by Jiri Mruzek

from PrehistoricScienceArt Website

Testing for Geometry

Table 1 (photographed November 1992 by Bruce Rawles )

> Deus ex Machina says:
> No scholar has dealt with this?  In fact MANY have, as the website
> comments indicate, Jiri.  It is acknowledged by all (AFAIK), that is a
> carved limestone that  was altered in antiquity with plaster, to give a
> new meaning to the phrases.  That is, BTW, part of the definition of
> a_palimpsest_, of which these inscriptions are a prime example.
> As I note, Mike Dyall-Smith, Aidan Dodson, Jacques Kinnaer, Eugene
> Cruz-Uribe, and Tine Baugh all gave similar explanations..<snip rest>

> Regards.

> Katherine Griffis-Greenberg

> Member,   American Research Center in Egypt
> International Association of Egyptologists University of Alabama at Birmingham  

Years ago, I got briefly involved in a discussion on the so called Abydos Helicopter. The widely accepted Egyptological solutions to the mystery of Abydos Helicopter (like the one Lumir G. Janku gives) seem correct at a glance, but soon doubts set in. To register my dissent, I put the short debate with Katherine on the web.

From there the matter was dormant until I noticed that searching the web for ’Abydos helicopter’ googles up my article as number 1. Being in the spotlight was a strong incentive to improve the article’s intrinsic scholarly value.  How?
Geometry has been my key a couple of times before to discovering secrets of prehistoric art. No one mentioned any previous geometrical analyses of the Abydos glyphs, yet the eerie Abydos scene gave me a feeling that it might be worth the effort of checking out.

Importing the image into CAD (computer assisted drawing) enables the type of exploration I like. If the work had been extensively planned and measured, CAD will provide excellent means of detecting the fact.


Egyptology Skipped Past It

Egyptologists have identified at least two sets of overlapping hieroglyphics in this picture. So, what we see is a palimpsest, something that never was intended to be seen like it is now. It used to be that only one set of hieroglyphs had been visible, first one then the other. Then the plaster fell out of the stone. (click image right)

What could rival such solid science?

Secret Science

Solon, Plato, Pythagoras, and other Greeks went to Egypt as the place to get the very best education. Back in Greece, they spoke of the secrets of the Egyptian Temple. Pythagoras taught novelties -  the Golden Section, and what is now known as his triangle. Having left no writings, he staked no claim to discoveries attributed to him in later times.

By Ockham’s Razor, the simplest explanation would be that Pythagoras, who reached the top echelon of the Egyptian Temple, had unlimited access to all its secrets - like the Golden section. He left no writings, because he disseminated his knowledge in secret - to selected initiates. It is patently obvious that this mode of behaviour is his legacy from the Egyption institution. A mathematician hardly ever wishes to keep his achievements secret. 

Due to their discretion, Pythagoreans are tabbed as a cult. The distinguished keepers of knowledge get slammed for preserving the secrets of the Egyptian Temple for us. Egypt had a religion, and the Pythagoreans were its extension in Greece, like Solon, and like Plato. These men founded academies and disseminated knowledge. Therefore, dubbing them cultists is unjust if not malicious.

Granting the possession of secrets by the Egyptian Temple, why should some of those not be perpetuated  in enigmatic scenes created out of hieroglyphical Lego?

Our Abydos inscription holds one crucial ingredient - the secret of the Golden Section, to which Egyptology is so steadfastly oblivious. Suppose, we can show this fact to be true - Why the secret geometry? It guarantees and dignifies the scene of the Abydos Helicopter, by endowing it with the unalterable logic of the Golden Section, thus making it the opposite to the concept of chaotic palimpsests.


Can anyone just fire up a CAD program, and recreate the area under the helicopter in its exact main proportions from memory?

Absolutely, this engraving follows a general case from Geometry.

The layout of the area of what is known as the Abydos Helicopter is a study on the basic Golden Section, with emphasis on Golden Rectangles as products.  All objects are in the required proportions, and repose in defined positions:

1 - a unit circle
2 - a square
3 - a horizontal distance divided in the Phi ratio
4 - an axis
5 - a big Golden Rectangle over the horizontal width (base 2.618.., height 1.618 units)
6 - Golden Rectangles based on the unit circle (base 1 unit long, height 0.618)
7 - Golden Rectangles based on the square
8 - 9 - 10  Squares corresponding to each rectangle size

These ten elements of one unique construction are all comprised in the area immediately under the so called Abydos Helicopter.


