow/ The Math Forum's Problems of the Week (PoWs) are designed to provide creative, non-routine challenges for students in grades three through twelve. Problem-solving and mathematical communication are key elements of every PoW. -|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|- MATH AND TECHNOLOGY TOOL FEST http://mathforum.org/workshops/toolfest04/ Nineteen participants who travelled to Philadelphia and twenty-three online members of the Math Tools community have spent the week getting familiar with the recently implemented features of the Math Tools site. They have collaborated to create classroom activities, software-related resources, and services for themselves and others. Onsite Participants http://mathforum.org/workshops/toolfest04/onsite/ Online Participants http://mathforum.org/workshops/toolfest04/online/ The Tool Fest's schedule has provided opportunities for presentations of tools, conversations about how to teach with them, and discussions of favorite tools: Hot Topics http://mathforum.org/workshops/toolfest04/hottopics.html -|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|- AN AMAZING, SPACE FILLING, NON-REGULAR TETRAHEDRON http://mathforum.org/pcmi/hstp/resources/dodeca/ In "On the Heavens," written in 350 B.C., Aristotle proclaimed that the regular tetrahedron fills space with no gaps. He was mistaken. However, a particular tetrahedron, with dimensions derived from the cube, does fill space. This non-regular tetrahedron, and its closely related polyhedra -- the cube, the rhombic dodecahedron, and the first stellation of the rhombic dodecahedron -- share dimensions and space filling properties. The rhombic dodecahedron derives its name from its twelve ("dodeca-") faces, all of which are congruent rhombi, each formed by joining two tetrahedra. In this article, Peg Cagle and Joyce Frost explore these related polyhedra, showing how to exploit their space filling properties to create nets for three intriguing puzzles. -|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|- 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/ Math Tools http://mathforum.org/mathtools/ 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 Donations http://deptapp.drexel.edu/ia/GOL/giftsonline1_MF.asp Ask Dr. Math Books http://mathforum.org/pubs/dr.mathbooks.html _o \o_ __| \ / |__ o _ o/ \o/ __|- __/ \__/o \o | o/ o/__/ /\ /| | \ \ / \ / \ /o\ / \ / \ / | / \ / \ |

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