HW Ash p. 34, 1, 2, 6, 7. Read #3 and its answer.
Famous old problem: Buffon's needle.
Handout.
INTERACTIVE PROBABILITY package
On Dell computer (Math dept. computer) in Macintosh lab.
If needed, Start>login as "student" with password "student".
Start>Programs>Interactive Probability>Interactive Probability Simulations
Choose Buffon's needle.
Run the simulation, understand it. (They're measuring x, the
angle, clockwise from the horizontal. My picture shows it
in standard form, counterclockwise. Sorry.) D (board
width) = 1, so only L, needle length, can be changed.
J is 1 if the crack is crossed, 0 otherwise.
U is 2L/(proportion of J's), so should estimate Pi.
HOW TO: Single arrow (F5) does it once ("steps"). Double
arrow (F6) does it a bunch more at a time. Backward arrow clears
everything. (Square stops the running.)
Simulation>Run Options: Stop frequency = # of runs to do on the double
arrow. Update frequency = # of runs to do before posting results.
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HW (Due W if computer access is a problem.)
1) With L = .5, run the simulation, long enough so the pi estimate
looks stable. (Increase the update frequency to at least 100 to make it
faster. Hint: hold down the F6 key.) Record the number of runs where
it first got between 3.1200 and 3.1599 and didn't stray for at least 10,000
or so afterward.
2) Increase the needle length to 1 and repeat the above.
Repeat the above, 4 times for each needle length. What effect does needle length seem to have on the efficiency of achieving a good estimate?
In general, does this seem like a good way to estimate pi?
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(The handout was extracted from Help>Buffon needle discussion. In general,
Buffon's needle is a very inefficient way to estimate pi computationally.)
(If you like, check out the Poker option. The Help>Poker discussion
describes all the winning hands and does some of the computations)
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