The above diagram shows the classic construction of the Phi ratio. Let’s lay this diagram over the Abydos Helicopter by scaling the unit circle over the (semi)circle in the image.


The test above shows the glyph (t) to be a rather accurate semi-circle. It is our unit (semi)circle.

1) The circle’s diameter is one half of a square’s diagonal.
2) Divide the horizontal diagonal of the square by the Golden Section.
3) Extend this distance (1.618.. Phi-ratio) by 1 unit. It becomes 2.618.. Phi to the second power, and also the breadth of the row of six columns. 

The Golden Section lines fit the glyph lines - on the column edges.  

The square from the construction is the same as the square formation of columns, and triangles in the engraving. To get the square to its present location,  it had to be rotated 45 degrees, and moved to the far line on the left, then lowered, so that the original diagonal becomes the rotated square’s upper Golden Section line (Table 6).


Table 6
the square is inscribed in a circle with a diameter of two Units

The square fits the glyphic square of columns, and triangles:

a) The left side of the square snaps onto columns.
b) The bottom side of the square snaps onto columns on the left, and triangles on the right.
c) The top side of the square snaps onto the top triangle on the right.
d) The right side of the square snaps onto the outside edges of the top two triangles, and the inside edge of the low triangle line.

Table 7

e) The middle row of triangles also sets the horizontal lines dividing the square  into golden sections (see E, F above).  Here, the later construction (triangles) clarifies how the older columns got there.

The square above shows no less than eight Golden Rectangles, plus corresponding squares. Check them all out, as these objects fit the layout of the engraved square. 

Table 8

We can now also recreate the Golden Rectangle for the width of our area under reconstruction, because its left lower corner coincides with the square’s corner.

As shown, this rectangle contains five smaller Golden Rectangles, and they all fit the engraving. The entire area forms a perfect Golden Rectangle, since the helicopter’s belly rests upon the upper line of the rectangle, although the reader does not see it at the moment. However, this marvellous fit is easy to see in the blow-up below (Table 9). A part of the rectangle line was cut away, because it was masking the belly line of the helicopter. The fit is visually perfect. Mindful of the good fit of the other three sides, we can say that this rectangle is highly accurate.

Duplicate this rectangle on the upper right side, and it fits again : width-wise, at the bottom, and horizontally through the body of the middle row craft.

A close-up then shows that the rectangle fits at the top, too (table 10).

Yet, while the rectangle on the left is set by the original Seti I’s glyphs, on the right the same rectangle encloses the palimpsest, i.e., the unpredictable result, which occurred long after the alleged re-engraving - a miracle!


Table 9

Table 10
top of the boat  is a circle arc, whose center falls upon the top of the object below

Table 11

Adding, or taking away a square from a Golden Rectangle gives another Golden Rectangle.

The table above shows that for each of the Golden Rectangles (from the unit circle), the line dividing it into a square & a smaller Golden Rectangle - then fits over a line  in the inscription.

It definitely looks like the Egyptian priests knew this geometrical procedure. The same rectangles and squares must have been once seen by the engravers, as they regulated the glyph groups. In this regard, their work is admirably accurate.

Table 12

The overlap between the rectangles propped against both sides of the square then sets the column thickness for reconstruction. This works very well on all the columns.


The overlap between the rectangles sets the thickness of the triangle baselines for reconstruction.

Table 13

In principle, we can reconstruct the rectangles above.

Table 14

Movement or Inaccuracy?

The upper set of columns in the engraving is definitely swaying to the right, as opposed to the plan.. Its rectangular frame is also moved slightly to the right. On the other hand, these columns still fit the Golden Rectangle really well.  So, is this a deviation from the plan, or is there a purpose behind it? I tend to think that there is a purpose. One thing to consider - the upper three columns were not needed for the decoding of the main idea. In contrast,  the crucial elements for the solution were adequately and admirably accurate.

Janku points out the high quality of craftsmanship throughout the Abydos temple, and wonders why only this one inscription and no other suffers from shoddy quality. Well - we know that it is not true. We can actually reconstruct almost everything in the Abydos glyphs based on the Golden Section. This is only going to change for the better, given time.

