Draw a unit circle.
Around it, circumscribe an equilateral triangle.
Circumscribe another circle around that.
Circumscribe a square around this circle.
Circumscribe another circle around that.
Circumscribe a regular pentagon around this circle.
Circumscribe another circle around that.

Continue, ad infinitum, with the next regular polygon.

Do the radii of these circles converge? If so, what is the limiting radius?

 

The diameter of circle increase every time by 1/ cos ( PI/n)

hence limit of the diameter of circle is 1/(cos(PI/3)*cos(PI/4)*cos(PI/5)*.........cos( PI/Inf) 

I am not a programmer based on Excel limits this would finally converge at around approx 8.7.

 

Posted by salil on 2006-02-15 02:32:34