Squaring a circle by just a ruler & compass.

Originally posted by STANG
I disagree. You need to consider the following ...

How much concern do American's have when allowing for the possibility that the balance of power is going to shift over the next 50 years whilst America continues to be perceived as an aggressor with suspect motives ?

This is a question about how the world will be when America no longer enjoys its curre ...[text shortened]... ing point, which presidential candidate is better for the longer term viability of the world ?

Aah..you seem squared up already.
What does your responce have to do with the puzzle of this thread???

Originally posted by STANG
I disagree. You need to consider the following ...

LOL. And I thought ivanhoe had a one-track mind... 🙄

Originally posted by TheMaster37
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If you allow distances to be moved like that, you CAN square a circle.[/b]

Repositioning of length is always possible with a ruler & a compass.

Now , given that, how CAN you square a given circle?

Originally posted by cosmic voice
The iterative method which I have found , is as follows:
Let ACB be the given circle with centre O, AB its (horizontal) diameter, and C is a point on its circumference such that OC is perpendicular on diameter AOB.

With ruler and compass, draw /_BOP1 = 22.5 deg. Take point P1 on OP1=BC in length. Draw perpendicular P1Q1 at P1 on ...[text shortened]... ometrical identity
Z = sin Z*{sec Z/2 * sec Z/4 * sec Z/8......sec Z/(2^n).....to infinity}.

Yes , it seems correct . But there sure is some simpler method.

Originally posted by rspoddar82
Yes , it seems correct . But there sure is some simpler method.

See the site http://www.uwgb.edu/dutchs/PSEUDOSC/SquareCirc.htm

Originally posted by sarathian
See the site http://www.uwgb.edu/dutchs/PSEUDOSC/SquareCirc.htm

I saw this site. This site too gives only approximations. In exact terms this puzzle is an unsolvable classic puzzle.

"Square a circle" is very ambiguous. I thought you meant make the smallest square that could contain the circle.

So we're supposed to make a square with the same area as the circle?

Originally posted by AThousandYoung
"Square a circle" is very ambiguous. I thought you meant make the smallest square that could contain the circle.

So we're supposed to make a square with the same area as the circle?

Squaring a circle means constructing a square equal to a given circle in area.

"Squaring the circle" in an ancient problem, it is impossible to do, check any math site and they'll mention it. Every now and then some charlatan will claim they've done it, but no one ever has.

?

Determine the area of the circle. The sides of the square have the square root of that area for sides. What's so hard about that?

Originally posted by AThousandYoung
?

Determine the area of the circle. The sides of the square have the square root of that area for sides. What's so hard about that?

Ah yes. You are right , but the iterative construction suggested in the post of Cosmic Voice (see post on page 1) does square a given circle to any desired degree of accuracy, as close as one likes to specify.

Originally posted by Dodger11
"Squaring the circle" in an ancient problem, it is impossible to do, check any math site and they'll mention it. Every now and then some charlatan will claim they've done it, but no one ever has.

It is like this - no one can write the exact numerical value of pi,this is absolutely true.

BUT ,one CAN write its value correct to as many decimal places as you want , by using a suitable fast convergent sequence or series.