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THE POINT OF CONVERGENCE


The point of convergence is located in the great descending shaft. It is at the conjunction of the axis of the 2 Southern shafts and perpendicular line to the King Chamber's Northern shaft at the point of intersection of it with the axis of the pyramid.

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1- Location: -30 cubits (under the reference level 0) and 80 cubits towards North, i.e. straight above the low end of the Great Gallery.

Which would be the geometrical characteristics of this point?

2- The southern Shaft of the King Chamber has a slope of 45 degrees and its external opening is located at a distance of 100 cubits from the vertical axis with an altitude of 150 cubits.

This opening is thus located compared to the Point of Convergence at a horizontal distance from 100 plus 80 and at a vertical distance from 150 plus 30 is also180. I.e. that the line which the King Chamber's southern Shaft represents will necessarily pass by this Point of Convergence.

3- The end of the Queen Chamber's southern shaft is also at a distance of 100 cubits from vertical axis but at an altitude of 120 cubits.

(One can note this difference of 30 cubits which corresponds to the Gizeh secondary grid's pitch, but also with the negative altitude of the Point of Convergence).

We will thus have a differential of altitude of 120 plus 30 equal to 150 and one horizontal distance of 100 plus 80 equal to 180.

The slope of this right-angled triangle will be thus... 39 degrees 48 minutes, which is matched with the measurements raised by the Upuhaut robot.

This allows us to say that the intersection line consisted by the two Southern shafts is exactly located at this Point of Convergence.

4- This Point of Convergence is also located straight above the low end of the Great Gallery.

5- We thus have already three major lines which converge in this point. I had also previously said that the line raised from the Point of Convergence is perpendicular to the King Chamber's Northern shaft at its intersection with the axis of the shaft.

To do this, it is enough to calculate the altitude of this point of its intersection with the axis of the King Chamber's Northern shaft.

The vertical axis of the King Chamber is shifted of 21 cubits from the axis of the pyramid, towards the south, and the King Chamber measurement is a 10 cubits width.

The starting point will be thus at a distance of 21 cubits minus half of the King Chamber's width (10 cubits), and we must consider the thickness of the wall. (Close to 3 cubits).

If I consider this point to15cubits, it will be to get closer to the previously evoked concept of knowing what one takes as reference. Interior or outside?

I also said that I have not the answer.

In any case, the absolute error which could result from it would be 40centimetres...

To compare with the size of the building.

Therefore if we choose this value of 15 cubits, the slope of the shaft Equal to 33°41 minutes, i.e. a ratio of 2/3, the rise on a vertical axis will be very close of 10 cubits.

It will result from it a vertical distance between this point and the Point of Convergence of 10 plus 80, plus 30, equal to a total of 120 cubits.

However the horizontal distance from the point of convergence is 80 cubits.

6- There too it is also a ratio 2/3 which enables us to say that the line resulting from the Point of Convergence is rigorously perpendicular to the northern Shaft of the king Chamber in its point of intersection with the vertical axis of the pyramid because it also has a slope ratio of 2/3.

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The Point of Convergence

In addition to the precise relation of the remarkable angles of 90, 60 and 45 degrees which connect the shafts with the whole of the pyramid, this point of convergence is neither random, nor neutral and here at least five remarkable lines are directly involved.

In all the previous matter, it does not have any esotericism or free assumptions.

It is a mathematical report which can only testify the fact that this knowledge was acquired there is more than 4600 years.

The question will be: did old Egypt use the angles like means of calculation or they were only the resultant of the ratios used?

If one refers to the papyrus of rhind, the formulation of the papyrus shows that measurement was made by a whole value, 93, plus a complement, 1/3, itself being made up by a proportion.

The objective being to obtain or preserve the dimension of the apothem of the wanted face, (hypotenuse), in this cases 140 cubits.

The angle itself was not being determining, but simple consequence but it is however asked which will be the value.

In my opinion, at least for Cheops' measurements, I think that it was only the use of simple ratios which could be mainly summarized to 1/1, 1/2, 2/3, 4/5, 5/7, 7/9, 7/11, ratios determined by means of the number of squares of the grids, and then drawing by the use of the diagonal of the generated rectangle.


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