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 )
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 )
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 $\displaystyle \pi r^2= \pi \frac{d^2}{4}= \frac{\pi}{4}d^2$.
A square with diagonal d (so the it is inscribed in the circle) has sides of length $\displaystyle \frac{d}{\sqrt{2}}$ and so area $\displaystyle \frac{d^2}{2}$.
The ratio of "area of circle to area of square" is $\displaystyle \frac{\frac{\pi}{4}d^2}{\frac{d^2}{2}}= \frac{\pi}{2}$.
And the ratio of "area of square to area of circle" is $\displaystyle \frac{\frac{d^2}{2}}{\frac{\pi}{4}d^2}= \frac{2}{\pi}$, 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 $\displaystyle \frac{\frac{4d}{\sqrt{2}}}{d}$, that is equal to $\displaystyle \frac{4}{\sqrt{2}}$. The "d"s cancel and that certainly is not the area of the square. And why is the $\displaystyle \pi$ squared in "(pi * d)^2". That is NOT the area of a circle of diameter d.
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: $\displaystyle \tfrac{d}{\sqrt{2}}.$ .Its perimeter is: $\displaystyle 4\left(\tfrac{d}{\sqrt{2}}\right) \,=\,2\sqrt{2}d$
The circumference of the circle is: $\displaystyle \pi d$
The ratio is .$\displaystyle 2\sqrt{2}d: \pi d \;=\;2\sqrt{2}:\pi$
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: $\displaystyle \tfrac{d}{\sqrt{2}}.$ .Its area is: $\displaystyle \left(\tfrac{d}{\sqrt{2}}\right)^2 \:=\:\tfrac{1}{2}d^2$
The radius of the circle is: $\displaystyle \tfrac{d}{2}.$ .Its area is: $\displaystyle \pi\left(\tfrac{d}{2}\right)^2 \:=\:\tfrac{\pi}{4}d^2$
The ratio is .$\displaystyle \tfrac{1}{2}d^2 : \tfrac{\pi}{4}d^2 \:=\:2:\pi$