Quarter_Circle
### A Quarter Circle in a Square with unit length

Draw a unit radius quarter circle arc in a square with unit side length.

Draw points Pi(xi, yi), where xi and yi are independently generated random numbers in the range 0 - 1.0

Then the probability of the points falling inside the quadrant is the ratio of the area of the sqaure and the quadrant,i.e.

(area of the quadrant )/ (area of the square ) = (p/4) R^{2} /(1 * 1) = p/4

********************* pi_mc_001.dwg** ********************

************************************* pi_mc_002.dwg** ************************************

You can see the process in animation.animation

**To create this drawing and animation: **

** Load random_1.lsp (load "random_1")**

** Load random_2.lsp (load "random_2")**

** Load Monte_Carlo_pi.lsp (load "Monte_Carlo_pi")**

Then from command line, type **pi_mc**

#### References

- Nelson,R.B. : Proofs Without Words: Exercises in Visual Thinking. MAA, 1993.

- Nelson,R.B. : Proofs Without Words II: More Exercises in Visual Thinking. MAA, 2000.

Copyright © 2006 Takaya Iwamoto.

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