Math Forum Internet News

Volume 3, Number 21

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25 May 1998                                   Vol. 3, No. 21


 MathCounts | Perimeter Efficiency - Blackwell | Geometry POW

                MATHCOUNTS - Problem Solving

MathCounts offers a Problem of the Week contest of 
current-events-based math challenges, with an archive of
previous questions and answers. Also included are:

    -  warm-ups and workouts
    -  problem-solving strategies
    -  extended activities
    -  algebraic reasoning
    -  permissible calculators

and a MathCounts F.L.I.P. (Formulate Logical, Interesting 
Problems) Contest for the submission of creative math 
problems for use in a MathCounts School Handbook Warm-Up 
or Workout.

MathCounts is the national math coaching and competition 
program for 7th and 8th grade students.



           PERIMETER EFFICIENCY - William Blackwell 

   Perimeter efficiency, also known as isoperimetric
   inequalities, compares the actual perimeter of a
   shape with the circumference of the circle that
   encloses the same area. Since a circle will enclose 
   any given area with the smallest perimeter, it is 
   100 percent efficient as an area enclosure. 

   Blackwell's pages include information about perimeter 
   efficiency, with examples of practical uses:

     - tall office buildings 
     - increasing wall area 
     - splitting a log 
     - two-story vs. one-story houses 
     - the Indianapolis Motor Speedway 
     - the Pentagon 
   There is also a table for Examples of Perimeter 
   Efficiency that reveals how pi compares with other 
   perimeter-to-diameter ratios.





The archives of this Math Forum's Internet project feature 
interesting and colorful examples of graphics created by
students in support of their submissions to the weekly 
Geometry POW. In addition to the usual carefully crafted
ASCII drawings, there are GIFs, sketches made using the
Geometer's Sketchpad, and sketches converted to HTML using
JavaSketchpad, a Web component of The Geometer's Sketchpad 
by Key Curriculum Press, Inc.

Check out these answer highlights in the archives:

Splitting a Parallelogram (JavaSketchpad graphic)

Daytona Speedway/Roof Pitch - Matt Smawfield

Areas of Overlapping Squares (JavaSketchpad sketch)

Triangles, Area, and Congruence
  - see Tim Peterson's animated triangle at


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