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Scheme „B“ – full configuration

SCHEME „B“ – FULL CONFIGURATION

Full configuration of scheme „B“ trisection

Since we have plotted scheme „A“ or freely referred to the scheme as “gene A” trisection, we can perceive the equilibrium and seemingly complex construction, even though it is actually simple, especially when we split up only one or two segments to trisect an arbitrary angle. The groundwork is simple, but when we multiply it six times, then it seems complex. What’s the purpose? It attends to a succession of new products which I would rather not talk about in this chapter on trisection, but will instead strictly adhere to our fundamental goal; the quest for the trisection points from which we can divide an angle into three equal sections. Therefore we will in geometrically full configuration show scheme „B“ to perceive the differences and the conformities that then, either lead to or do not lead to, the same goal, albeit that scheme „B“ differs, to then perceive something that may also serve as food for thought in other domains of the natural sciences. This remark refers to scheme “B“ which we have in a free manner named „gene B“ trisection , and we hope to confirm this subsequently after our demonstration of scheme „B“.

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Therefore, the hexagon: the initial (base) circle with its six divisional circles.

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The chord of each hexagon segment and linear division into six segments.

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Bisectors of each segment.
(Always focus attention on the initial central circle). 

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In short:
The circles of each segment of chord diameter with segment of center of intersection of bisector and chord segment.

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Inscribe:
Segment of chord diameter circles from the chord ends (poles) of the initial circle’s hexagon.

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Inscribe:
Circles from intersections of segmented circles and bisectors (exterior and interior). We get four-leafed floral patterns, six times.

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Like up to now, we inscribe right angles into the the segmented circles.

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As previously presented, we circumscribe each right angle’s arc with its full circle (the chord radius of the right angle).

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As we have learned, the four-leaf floral pattern is actually the descriptive square of the hexagon segment’s circle of the initial circle, in other words, we inscribe diagonals to each pattern.

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Diagonals divide the arc of the right angle’s hexagon circle segment of the chord diameter segment into three equal sections.

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Thus we now know the following: the intersection of diagonals on the right angle’s arc of the chord’s circle are trisection points from which half-lines, drawn towards the center of the base circle, divide the hexagon segment’s arc of the base circle into three equal sections.

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In such a manner we have trisected the arc of the initial circle into 6×3 sections with full circle plotting, but have nevertheless somewhat shortened the straight line plotting and obtained the full configuration of trisection scheme „B“ or „gene B“ respectively.

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