| Radius of the circle |
| Number of splits |
|
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| Distance from the center of the circle (first all points to the right, then to the left) |
| Length of the chord of the nth section |
Let's consider a simple problem - how to dissect a circle with parallel straight lines into N - parts with the same area. We use only the formula of the circle segment and our own conclusions.
Any division of a circle into equal parts implies that we will always have a circular segment S. Its area is known
\(S_1=\cfrac{R^2}{2}(f-sin(f))\)
Since we divide the circle into n parts, it is logical that the area of each "piece" should be \(S_1=\cfrac{\pi{R^2}}{n}\)
by equating the two above equations, we get the relationship of the angle with the number of partitions
\(\cfrac{2\pi}{n}=f-sin(f)\)
The second segment will be twice as large and therefore \(\cfrac{2*2\pi}{n}=f-sin(f)\)
We see that they do not depend on the radius at all.
Then counting to the right we can find out at what distance from the center of the circle we should draw the next straight line.
\(x_n=Rcos(\cfrac{f}{2})\)
Don't forget to measure the same distance from the center and to the left, too.
The chord, that is, the part of the straight line that passes through the circle and cuts off the next segment from it has a length
\(h_n=2Rsin(\cfrac{f}{2})\)
That's basically the whole calculation.
With an even split, one of the lines will always pass through the center of the circle.