# Thread: another portion of dependence area of square to area of circle based on the same diag

1. ## another portion of dependence area of square to area of circle based on the same diag

dependence diameter of square to diameter of circle based on the same diagonal is ( 4 * d / sqrt(2) / d ) to ( pi * d / d )
area of square to area of circle based on the same diagonal is ( ( d / sqrt(2) ) ^ 2 / d ) to (( pi * d ) ^ 2 )

2. ## Re: another portion of dependence area of square to area of circle based on the same

That is so "terse" it is difficult to tell what you are saying.

A circle with diameter "d" has radius d/2 and so area $\pi r^2= \pi \frac{d^2}{4}= \frac{\pi}{4}d^2$.

A square with diagonal d (so the it is inscribed in the circle) has sides of length $\frac{d}{\sqrt{2}}$ and so area $\frac{d^2}{2}$.

The ratio of "area of circle to area of square" is $\frac{\frac{\pi}{4}d^2}{\frac{d^2}{2}}= \frac{\pi}{2}$.
And the ratio of "area of square to area of circle" is $\frac{\frac{d^2}{2}}{\frac{\pi}{4}d^2}= \frac{2}{\pi}$, the reciprocal, of course.

But that doesn't appear to have anything to do with what you wrote. I can't make anything out of "4*d / sqrt(2) / d". What do the two "/" mean? If that was supposed to be $\frac{\frac{4d}{\sqrt{2}}}{d}$, that is equal to $\frac{4}{\sqrt{2}}$. The "d"s cancel and that certainly is not the area of the square. And why is the $\pi$ squared in "(pi * d)^2". That is NOT the area of a circle of diameter d.

3. ## Re: another portion of dependence area of square to area of circle based on the same

Hello, razera!

Sloppy wording . . . I had to guess what you meant.

We have this scenario:
Code:
              * * *
*           *
o - - - - - - - o
*|             * |*
|           *   |
* |         *     | *
* |       o       | *
* |     *  d      | *
|   *           |
*| *             |*
o - - - - - - - o
*           *
* * *

dependence diameter of square to diameter of circle based on the same diagonal is:
. . . ( 4 * d / sqrt(2) / d ) to ( pi * d / d ) . Why did you divide by d?

You want the ratio of the perimeter of the square to the circumference of the circle.

The side of the square is: $\tfrac{d}{\sqrt{2}}.$ .Its perimeter is: $4\left(\tfrac{d}{\sqrt{2}}\right) \,=\,2\sqrt{2}d$

The circumference of the circle is: $\pi d$

The ratio is . $2\sqrt{2}d: \pi d \;=\;2\sqrt{2}:\pi$

area of square to area of circle based on the same diagonal is:
. . . ( ( d / sqrt(2) ) ^ 2 / d ) to (( pi * d ) ^ 2 ) . no

The side of the square is: $\tfrac{d}{\sqrt{2}}.$ .Its area is: $\left(\tfrac{d}{\sqrt{2}}\right)^2 \:=\:\tfrac{1}{2}d^2$

The radius of the circle is: $\tfrac{d}{2}.$ .Its area is: $\pi\left(\tfrac{d}{2}\right)^2 \:=\:\tfrac{\pi}{4}d^2$

The ratio is . $\tfrac{1}{2}d^2 : \tfrac{\pi}{4}d^2 \:=\:2:\pi$