## Related questions with answers

A, B and C are three circles of unit radius with centres in the x y-plane at (1,2),(2.5,1.5) and (2,3), respectively. Devise a hit or miss Monte Carlo calculation to determine the size of the area that lies outside C but inside $A$ and $B$, as well as inside the square centred on $(2,2.5)$, that has sides of length 2 parallel to the coordinate axes. You should choose your sampling region so as to make the estimation as efficient as possible. Take the random number distribution to be uniform on $(0,1)$ and determine the inequalities that have to be tested using the random numbers chosen.

Solution

VerifiedThe equations for the circles and square (composed of line segments) are given by

$\begin{align*} &(x-1)^2 + (y-2)^2 = 1, \text{ for circle A}\\ &(x-2.5)^2 + (y-1.5)^2 = 1, \text{ for circle B}\\ &(x-2)^2 + (y-3)^2 = 1, \text{ for circle C}\\ &(1,1.5) \text{ to } (1,3.5); (3,1.5) \text{ to } (3,3.5);\\ &(1,1.5) \text{ to } (3,1.5); (1,3.5) \text{ to } (3,3.5), \text{ for the square}. \end{align*}$

## Create an account to view solutions

## Create an account to view solutions

## Recommended textbook solutions

#### Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

4th Edition•ISBN: 9780133942651 (4 more)Randall D. Knight#### Mathematical Methods in the Physical Sciences

3rd Edition•ISBN: 9780471198260Mary L. Boas#### Mathematical Methods for Physics and Engineering: A Comprehensive Guide

3rd Edition•ISBN: 9780521679718K. F. Riley, M. P. Hobson, S. J. Bence#### Fundamentals of Physics

10th Edition•ISBN: 9781118230718David Halliday, Jearl Walker, Robert Resnick## More related questions

1/4

1/7