A circle and a square have the same area. What is the ratio of the area of a square inscribed in the circle to the area of a circle inscribed in the square? (Draw nice pictures.)

*r*

^{2}=

*s*

^{2}→

*r*

^{2}=

*s*

^{2}/

A

_{1}= A

_{square}= half the product of the diagonals = ½(2

*r*· 2

*r*) = 2

*r*

^{2}

A

_{2}= A

_{circle}= (

*s*/2)

^{2}=

*s*

^{2}/ 4

A

_{1}/ A

_{2}= (2

*r*

^{2}) / (

*s*

^{2}/ 4)

= (2

= 2

= 8/

*s*^{2}/) / (*s*^{2}/ 4)= 2

*s*^{2}/ · 4/*s*^{2}= 8/

^{2}