Go to Fun_Math Content Table Three Famous Problems Greek Circle Squarer Later Squarer

René Descartes (1596 - 1650) ,the famous founder of analytical geometry, also used polygon approach to determine the value of p. But instead of computing the perimeters of polygons inscribing (and/or) circumscribing a given circle, he kept the perimeter length constant, and doubled its sides until the polygon approaches the circle.

From the figure, the perimeter of the n-sided polygon (L) is L = n.AB = 2 n r tan(q/2) (1) Then after doubling the sides k times ( 2 |

********

********** Descartes_circle_square_model.dwg** ********

From (3) x |

******************* Descartes_circle_square_desc.dwg** *****************

**To create this drawing : **
** Load Descartes_pi.lsp (load "Descartes_pi")**

Then from command line, type ** Descartes_pi **

The result of this program is shown below: 15-th decimal place is correct after 25-th step. |

Go to Fun_Math Content Table Three Famous Problems Greek Circle Squarer Later Squarer

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Last Updated Feb 17,2007

Copyright 2006 Takaya Iwamoto All rights reserved. .