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28 September 1998 Vol. 3, No. 39 THE MATH FORUM INTERNET NEWS Germantown Academy Projects | The Integrator | Triangle Trisectors Theorem MATH PROJECTS, GERMANTOWN ACADEMY - Ruth Carver http://www.ga.k12.pa.us/academics/US/Math/Index.htm Projects by students at Germantown Academy in Pennsylvania, designed to explore topics in mathematics not part of the regular curriculum. Major units include: Backpack Project http://www.ga.k12.pa.us/academics/LS/5th/Backpack/Index.htm Examining student backpack weights in relation to body weights in all three divisions of the school. An interdisciplinary project done by fifth graders and Senior statistics students. Independent Geometry Projects http://www.ga.k12.pa.us/academics/US/Math/Geometry/GEOMPROJ/index.htm Using books, magazines, and the Internet for their research, students in Ruth Carver's Geometry Honors classes made presentations that involved hands-on activities, including multicultural math games, ancient number systems, making violins and violas, Sketchpad animations, and more. Mathematical Legends http://www.ga.k12.pa.us/academics/US/Math/Millar/Index.htm Imaginary interviews with influential mathematicians, from Archimedes to Zeno, written by students in John Millar's calculus class. Philadelphia Math Trail http://www.ga.k12.pa.us/academics/US/Math/MathTrail/Index.htm Students took a tour of Philadelphia with a math twist. Read about math at Germantown Academy and the role of Ruth Carver, chair of the upper school math department and an adjunct professor of mathematics education at Beaver College, in an interview in the Philadelphia Inquirer: "A Great Backpack Project draws math students into technology" http://www.phillynews.com/inquirer/98/Sep/17/tech.life/SKUL17.htm -|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|- THE INTEGRATOR http://www.integrals.com/ A Web interface to Mathematica 3.0. Type in any integral or choose a random sample, and the Integrator sends a Mathematica link message to a Mathematica kernel, which then does the integral using its built-in integrate function. The result is sent back within seconds to the Integrator Web page. From this page you can also follow links to read about what integrals are used for, the history of integration, how to enter an integral, and how the Integrator works. -|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|- A THEOREM CONCERNING THE TRISECTORS OF A TRIANGLE (from the discussion group geometry-research) http://mathforum.org/epigone/geometry-research/jahclumyax Theorem: If the angular trisectors of a triangle are produced to the circumcircle, then the chords determined by the pairs of trisectors adjacent to the edges form an equilateral triangle. Den Roussel's initial question, connected to Morley's theorem, sparks a discussion among John Conway, Richard Guy on the Lighthouse theorem, Floor van Lamoen, and others interested in triangle centers and 3D applications: "trisecting the dihedral angles of a tetrahedron ... may indeed may be the best 3D analogy to trisecting the interior angles of a triangle." - Russell Towle A high-level, focused conversation that illustrates how mathematics can be worked out live on - or as a result of - the Internet. Browse the geometry-research archives, post from the Web, and find out how to subscribe to the group: http://mathforum.org/discussions/about/geometry-research.html -|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|- 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/ Internet Resources http://mathforum.org/~steve/ Teacher2Teacher http://mathforum.org/t2t/ 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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