Table 15

Table 16

The next Golden Rectangle we find is a monster! It fits the palimpsest, which it should not do by any other means than coincidence. Yet, coincidence is exactly what we have eliminated with regard to the existence of the countless Golden Rectangles here - we have found so many - we lost the count.

So, if the Golden Rectangle is not a coincidence - it was meant as the frame for the scene we see - just like the other rectangle framing the scene under the helicopter. It certainly is the tightest rectangular container for the two objects below the gunboat/tank. The conclusion is inescapable - this particular ’palimpsestis a deliberate creation. Such facts nip Egyptological explanations of the Abydos Helicopter in the bud.

Table 17

We see a couple more more alignments, which should not be there, if the scene were really a palimpsest.


a) The unit circle will be found to be the basic unit of length used in the temple
b) The unit of length used in the temple will be found by substituting the Cone &  Square formation (learned from my study of La Marche, and Nasca) over the square in our Abydos construction, and will be the same as the La Marche, and Nasca units.  If so, this would prove a direct connection between La Marche, Nasca, and Abydos.

April 18th, 2003 - A note from the author:  

I haven’t quite finished rewriting this article, but decided to put what is there on the web anyway, as is, as it is much better than the old one already. The reader should view the stuff below this line as simply a collection of notes.


In December, 1998 I pretty well signed off from the discussion with this observation: ... contrary to the popular scientific myth that the glyphs are engraved on a solid block,  photographs indicate otherwise. The glyphs appear to be engraved on a thin layer of stone facing covering the solid stone below, except, where the facing broke away.

There is the self-evident - the smooth surface of the inside block laid bare, where the limestone plate fell off -  the jagged dark break line in the facing against the smooth unbroken block - the ledge, which looks chiseled into the pillar itself, on which the now broken plate had rested.

Table 18   (click image)
Abydos ceiling

The glyphs are engraved on stone plates encasing solid stone block, except where the plate broke away. This reveals an option the ancient Egyptians had.  Being the great stone masons that they were, wouldn’t it be better to: Strip the Old Facing, and replace it with a brand new one?

Using a ’tabula rasa’ should be far superior to hocus-pocus  plaster.  If the objective was to get rid of the old writing, so as not to play games with the new writing’s future, the technique of using new outside plates of limestone would have been most efficient in accomplishing this goal.

The engraving work on the plates was most likely done on the ground, then elevated into position on the supporting ledge. For any subsequent changes, I believe, the facing plate could be brought back to the ground, and resanded, or replaced by a new limestone plate. This could explain the fine quality of the glyphs.

Some obvious disadvantages of plaster

The inscription on the stone plate was important, how could it have been sloppily patched over with plaster?

  • For one, plaster would be hard to match exactly to the stone’s texture and shade of color. There would always be some shadows of the old writing haunting the new.

  • Two, the plaster filling is bound to react differently to changes in moisture and temperature than the solid stone.  It should become loose in its long, narrow, and shallow bed fairly fast, and fall out during earthquakes.

  • Three, whoever was to alter the text had to become a willy nilly composer of the form created out of the old and the new texts seen together. This person had to be aware of the combined shapes lurking on the limestone with the plaster absent, unless we presume him senseless. Therefore, it is likely that the designer-composer would strive to give these shapes some meaning. It is not my fault, this meaning  translates into an array of high-tech machines.

  • Four, how could the solid, perfectionist Egyptian artisans and architects be so naive as to rely on future help for the preservation of the usurping  texts over the old ones?

  • Lastly,  the work on the temple was still in progress in Ramses’ time. There were materials and artisans available on site to do a solid job, no need for the monkey business of the palimpsest unless the palimpsest was deliberate.

Most all of Katherine’s colleagues seem oblivious to these options. Martin Stower thought that the blocks were solid, as he wrote that the ’structural integrity’ of the blocks holding up the weight of the massive roof might have been compromised if the Egyptians had exercised yet another option, I had mentioned in our discussion:

Completely Rubbing Out the fairly shallow "Old Glyphs"

Doing a solid job on the inscriptions would not require much extra effort, considering all the work that had to be done - like scaffolding.

Using sanded or resanded stone instead of plaster was the only permanent solution, and the Egyptians knew it. That’s how things were done throughout the temple with one alleged exception - our Abydos Helicopter scene.  This strains my credulity.

