problem

• Jul 7th 2013, 10:17 AM
razera
problem
problem :

dependence between area of circle to area of square around this circle ( 2 * ray of circle is side of square ) is 2 / pi, however the dependence of sector of this square ( quarter ) to sector of this circle ( quarter ) made on the ray of circle isnt correct with
2 / pi

r^2 / ( pi * r^2 / 4 ) != (nie równa się) 2 / pi
• Jul 7th 2013, 01:55 PM
Soroban
Re: problem
Hello, razera!

Quote:

Dependence between area of circle to area of square around this circle is 2 / pi. . Not true
However, the dependence of sector of this square (quarter) to sector of this circle (quarter) isn't correct with 2 / pi.

The circle has radius $r=1.$
Its area is:- $\pi r^2 \,=\,\pi(1^2) \,=\,{\color{blue}\pi}.$

The side of the square is $s =2.$
Its area is:- $s^2 \,=\, 2^2 \,=\,{\color{blue}4}.$

Ratio of areas: . $\dfrac{\text{square}}{\text{circle}} \:=\:\frac{4}{\pi}$