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PRODUCT: 9-sided & 18-sided polygons

The objective of this manner of drawing „gene A“ and „gene B“ is as follows: the possibility of trisection points that divide the arbitrary angle into three equal segments only with a compass and unmarked straightedge. The full drawing of the system in either way is not only geometrically desired, but is essential if we want to obtain new data (products).

At the start, we perceive: the compatibility of both “genes” (schemes). In free translation it is like the compatibility between “female” and “male” genes. These and such road maps of mine might arouse the attention of persons involved in other fields of natural science.

But let’s go back to geometry – sacred, ancient geometry. With the full configuration of both trisection schemes, we attain a sequence among a variety of products that are also partially connected with trisecting, in their own characteristic way; these are the nine-sided polygon and (logically) the eighteen-sided polygon that originate from trisection of the hexagon.

However, we will not fully demonstrate it, and doing so we caution that any similarity with the esoteric should be avoided (because that field is unknown to us). Isn’t that simple? The truth is that the nine-sided polygon originated from trisection of the arc of the hexagon circle, and indeed, the two times of the nonagon are the eighteen-sided polygon. This is an extensive field and it requires at least five chapters dedicated to constructions of the nonagon and eighteen-sided polygon in several ways with trisection examples of their arbitrary angles.

Therefore, let’s summarize: 

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Full scheme „A“ – „gene A“ trisection of a hexagon circle.

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The supplemented scheme „A” & full configuration scheme „B“– „gene B“ = „AB“ scheme & scheme „A“ & scheme „B“ have common trisection points on arc of segmented right angles. Therefore, they are compatible.

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If we take every next point of a divided arc of a circle’s hexagon radius starting from its vertex pole, the next trisection point of the segment – we have a nine-sided polygon. (The nonagon circle is smaller than the circle of the hexagon).

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Logical: The radius from the hexagon vertex and each real trisection point divides the arc of the initial circle into 18 parts.
These are products of scheme „AB“ trisection of the hexagon circle’s arc. As for the other products, we will talk about them in subsequent chapters.

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