A fascinating number; just divide the perimeter of any circle by twice of its radius, you get then a strange number whose digits can evolve for ever in a random like sequence; it is 𝝅.
That is, 𝝅 is 3 plus an irrational decimal part d whose expansion is limitless. Therefore, suppose the radius is half the unit, then the perimeter is about 3+d.
That is the point!! the shape of the circle is quite trivial, it is gently regular, it is kinder than a square, I do understand the 3, but from where does the d part comes from?
Is there a fractal structure hidden within the gentle circle, so 𝝅 is actually some kind of fractal dimension. Therefore, the circle shouldn't be that regular in fact.
I am fascinated by √2 off course, it comes from the square and Pythagora did well to find the relationship between the square's side and the virtual diagonal; yet I think from geometrical viewpoint, I can still handle and compute squares's perimeter without any knowledge about the diagonal and its irrational √2 length (in case the side is unity). But for the circle I can't avoid the irrational 𝝅!!!
So, I keep on looping around my mind, what does 𝝅 mean ???
Does it have the sense of an error of some estimation, as we human failed to get to the true feature measurment of the circle since it seems that we need always to get through a polygonal approximation of the circle???
I might indicate that indeed it is impossible to determine accurately the position of point on the circle's boundary without a loss in the accuracy of the curvature in that point (Heisenberg like si j'osais le dire)?
Probably, like the square's virtual diagonal, that is not physical, doesn't belong to the square, and that leads to the problematic √2 , the circle's radius which is virtual too and doesn't belong to the circle, has lead to the phenomenon of 𝝅; remind I can stil build a circle starting from three points!? It needs a discussion.
Does the 𝝅 indicate hidden dimensions within the circle, both the square and the circle have topologically dimension unit, yet the square may have two degrees of liberty, one for each side ; but the circle does have a unique (or infinitely many) degree/s of liberty linked to the radius. Wonderful 𝝅.
That is, 𝝅 is 3 plus an irrational decimal part d whose expansion is limitless. Therefore, suppose the radius is half the unit, then the perimeter is about 3+d.
That is the point!! the shape of the circle is quite trivial, it is gently regular, it is kinder than a square, I do understand the 3, but from where does the d part comes from?
Is there a fractal structure hidden within the gentle circle, so 𝝅 is actually some kind of fractal dimension. Therefore, the circle shouldn't be that regular in fact.
I am fascinated by √2 off course, it comes from the square and Pythagora did well to find the relationship between the square's side and the virtual diagonal; yet I think from geometrical viewpoint, I can still handle and compute squares's perimeter without any knowledge about the diagonal and its irrational √2 length (in case the side is unity). But for the circle I can't avoid the irrational 𝝅!!!
So, I keep on looping around my mind, what does 𝝅 mean ???
Does it have the sense of an error of some estimation, as we human failed to get to the true feature measurment of the circle since it seems that we need always to get through a polygonal approximation of the circle???
I might indicate that indeed it is impossible to determine accurately the position of point on the circle's boundary without a loss in the accuracy of the curvature in that point (Heisenberg like si j'osais le dire)?
Probably, like the square's virtual diagonal, that is not physical, doesn't belong to the square, and that leads to the problematic √2 , the circle's radius which is virtual too and doesn't belong to the circle, has lead to the phenomenon of 𝝅; remind I can stil build a circle starting from three points!? It needs a discussion.
Does the 𝝅 indicate hidden dimensions within the circle, both the square and the circle have topologically dimension unit, yet the square may have two degrees of liberty, one for each side ; but the circle does have a unique (or infinitely many) degree/s of liberty linked to the radius. Wonderful 𝝅.
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