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             Hesire's Tomb Engraving  & The Golden Section

The below arrticle is really interesting in that it contains certain findings I made in 2007, which it seems, might have been made by a Russian architect long time before me. I can't be sure of exactly how the other work goes, because it is onily available if you buy the book. I don't buy such books out of principle just like I don't try to make anyone pay for the information available here. 

The Graven Image of
Hesire from a wooden door in hs tomb is almost 47 centuries old. Like Imhotep, architect of the first pyramid in Egypt, Hesire belonged to King Djoser's (Zoser's) intellectual elite, and held many titles like Overseer of Scribes, and Chief  Dentist.
In this image, Hesire grips two staffs in such a manner that they form a right angle. The upright staff looks approximately twice as long as the level one.
If there is a clue that the image is constructed on a geometric basis, this is it. At the same time, Hesire looks not unlike a warrior 'en guarde' with a sword, and a shield . Indeed, these weapons refute those Egyptologists, and historians, who uphold the present consensus that ancient Egyptians had only rudimentary knowledge of mathematics, their value for Pi was about 3.16, and they didn't know and use the Golden Section. Yet, the truth is that Egyptians had considered the Golden Section sacred, and thus perfectly suitable, one could say a must, for the planning of their temples and tombs. We have seen, how extensively the three Giza pyramid temples embody the Golden Section. 


                 


To put the clue to a test, the length of the upright shaft serves as the basis for two side by side squares. The diagram below shows that the testing squares fit the figure. For example, the line dividing the rectangle into two squares is also a line of Hesire's belt.

The cut of Hesire's sword

The line along the lower edge of Hesire's 'sword' gives the Golden Proportion with the (parallel) central axes of both squares in the column.
When we fit two golden rectangles below the top of the lower square, as in the image, or when we center a golden rectangle in the middle of the two-square column, in the process, we recreate the lower edge of the engraved clue line.


                        



 A natural progression of experiments  


Since Hesire's right foot meets the ground at a perfect right-angle, it provides an experimental socket for the two-square column from above. First, we just transport the column to the socket to anchor it there without changing its angle. In this case, the left side of the column shows definite alignment with Hesire's body. The yellow lines in the diagram below are those of the Golden Section. The Golden Section line on the right runs with the edge of the long staff. On the other side the equivalent line runs to Hesire's eye. There are other harmonies. One diagonal of the top square runs with the edge of Hesire's forearm for most of its length. The top side of the column limits hesire's left shoulder at the armpit.
All details considered, this experiment also shows some merits, and yields further insight into the designer's methods.




                      



The obvious next step

Next, the anchored column is aligned to Hesire's foot. The result is more harmony between Hesire's figure and geometry. For example, a different golden-section line now passes through the same corner  of Hesire's eye. Notably, the column in this position determines the limits of Hesire's figure on two sides, the bottom, and the right.
This leads to an idea that these two limit lines are like half
a bounding box (frame) for the figure, and so, completion of this bounding box is the subject of the (for now) final experiment.

                                 


The short staff sets the width of the bounding box (the frame) on the left. The top side is then added automatically. This is a standard experiment, in which three rectangular lines form a socket for corresponding figures. We can insert a square, or golden-rectangles, or their combinations into the socket. If the designer had worked with the Golden Section at all, then these experimental expansions make it possible to fall in tune with the original design.


                                 
                                                  

Hesire's frame can be seen in several ways - a square sandwiched between two horizontal golden rectangles, or two stacked golden rectangles, one vertical, one horizontal. Careful scrutiny of the result reveals much harmonious correlation between the image and the grid. For instance, the vertical limit line on the left of the previous column is also incorporated into the new grid, and so is the top line of Hesire's right foot.

Conclusion: The designer of Hesire's image on the wooden door in his tomb had deliberately integrated the Golden Section in its layout.

 
©Jiri Mruzek  
August 8, 2007

Vancouver, BC



Note: The rasterization module in my vector driven program  has a stubborn kink, which elongates the rasterized images vertically by about three and a half percent (1.034 to 1.035). This is a recent problem, dating from  "The Giza Pyramid Temples & the Golden Section. I am not willing to readjust raster images, it just does not seem right. But, such adjustment will produce the optically correct ratio.



 
Index page

The Abydos Helicopter & the Golden Section

   
Giza Pyramid Temples & the Golden Section
 
 35,713.1 inches = 907,113 mm = 1,732.45 royal cubits
   9,068.8 inches 230,348 mm 439.9 royal cubit
 39154.24942702 inches of the golden diagonal 31.71747441 degree = 994,518 mm = 1,899.38 cubits
Menkaure puramid:

4147.52920404 inches  = 105,347 mm = 201.197 cubits
17237.02919002 inches SN between southern edges of the second and third pyramid
= 437,821 mm = 836.17 cubits