Ejup Dermaku Posted January 19, 2020 Share Posted January 19, 2020 A given circle with area A = 1 has a radius = 1/sqrt(pi). In this case there exist a square with the sides of length = 1 which has an area equal to 1. This problem is referred as a "squaring the circle". Due to the "irrational" and "transcendental" nature of number pi , squaring of circle is not possible to be constructed only by ruler and compass. However, I've read in an old mathematical book, that a construction is possible only in case when circle area A=1, without any further explanation given. Is there any one who can support this claim? Link to comment Share on other sites More sharing options...
taeto Posted January 19, 2020 Share Posted January 19, 2020 22 minutes ago, Ejup Dermaku said: A given circle with area A = 1 has a radius = 1/sqrt(pi). In this case there exist a square with the sides of length = 1 which has an area equal to 1. This problem is referred as a "squaring the circle". Due to the "irrational" and "transcendental" nature of number pi , squaring of circle is not possible to be constructed only by ruler and compass. However, I've read in an old mathematical book, that a construction is possible only in case when circle area A=1, without any further explanation given. Is there any one who can support this claim? That is not what "squaring the circle" means. Given a circle of area 1, yes, there also does exist a square also of area 1. That is not a problem. The problem is that from a line segment of length equal to the radius (or equivalently the diameter) of such a circle, it is not possible only using ruler and compass to construct a line segment to make a side of a square of the same area as the circle. The claim in your old book does not make immediate sense. It is true that if you are given a line segment of unit length, then you can quite obviously construct a square of unit area. But having been additionally given a circle of unit area would not be helpful in any way to do it. 3 Link to comment Share on other sites More sharing options...
studiot Posted January 19, 2020 Share Posted January 19, 2020 23 minutes ago, taeto said: That is not what "squaring the circle" means. Given a circle of area 1, yes, there also does exist a square also of area 1. That is not a problem. The problem is that from a line segment of length equal to the radius (or equivalently the diameter) of such a circle, it is not possible only using ruler and compass to construct a line segment to make a side of a square of the same area as the circle. The claim in your old book does not make immediate sense. It is true that if you are given a line segment of unit length, then you can quite obviously construct a square of unit area. But having been additionally given a circle of unit area would not be helpful in any way to do it. Short and sweet. Nothing more that needs adding here. +1 Link to comment Share on other sites More sharing options...
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