IE 415/515: SUMMER 2015
LAB 3:
Monte Carlo Simulation to Estimate π
1. Introduction
In this lab you will work in pairs to develop a Monte Carlo simulation of
“Buffon’s needle” to estimate π. Buffon’s needle will be explained and
observations useful for the simulation model will be noted. You must then work
in pairs to complete the simulation.
2. Buffon’s Needle – George Louis Leclerc (1733)
Randomly toss a straight needle of length l onto an infinitely large table painted
with parallel lines spaced d > l apart. Then the probability the needle crosses after
is has stopped moving is
p = (2*l)/( πd)
3. Lab Assignment
Develop a Monte Carlo simulation using Crystal Ball that generates an estimate of
π. Clearly there is no need to estimate π, so the main point of this lab assignment
is the modeling involved. The following observations will be helpful in
developing your simulation model.
Observations
1.
2.
3.
4.
In your simulation of a needle toss, you only need to consider what happens
relative to the two adjacent lines between which the needle center lands.
d > l so the needle can cross only one line, if it crosses a line.
You should use specific values for d and l.
The Excel function ACOS(x) for an argument -1 ≤ x ≤ 1 returns the angle θ
in radians such that cosine(θ) = x.
Develop the simulation so that it can be run with a forecast cell that directly
estimates π.
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What to turn in
E-mail your completed spreadsheets to the TAs (ie415lab@gmail.com). Include the
following:


Names of team members(Email Subject and File Name: Last Name-Last
Name-Lab#),
Labels and documentation must be clear. Use more rather than less
documentation. If the simulations are too hard to understand, points will
be deducted. You need to present the reasoning behind the formulas
used in the cells that are part of the simulation.
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