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) R2 /(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


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

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

Copyright 2006 Takaya Iwamoto.