Circular Pastures and Arbelos
COMMON CORE STATE STANDARD – HS GEOMETRY - MATHEMATICAL PRACTICE
MEASURING PASTURES USING DYNAMIC SOFTWARE
Pasture A's perimeter is:
Pasture A's area is:
Pasture B's perimeter is:
Pasture B's area is:
Pasture C's perimeter is:
Pasture C's area is:
Pasture D's perimeter is:
Pasture D's area is:
Make a conjecture about the relationship among the perimeter and area of Pastures A, B, C, and D.
EXPLAINING THE CONJECTURE
Use proportionality and distributivity properties to verify that the conjecture is true for any set of diameters d1, d2, d3, ..., dn; where d1 + d2 + d3 + ... + dn = diameter of the big circle.
FURTHER EXPLORATION - ARBELOS
Use the "Area" tool to find the area of the above arbelos.
Construct a circle with diameter PR and calculate its area.
Make a conjecture about the areas:
Proof your conjecture by building a logical progression of statements.