Is there a circle which has same area as a square?

Question

In equation ; Pi x r^2 = a^2

Answer 1

Well, yes, of course, just let a=sqrt(pi) r. But the ancient problem of squaring the circle was to find this length a from r using only a straightedge and compass. It turns out that *this* is impossible. The reason is that every step in a straight-edge and compass construction essentially solves either a linear equation or a quadratic equation. So all lengths that can be constructed are solutions of polynomial equations with rational coefficients. However, pi, and hence sqrt(pi) is transcendental, which means it is *not* a solution of such a polynomial equation.

Answer 2

Not sure what you're asking here... are you saying the side of the square is the same length as the radius of the circle? In that case, I don't think so, because if you look at the two equations, if the side and radius are equal, then the area of the circle will be 3.14 times as large as the area of the square every time. So unless you're asking something different, it's not possible.

Answer 3

If the area of a circle is (Pi)(r^2)

and the area of a square is x^2

and the area of the circle = the area of the square,

then the radius of the circle must be equal to (x divided by the square root of Pi) for the areas of the circle and the square to be equal

Answer 4

This is called "squaring the circle" and people have been trying to do it with a compass and pencil for millenia; no one had demonstrated a working method yet.

The sides of the square would all have to equal the square root of Pi times the radius of the circle, (sqrt(pi)*r)^2 = pi*r^2

If you really wanted to, I'm sure there's some way you could approximate it by using numerical calculus (viz. Newton's method) to find the sqaure root of pi times r, but it would be pretty difficult, and not precise.

Answer 5

1) Pi x r^2 = a^2 , here if a is any number, then the answer is `Yes', ie, it has an equivalent square. But if,
2) a is considered as a natural number, the answer is `No' because pi is not a natural number.

Answer 6

In modern times, the answer to your question is yes.
a² = π r²
a = r √(π), disregarding the negative solution because a represents a length.
If the side of your square is the same length as the radius of the circle times the square root of pi, the areas of each would be equal.

In ancient times, no. "Squaring a circle," as they called it, was one of the three great unsolvable problems in the days of using compass and straightedge, only.

Answer 7

any square that has sides = Pi(r) will have the same area as the circle.

Answer 8

using that equation you'll need to set the length of the side of the square, and solve for the radius of the circle, since pi is a cte. Alternatively, you could set the radius, and solve for the length of the sides of the square.

Answer 9

I assume 'a' is the length or width of the square. Of course it is possible for a circle and square to have the same area. As you know, the area of the circle is controled by its radius and the area of the square is controled by its lenght (or width).

Answer 10

For every circle, there is a square with the same area.