# lenght

• Jun 29th 2013, 03:45 AM
razera
lenght
perimeter of suare / d ( diagonal ) = a / \sqrt{2}

perimeter of suare = a / \sqrt{2} * d

a ( side of square) = perimeter \sqrt{2} / d

a = a / \sqrt{2} * d * \sqrt{2} * 1 / a \sqrt{2} =
= ( 1 / \sqrt{2} * d * \sqrt{2} ) / \sqrt{2} = d / \sqrt{2}

knowing the proportion of perimeter of square to his side, count the proportion of perimeter of oval to perimeter of suare based on the same diagonal :

perimeter of suare = a / \sqrt{2} * d ( diagonal )
perimeter of oval = 2 pi * d
a ( side) = perimeter \sqrt{2} / d

( a / \sqrt{2} * d ) / ( 2 pi * d ) = d / 2 pi

( i dont know if its good )
• Jun 30th 2013, 10:25 AM
HallsofIvy
Re: lenght
Quote:

Originally Posted by razera
perimeter of suare / d ( diagonal ) = a / \sqrt{2}

perimeter of suare = a / \sqrt{2} * d

a ( side of square) = perimeter \sqrt{2} / d

You may just be writing it wrong but if a is a length of a side, then the perimeter of a square is 4a. The length of a diagonal is $a\sqrt{2}$ so that the ratio of a side to the diagonal is $\frac{1}{\sqrt{2}}= \frac{\sqrt{2}}{2}$. The ratio of the perimeter of the square to the diagonal is $2\sqrt{2}= d\sqrt{2}$. The perimeter of the square is NOT "a/\sqrt{2}*d" It is either 4a or $d\sqrt{2}$.

Now, by "oval" do you mean "circle"? An "oval" is not usually the same as a "circle"- more like a generalized ellipse.

Quote:

a = a / \sqrt{2} * d * \sqrt{2} * 1 / a \sqrt{2} =
= ( 1 / \sqrt{2} * d * \sqrt{2} ) / \sqrt{2} = d / \sqrt{2}

knowing the proportion of perimeter of square to his side, count the proportion of perimeter of oval to perimeter of suare based on the same diagonal :