The "Real" Complete Pyramids

Fixing the glaring geometric errors in Egyptology that have been ignored for far too long

Please note that all quick comments and images in this presentation have been graciously allowed to be posted by Jon Bosworth, who’s images of Egypt are simply legendary ! Please be reminded that they are copyrighted to him and if you want to use them you must contact him . Here is his home site:  Home site of Jon Bosworth

In this presentation I will show that almost all of the measurements, save those we have studied at Giza, are totally in error and that little or no thought has gone into the publication of this data. As a simple exercise I decided to check one of The 12th dynasty pyramids and found, much to my surprise, that the height, base and slope angle given in the publication, The Complete Pyramids by Mark Lehner, did not check with geometry and trigonometry and that it appeared no one cared. Even though some of the bases and heights may have been impossible to measure, once a value had been assigned to them the slope angle became fixed. For example in a 3, 4 and 5 triangle the slope angle of the 3 by 4 angle side will always be .75 or 53.13 degrees. This is a given so if any of the pyramids had these dimensions then the slope, if it could not be measured had to equal 53.13 and if we knew the slope and the base accurately then the height would have been 1.3333 (.75 reciprocal) times the base. This is basic geometry yet as I started studying the pyramids I found that almost all had been erroneously listed in a publication that many had referred to as being the pillar of pyramid study.  The only conclusion I could come to was that either he did not know simple geometry or that he simply didn’t care. A third darker possibility was that he was deliberately hiding and suppressing the data. I will let you be the judge.

In the beginning ...

The Step Pyramid of King Djoser


Image supplied and copyright Jon Bosworth

The step pyramid of King Djoser sets the mood for the whole Saqqara necropolis. Djoser was the 1st king of the 3rd dynasty and ruled Egypt for some 20 years. His Horus name is Netjerykhet Djoser. The step pyramid bears witness the a series of enlargements. The structure was started as a masataba and enlarged twice. It was further enlarged to a 4 step pyramid and finally to its current 6 step shape. What we see today is mostly thanks to the 70 years of work by Egyptologist Jean-Philippe Lauer. Originally the pyramid was encased in fine Tura white limestone, some blocks still remain in situ on the east side.

Pharaoh: Djoser
Location: Saqqara
Dynasty: 3
Base in meters: 121 x 109
Height in meters: 60
Slope: NOT GIVEN
Volume in cubic meters: 330,400


According to this we would have two slope angles.

The first angle would be (121 / 2) / 60

= 60.5 / 60

= 45.238 degrees

If base was 120 or height was 60.5 we would have a perfect 45 degree angle. This would indeed make geometric sense for "the first pyramid" as this is the fundamental and primary angle and basic triangle in geometry. 45 by 45 by 90

The second angle would yield (109 / 2 ) / 60

= 54.5 / 60

= 47.75 degrees

OR

= 54.5 / 60.5

= 47.987 degrees

Not exactly sure what this angle reveals but I think it is very interesting that the pyramid that all claim is the first of The Third Dynasty is built to the fundamental and basic and simplest of the right angled triangle. A 90 degree angle with their two 45 degrees angle.

Here is a beautiful image taken by Jon: [egyptphoto.ncf.ca] that appears to show 6 levels of 10 meters each.


Image supplied and copyright Jon Bosworth

And 10 meters = 19.0949 cubits

.................. or ...................

60 (the height in case you have forgotten) / Pi

Another interesting development ..

The Step Pyramid was added on to but nowhere have I ever read a description of why it was added on to. I wonder if any Egyptolgist has ever given it a second thought but it leads to some interesting geometry and mathematics.

First here is an image of the two large parts of The Step Pyramid


[www.touregypt.net]

If the original size of The Step Pyramid was 120 x 120 x 60 then we would have a volume of 864000 cubic meters.

Length of Mars year in Earth days is 686.98

Half of this yields us 343.49. Divide this by a hundred and we get 3.4349

Now if we divide 864,000 cubic meters by 3.4349 we get 251535.70700748202276631051850127

If we allow 40 meters for the height then the base becomes ...

Square root of 251535.70700748202276631051850127 / 40

Sq rt of = 6288.3926751870505691577629625317 = 79.299386348111487571771080189072

(Please note here: 6288.392675 divided by 2 = 3144.1963376 which is 1000 times Pi to within 0.002
If we want Pi exactly we would need a base of 119.95. This would be:
3141.5926535897932384626433832795 x 2 = 6283.185307179586476925286766559
6283.185307179586476925286766559 x 40 = 251327.41228718345907701147066236
251327.41228718345907701147066236 x 3.4349 = 863284.52846524646358362670057814
863284.52846524646358362670057814 / 60 =14388.075474420774393060445009636
Square root of 14388.075474420774393060445009636 is
119.05 meters )

However to make it jive with our 45 degree angle it needs to be ...

79.5322 by 39.7661 = 251535.7070074820227663105185012

So the old pyramid inside was probably very close to 79.5322 by 39.7661

On the other hand if we allow the hidden part to equal 80 by 40 (256000 cubic meters) then the outer one becomes (256000 x 3.4349 = 879334.4) 60 height by 121.06 base

All to within 2.4 inches ....

The Perimeter Wall

The Perimeter Wall of the Djoser's complex is one of its best known features. It stood 10.5 meters high and was 1,645 meters long, covering an area of about 15 ha. The longer sides of the wall faced the East and the West. It was composed of a thick inner core of roughly laid masonry, encased entirely on the outside and partially on the inside with fine limestone. ...


1,645 meters long = 65306.5 inches = 3141.1246356145296125497954622955 cubits

However

If we start with 3141.5926535897932384626433832795 or 1000 x's Pi we get ...

3141.5926535897932384626433832795 x's 20.618033988749894848204586834366 = 64773.464110521331346599733295525.

64773.464110521331346599733295525 / 39.3701 = 1645.2450999748878297642051530355 meters.

Close to 1000 times Pi to within 9.65 inches. Hmmmm ...

Pi again ...

While the wall is 20 cubits high

According to Lauer, there was an 0.524 m. cubit used at Saqqarah: Lauer, J.-p., "Etude sur quelques monuments de la IIIe dynastie (Pyramide a degres de Saqqarah)", Annales du Service des Antiquites 31, 1931: 49-64; 59. According to his survey, the perimeter measured 3,136 cubits.

... King Djoser's Step Pyramid & it's Perimeter enclosure wall. Built during the III Dynasty (2727-2655 BC). The model is a faithful attempt to reconstruct the temple to scale using ancient Egyptian measurements of royal cubits (RC). 1 Royal Cubit = 0.524 mtr. / 52.4 cm. The Perimeter Wall, is one of the best known features of King Djoser's complex known in the world. It stood 10.48 meters (20 royal cubits) and was 1,655.884 mtr. (about 3160 rc.) long, covering an area of about 15 ha. The longer sides of the wall faced the East and the West. The Step Pyramid, rose to a height of about 62.88 mtr. (120 rc.) with a ground plan measuring 125.76 mtr. (240 rc.) by 110.04 mtr. (210 rc.), with an outer casing of fine Tura limestone. Imhotep, who's name means "the one that comes in peace" was the world's first named architect who built Egypt's first pyramid (king Djoser step pyramid), is often recognized as the world's first doctor, a priest,. scribe, sage, poet, astrologer, and a vizier and chief minister. ...

Who has the definitive measurement on this.

Once again it appears we are all over the map on these measurements. Strange how Egyptology does not think it is important to get the exact measurements and set the standard sizes for these pyramids and enclosure walls.