Estimate Pi using perimeter:
1. If a circle has circumference (note this is just a fancy way of saying perimeter) pi,
what would its radius be? _________
Suppose regular n-sided polygons are inscribed and circumscribed using this circle.
Inscribed
Regular polygon: a regular polygon is______________________________________
Start with a 3 sided regular figure.
circle with circumference of PI
A
B
2
1
r:radius
M:Midpoint
C
What is the measure of angles 1 and 2?_______
Why?__________________________________
If a figure has n sides, what is each of the angles? ______________________________
Find the perimeter of the triangle.
How will this value relate to PI? How can we get a better estimate?
Pick a number of sides between 12 and 18. ______ Find the perimeter of this polygon
inscribed in the same circle above.
Determine a formula where the value of n (the number of sides) will produce the
perimeter of the regular polygon.
Now try circumscribed perimeter. How will this value relate to PI?
Find the formula for the perimeter of an n-sided regular polygon for the circumscribed
scenario.
Final Product
Show where the formulas come from (diagrams and explanations) (5 pts)
Solve upper and lower bound for n between 5 and 15 (show work) (5 pts)
2 formulas (one for upper bound and a second for lower bound) (5 pts)
Graph for each formula( may want to also graph y=π) (2 pts)
Explanation of upper and lower bound and graph (3 pts)
For perimeter determine the number of sides necessary for a regular polygon such that if I
inscribe a circle and circumscribe a circle in the same polygon, I get π accurate to 4
decimal places. (3.1415) (5 pts)
History/Usefulness/Interesting
Search the web and provide a brief history of the ancient groups that used PI, why
they needed it, and how accurate their approximations were.—Provide a
bibliography of sources (5pts)
Area: same problems as above (Extra Credit) (10 pts)
Total: 30 points