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Star of david (part one)

STAR OF DAVID (part 1)

18-sided polygon and nonagon

– EXAMPLE OF TRISECTION –

STAR OF DAVID (part one)

It’s all here – I cried out when I saw it in its full (geometrical) splendor. With heavenly luck on our side, step by step and only with a compass and unmarked straightedge, we will demonstrate the meaning of that exclamation to all those who want to come into possession of something higher than just the cognition of sacred geometry. Yes, everything is in it! The alpha and omega of every geometrical code, angle, scheme, known and “unknown” perspective, possible and “impossible” view; every enigma, every (from a geometrical aspect) vagueness;  because that is the route and aim that I am steering towards and it would not surprise me if many of you will come upon much more! But… bear in mind that everything on earth is duality. Chapter 14 is an introduction to the above mentioned and still under the impact of the nonagon and its trisection, so that our presentation will only be partial or a “skeletal frame” of the Star of David or the hexagonal star-shaped polygon respectively in the service of the nonagon and its construction and by way of it the manner of trisecting angles up to 120° (or more with the doubled scheme) that we are already familiar with. However, only one example will suffice. Therefore I won’t dwell much on these deliberations but will rather leave it up to the language of geometry to speak for itself, although I still owe my readers a presentation of the procedure only with compass, as well as with compass and straightedge without markings; the kind of beginners’ procedure taught to children in primary schools – how to draw geometrical figures of triangles, squares, rectangles, heights, diagonals and other simplicities. However, precisely en route, we can make up for this omission in the chapter on the Star of David (the hexagonal star-shaped polygon) and its connectedness with various ancient geometrical artifacts – geometrical messages to us from the ancients.

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As always, everything begins with the circle of a certain radius. From the circle of that radius – we have a hexagon (six parts of circular arc of the basic circle).

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Every other pole connected by straight lengths (lines) a hexagonal star-shaped polygon.

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If we connect the subtended poles with straight lines we acquire the first centerlines of the star-shaped polygon’s vertices of its equilateral triangles.

* * *

If we take the basic circle’s radius into the compass and inscribe circles from the vertices of its triangles, we will get the bisectors of all sides of the peak triangles, in other words the midpoints of each triangle. However, we are interested in something else – namely, the circumscribed hexagonal polygon closest to the midpoint that was acquired by our search for the centers of the peak triangles, i.e. their lines of symmetry.

* * *

An array of “data” arises from this polygon, but only one is of essence for the 18-sided and nine-sided polygon, respectively. Namely, the magnitude of the basic circle’s pole (left and right sides of the subtended pole of the emergent hexagon) in the “quest” from the center of the circle divides the arc  of the basic circle into eighteen equal parts.

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Because of trisecting (and because of the nonagon) our foremost interest is in every other point of division of the nonagon. Hence, we now have a trisection scheme for trisecting angles larger than 90° (and smaller than 120°), so we apply the scheme in the example.

* * * *

Therefore: our presentation is that of a given arbitrary angle with its arc, chord, equilateral triangle sides of which are the magnitude of the chord and with its lines of symmetry – the midpoint of the triangle (truncated drawing).

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The described circle and its division into six segments (truncated without the partitive circles) – hexagonal star-shaped polygon (that circle is now the basic circle).

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In accordance with the scheme mentioned in this chapter, with the radius of the circle we “seek” its centerlines by way of its triangle vertices (star-shaped polygon with full circles).

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Now follows the star-shaped polygon scheme and its circumscribed hexagon with the radius of the closer center – the left and (further) right pole of the basic circle polygon closer to the center – dividing the basic circle into 18 parts.

* * *

Our interest is in every second divisible point above the chord and arc of the given arbitrary angle.

* * *

The arc above the arc of the arbitrary angle – and every other point are the points (tools) of the trisection A scheme that will be used to trisect the arbitrary angle.

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Drawing rays through them in the direction of the peak of the randomly given angle we have divided the arc of the arbitrary angle into three equal parts.

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In this way we have trisected the arbitrary angle only by using a small part of the Star of David, whereas all the rest by avoiding the system of the Star of David which has within itself a chain of “controls” of the nonagon and 18-sided polygon and much more, and this is one of the fundamental laws of sacred geometry. Namely, in scared geometry the accuracy and confirmation of its accuracy places at our disposal several “witnesses” of its correctness – rwo at least.

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One Response to “Star of david (part one)”

  1. John says:

    I knew there was something to the star of David, more than meets the eye. What comes to my mind regarding this Symbols is the moment of creation.

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