The Solution

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

Pedagogy

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

Java Demonstrations

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

Bibliography

Demonstration 5. Star Pentagons

This demo illustrates the construction of the midpoint pentagon from half the original pentagon and one quarter of the star pentagon. All vertices of the original pentagon may be moved. Also note that moving only one vertex of a regular pentagon does not change the area ratio (moving more than one vertex will change the ratio).