Class Assignment 2
Name ________________
© James J. Woeppel, 2000
(see note on last page)
π
This is π to 200 decimal places.
π=
3.1415926535897932384626433832795028841971693993751058
209749445923078164062862089986280348253421170679821480865132
823066470938446095505822317253594081284811174502841027019385
2110555964462294895493038196
I
Why are people fascinated with the number of places in the expansion of π?
II
Archimedes method for approximating π
A. Describe Archimedes’ method for approximating π. (You can draw a diagram
on the back of this page.)
B. Why does it work?
C. Approximate π to three decimal places using Archimedes’ method.
You can use the applet at URL:
www.math.utah.edu/~alfeld/Archimedes/Archimedes.html
III
Buffon’s needle is a seeming magical way to estimate π. You drop a needle on to
a rule page with a spacing of twice the needle. It is due to Georges Louis Leclerc
comte de Buffon, 1707-1788.
A.
Hold a toothpick about two feet above the center of the two parallel lines
below; then drop the toothpick. Count the total number of drops and the
number of time the toothpick touches either line. The ratio of the total
number of drops to the number of times the toothpick touches the lines is
the estimate for π. Unfortunately, it takes a lot of drops to get a good
estimate of π. (Try a hundred or so.) This method of estimating a value is
called a Monte Carlo method.
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B
When you tire of this you can use the applet at URL:
www.mste.uiuc.edu/reese/buffon/bufjava2.html
Set Needle Length to 0.5
© note: This material may be used by anyone. If it is reproduced, written permission must be granted by the author:
James J. Woeppel, Indiana University Southeast, New Albany, IN 47150. © James J. Woeppel, 2000