Table 19
 Lubomir Janku analysis

> There is a graphic representation of the original titulary, showing how
> it was rendered a certain way, and then, by visual overlay, how the
> successive titulary was imposed into the older one.  This representation
> is at the website as well.

That representation by Janku itself admits to a few question marks still remaining. However, I could see more problems, after looking closely:

1) Not some, but mostly all the plaster has fallen out. - This is attested to by the smooth and regular edges of the glyphs as they are now.
2) The glyphs are a finished, or final product.. - This is then, how the Egyptians had seen it too - three or four objects in a close knit formation looking like a helicopter, and a gunboat (?), and a submarine (?), and a (?) when seen left to right. These are the final images. They are perfectly composed.

Table 20
abydos helicopter

3) You do say yourself that the new glyphs were "imposed" upon the old ones. The whole must have been planned and tried on the ground. So, there is no way that the Egyptians did not see what we see today.

They knew,  that’s how the final glyphs will inevitably end up looking, after all the plaster falls off.

Table 21

What bird?

There is a bird perching on the (semi)circle. Janku believes it is a chick. So, we overlay the chick over the stone shape, and it fits fairly well, in the head area especially.  However, when we overlay another sign of a bird over the area - it fits even better! It fits everything perfectly except for the top of the head. This sign stands for negativity.



hieroglyph ur



Do the below birds look like birds? If so, they also fit the ’Rorschach blot’.


The Hand    

the hieroglyph d doesn't  fit the glyph


When we scale the width of a typical hand hieroglyph up to the width of the glyph, the two become completely disproportional in their length.

Janku’s interpretation of the glyph’s origin becomes most doubtful.  Let’s remember that hieroglyphs are generally very realistic representations  - whereas, the alleged hand glyph is highly unorthodox, and unrealistic. It must be a record setter for distortion.


K hieroglyph k    
Katherine said: 

It was decided in antiquity to replace the five-fold royal titulary of Seti I with that of his son and successor, Ramesses II.


In the photos, we clearly see:

"Who repulses the Nine Bows,"
which figures in some of the Two-Ladies names of Seti I,  replaced by

"Who protects Egypt and overthrows the foreign countries,"
a Two-Ladies name of Ramesses II.


Chronological Problems of  Janku’s Interpretation

Which set of hieroglyphs is older? Cyan or red? Remember, this Golden Section construction starts with the red (semi)circle, so all the reds (versions A and B above) should be older. Then the newer glyphs (C above) would be akin to solving the puzzle of the older ones.

If the (semi)circle were read as part of the newer inscription - and I do seem to recall reading somewhere that the later foreign countries’ is symbolized by the triangles in the inscription, red like the (semi)circle - we would have good reasons to view the fact with suspicion, because the (semi)circle, or at least its diameter line, had to be there at the very start, otherwise this Golden Section would have been impossible. You have to have something to start the section with. It’s as simple as that.

If the red glyphs are older, and the cyan triangles newer, then the columns should not be in the red set of glyphs, because the red set’s vertical position has to be set by the cyan triangles. Either way, something is wrong here. Janku’s interpretation does not agree with the geometrical procedures behind the inscription.  Of course, Janku is not a professional Egyptologist, although he gave it a valiant try.  I’ll have to ask Katherine for her opinion on sci.archy:)

Photo: Lumir G. Janku

Quote from an article by Lumir G. Janku

There is one aspect of the inscription which is puzzling. The temple in Abydos (or Abdjou, as the location was called by Egyptians), is quite a remarkable edifice,  specially as far as the quality of glyphs is concerned. They are all very precise and as far as I can judge, there’s no trace of sloppy workmanship anywhere in the temple, bare the above inscription.

!!! This really deserves an exclamation mark. How wrong can you get? I have proven the exact opposite. The inscription is a remarkably accurate exercise on the Golden Section...

Janku also wrote:

The temple was build by Seti I and finished by his son, Ramses II, during an era of classical revival. The obvious corrections on the inscription in question are thus seemingly out of place. But without the translation of the inscription, it is difficult to propose a hypothesis for why the original inscription was changed, apparently twice

This must be why we don’t see any Egyptologists commit to graphical explanation of the glyphs, preferably against the background of a high resolution photograph.  They sense that something is wrong.
Jiri Mruzek - Vancouver, BC

Send mail to:   JiriMruzek (at) Shaw(dot)ca