Midpoint Polygons

The Solution
   
  • Triangles: The Base Case
    •    
  • Convex Quadrilaterals
       
  • Non-Convex Quadrilaterals*
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  • Self-Intersecting Quadrilaterals*
    •    
  • Convex Pentagons
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  • Convex Hexagons And Up
       
  • The General Case*

    • Pedagogy
       
  • Math 104
       
  • Original Discussion
    •    
  • Oriented Area Part 1
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  • Oriented Area Part 2
    •    
  • Vector Notation

    • Java Demonstrations
       
  • Area of Midpoint Triangles
    •    
  • Area of Midpoint Quadrilaterals
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  • Area Max for Convex Pentagons
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  • Infinite Area Ratios
    •    
  • Star Pentagons
    •    
  • Non-Midpoint Polygons

    • Bibliography

    Bibliography

    Zbiek, Rose Mary, "The Pentagon Problem: Geometric Reasoning with Technology", The Mathematics Teacher 89 (February 1996) pp. 86-90.

    National Council of Teachers of Mathematics, "Principles and Standards for School Mathematics" (see especially this demo)

    Problem -- Solution -- Pedagogy -- Demos -- Bibliography