it is possible to square a circle?

Question

please do not answer a question with another question.

u guys talk to much. this is an squared circle o^2 easy.

Answer 1

The problem of squaring a circle is this: given an arbitrary circle, produce a square having the same area using only a straightedge and compass according to the classical greek rules (i.e. no marking the straightedge). This means building a square with a side of length r√π, where r is the radius of the circle. It has been known since antiquity that given two lengths, it is possible to construct their sum, difference, product, quotient, and the square root of either length, so if it were possible to construct a line segment whose length is exactly π, one could take its square root, multiply it by the radius of the circle, and build a square on the resulting line segment, thus squaring the circle. Conversely, if you could square a circle, then squaring the unit circle would provide you with a square whose side length is exactly √π, and multiplying that by itself would produce a segment whose length is exactly π.

So the relevant question is: can you construct a line segment of length π?

The answer is no. Here's why: there are exactly three things you can do in the greek rules of construction --

#1: given two points, construct the line through them
#2: given two points, construct the circle centered at one point and passing through another.
#3: given two lines, or a line and a circle, or two circles, find their point(s) of intersection.

That's it. These are the only things you can do. Now, all constructible geometric objects are formed from two points, thus the points of intersection of any two lines or circles can be completely determined from the two points used to construct the first object and the two points used to construct the second object. Examining the equations for lines and circles, we see that the x and y-coordinates of every constructible point can be obtained from the x and y-coordinates of the four (not necessarily distinct) points used to construct it by a finite number of additions, subtractions, multiplications, divisions, and square roots. And if we use these new points to construct even more points, then the coordinated of these other points will also be expressible from the coordinates of the original points using a finite number of additions, subtractions, multiplications, divisions, and square roots. And likewise, the distance between any two constructible points can also be so obtained. This means that, if we choose two points and declare the distance between them to be 1, and some pair of points can be constructed from them such that the distance between them is exactly π, then π could be obtained from 0 and 1 using a finite number of additions, subtractions, multiplications, divisions, and square roots. This would mean, in particular, that it must be the root of some polynomial with rational coefficients. However, it has been proven that π is a transcendental number -- that is, it is not the root of any polynomial with rational coefficients. Therefore, no segment whose length is exactly π can be constructed, which means that the circle cannot be squared.

Note that this is more a mathematical curiosity than any practical limitation. It is possible to construct a line segment whose length is arbitrarily close to π, in fact sufficiently close that the error arising from any physical performance of the construction would exceed the difference between what the construction would theoretically produce and π. And for real-world purposes, one may always use the eminently practical method of simply measuring the length to any required precision.

Answer 2

Impossibility

A solution of the problem of squaring the circle by compass and straightedge demands construction of the number \sqrt{\pi}, and the impossibility of this undertaking follows from the fact that π is a transcendental number—that is, it is non-algebraic and therefore a non-constructible number. If one solves the problem of the quadrature of the circle using only compass and straightedge, then one has also found an algebraic value of π, which is impossible. Johann Heinrich Lambert conjectured that π was transcendental in 1768 in the same paper he proved its irrationality, even before the existence of transcendental numbers was proved. It wasn't until 1882 that Ferdinand von Lindemann proved its transcendence.

It is possible to construct a square with an area arbitrarily close to that of a given circle. If a rational number is used as an approximation of π, then squaring the circle becomes possible, depending on the values chosen. However, this is only an approximation and does not meet the constraints of the ancient rules for solving the problem. Several mathematicians have demonstrated workable procedures based on a variety of approximations.

Bending the rules by allowing an infinite number of compass-and-straightedge operations or by performing the operations on certain non-Euclidean spaces also makes squaring the circle possible. For example, although the circle cannot be squared in Euclidean space, it can in Gauss-Bolyai-Lobachevsky space.

Note that the transcendence of π implies the impossibility of exactly "circling" the square, as well as of squaring the circle.

Answer 3

Your question is not precise enough. If you are asking the question the greeks asked themselves, "is it possible to square a circle with straightedge and compass", the answer is no as was proven in the 19th century. The reason is basically because you can't construct pi.

If the question is find a square whose area is equivalent to that of a circle, the answer is yes, as follows.

Assume the circle has radius r. Then the area of the circle is

A = pi r^2

The side of a square with area A is the square root of the area, so the side of the equivalent square in area to the circle of radius r is

l = sqrt(pi r^2) = r sqrt(pi)

And this squares the circle.

I suspect the question you were asking was the first one.

Answer 4

x^2+y^2=c^2
Basic circle formula
x^2+y^2-c^2=0
set = 0
(x^2+y^2-c^2)^2=0
Sq. the circle.
x^4+y^4+c^4+2x^2y^2-2x^2c^2-2y^2c^2=0
that is the only way I can think of to square a circle with x and y being the variables and c being the constant. To graph that, you would solve for y and put it in the calculator (replacing c for a number).

Answer 5

yes pie r SQUARED will give you a circle
or 360^2 this work to o o o o can you see it
o o
o o o o

Answer 6

Also known as Quadrature of the Circle...This is one of the famous unsolvable problems.

So in short, No

Here is the full story if you actually want to understand why...

Answer 7

Yes. But it will require a human sacrifice of twenty-nine virgins to the Machine god.

Answer 8

yes absolutely, if you referring to a solid matter then you can!!! but as mathematics is concern your not!!!

Answer 9

what are you talking about?