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Organic
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Please look at the attached pdf.
You will find in it a circle and some sub-area inside it.
The sub-area exists between the radius and a curve.
The curve is connected to both sides of some radius, and goes through the intersection points that exists between n radii and n-1 inner circles, where each radius is divided by the inner circles to n equal parts.
I have found that the sub-area(magenta) = circle's-area/3(cyan)
1) Can someone show why the magenta area = 1/3 of the cyan area ?
2) We can take any number of inner radii-circles intersection points, and create some border, which is made of straight lines between these points.
By doing this, we get a closed polygon (an area).
Now we take some closed polygon, find the total number of its vertexes and omit 2 (tolal - 2 = n).
By doing this, we get some Natural number n which is conncted to some polygon's area S (please see the attached pdf in the next post, called natural-areas.pdf.pdf).
Through this way we can put in 1-1 correspondence some n with some S.
When have this map, we can ask:
S1 is the area of some polygon, where the number of totel-2=aleph0.
S2 is the area of some polygon, where the number of totel-2=2^aleph0.
3) Is S1 = S2 ?
4) If the answer to (3) is no, then what is the difference between the two magenta areas, and how this difference related to the CH problem ?
5) Do you think that we have here some useful mathematical constant ?
Thank you.
Organic
You will find in it a circle and some sub-area inside it.
The sub-area exists between the radius and a curve.
The curve is connected to both sides of some radius, and goes through the intersection points that exists between n radii and n-1 inner circles, where each radius is divided by the inner circles to n equal parts.
I have found that the sub-area(magenta) = circle's-area/3(cyan)
1) Can someone show why the magenta area = 1/3 of the cyan area ?
2) We can take any number of inner radii-circles intersection points, and create some border, which is made of straight lines between these points.
By doing this, we get a closed polygon (an area).
Now we take some closed polygon, find the total number of its vertexes and omit 2 (tolal - 2 = n).
By doing this, we get some Natural number n which is conncted to some polygon's area S (please see the attached pdf in the next post, called natural-areas.pdf.pdf).
Through this way we can put in 1-1 correspondence some n with some S.
When have this map, we can ask:
S1 is the area of some polygon, where the number of totel-2=aleph0.
S2 is the area of some polygon, where the number of totel-2=2^aleph0.
3) Is S1 = S2 ?
4) If the answer to (3) is no, then what is the difference between the two magenta areas, and how this difference related to the CH problem ?
5) Do you think that we have here some useful mathematical constant ?
Thank you.
Organic
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