Math Forum Internet News

Volume 3, Number 39

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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


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                        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.


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     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


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