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Division of cube – the cube of five (5³)

CHAPTER „D“ FOR KIDS

DIVISION OF CUBE – THE CUBE OF FIVE (5³)

This chapter will not have many shortcuts because it of itself contains other important elements (geometrical depiction of square’s perimeter, of square’s circle), which we will deal with in subsequent chapters because before that we must first master the basic progressions of ancient geometry (laws and relationships between straight line drawing and spherical drawing, relationships between numbers and their fractions, their multiplying and dividing and their depictions, division of arcs, diameters, etc.). In behalf of future generations I sincerely hope to attain success by using only the compass and unmarked straightedge, and that I will have the adequate capital and time to accomplish this goal (in light of the fact that I’m not well-versed in English nor a computer literate able to autonomously maintain this site, but because of the direct opposition of the academic community and secret societies – and perhaps even because I’m a poet. Nevertheless, as said He whom I asked for these cognitions in behalf of the new generations and their knowledge, and His reply was: „Man shall live in accord with his belief”, and so I hold that it is good to reveal the unknown (judging by the encyclopedic and geometric sciences that we have hitherto been taught). So we, in our inquisitive pioneering spirit march onward toward the future like real kids whose aim is to acquire knowledge, step by step. Hence, this is not a pentagon, but the division into fifths, tenths and their progressions, or in accordance with my free translation as shown in a shortcut geometrical 4+1 version.

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Hence, with the radius entered into compass we circumscribe a circle and divide it with radius into six parts.

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Inscribe the sides of the hexagon.

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Inscribe lengths of subtended poles. Cube is under 30° angle of inclination (eigth angle hidden behind first angle which is at same time center of the circle).

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Now enter radius into compass: peak pole and third and fifth and connect them with curved lines (by compass) and then repeat this from each of the six poles of the hexagon. We acquire the inside intersections that we circumscribe with a circle.

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Into smaller circle we inscribe its hexagon and while inscribing we can project them to the sides of the first hexagon. Here we already have a fifth (as we will see).

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So, still extant is the smaller cube which we will, like in the previous chapter, divide into 2x2x2 = 2³ and thereafter once again with the help of intersections that will autonomously emerge, to be divided into 4x4x4 = 4³.

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Therefore, the star-shaped polygon of the smaller hexagon is divided by lines of symmetry.

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We are focused on the smaller cube. We divide it into 2x2x2 = 2³.

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Therefore by applying the same system, and with the aid of intersections resulting between the division of progression 2 and the star-shaped polygon, we divide 2x2x2 = 2³ into halves of 4x4x4 = 4³.

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Now we simply extend this division onto the six sides of the first hexagon and divide the cube into 4+1 = 5. On the radius we have 5 parts; on the diameter we have 10; in other words, fifths and tenths. We opened the progression of 5, and if we further combine it with the system of 2 and 3 that we learned, we can acquire other progressions (since it is apparent that every cube of five is a cube of the hexagon that can again be divided into 2 and 3). But that will be enough for the time being, until our next progression – the progression of 7.

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