Page 376 - Excel for Scientists and Engineers: Numerical Methods

CHAPTER 15 RANDOM NUMBERS & MONTE CARLO METHOD 353

Figure 15-12. Portion of table to calculate n by Buffon's Needle method. There are
2000 rows of calculation in the spreadsheet.
(folder 'Chapter 1 5 Examples', workbook 'Buffon's Needle', worksheet 'Calculation')

Figure 15-13 shows the result of recalculating the sheet 100 times, to provide
a total of 200,000 calculations. As you can see, the calculation does not
"converge'' very efficiently. Compare the result with the evaluation of n by
evaluation of a series (Chapter 4) or by integration of a function (Chapter 7); both
methods are much more efficient.
-_-_ ~ l_l_l__l_ll-l

3.15 -

3.14 1

3.13 -

3.12 -

3.11 4)

3.1
3.09
0 50000 100000 150000 200000 250000
Number of trials

Figure 15-13. Approach of simulation result to the value n as the number of trials
increases.
(folder 'Chapter 15 Examples', workbook 'Buffon's Needle', worksheet 'Many trials')