345 - and all that...

Here is a very simple explanation of how easy it can be to allow oneself to be led astray by apparent alignments.

I have used Mick Saunders' octagonal construction as a base because we know it to be 'accurate'...

Drawing 'a'
I have created a 3:4:5 Right Triangle (ABC) whose base is the same as the distance between the West face of G1 and the West face of G3.

This has been aligned with the South West corner of G3 at 'A'.

It will be seen that the upper point of the triangle (C) appears to make a neat alignment with the South West corner of G1...

Additionally the lower right corner (B) aligns with the outer octagon.

Drawing 'b'
Here I have slid the Triangle upwards (DEF) so that its base (DE) is aligned with the apex of G3, and the lower left point (D) is still aligned with the West face of G3.

It will now be seen that the diagonal (DF) appears to pass through the apex of G2...

Drawing 'c'
Here the Triangle has been moved further upwards (GHJ) so that its base (GH) is aligned with the North face of G3, and the lower left point (G) is aligned with the North West corner of G3.

It will be seen that the upper point (J) appears to align with the apex of G1...

The Test of these 'alignments' is actually very simple. The dimension AG is the same as CJ. If C and J are to be accurately aligned as stated then the North/South dimension of the side of G3 must be half the North/South dimension of the side of G1...

Just using Flinders Petrie's survey figures the side of G3 is given as 4153.6" - and half of the side of G1 is given as 4534.4". Thus it is not possible for my apparent alignments to be correct but, without survey data and accurate drawings, it is very easy to be 'fooled' into believing one's eyes.

Drawings such as these are also subject to the computer programme used - and the expertise of the operator. If you employ a 'vector' drawing programme you can create very accurate drawings which can be easily enlarged without losing the integrity of the lines. CAD programmes are basically much the same thing, but considerably more accurate.
However 'bitmap' painting type programmes are highly dangerous because, although they can be made to look very pretty, they are anything but accurate. And if you attempt to enlarge such a drawing you will enlarge each and every pixel of the lines and it will be impossible to tell whether any alignments exist or not.

Nevertheless many geometers exhibiting on the internet are using these 'bitmap' programmes and, regardless of the authenticity of their work, it is impossible for them to endeavour to prove their findings.

Drawing 'd'
Just to show this more clearly I have enlarged the relevant section of the above drawings just 200%, showing the South West corner of G1 and the North East corner of G2.

You will see that in reality neither C nor J are accurate alignments - and the diagonal DF does not pass through the apex of G2...
Back to the drawing board - except that many people stop right here... and proclaim their discoveries.

Note that I have also made the lines thinner, removed the dashes, and also removed the coloured fills. All this helps to provide a clearer picture...

Drawing 'e'
At the risk of labouring the point (but there do seem to be many people who do not understand this problem) I have taken the same section of drawing 'c' above and converted (rasterised) it to a 'bitmap' drawing and enlarged it by 200% as in drawing 'd'.

I hope you will agree that it is impossible to have any real idea of what aligns with what - and even if an alignment is accurate this type of drawing can never be used to 'prove' it.

It is also impossible to measure 'the gap' and give any indication of the percentage error.

NB: Although it might be argued that better quality 'bitmap' images than this one can be created, most of those that I have come across on the web are the same as this one without even being enlarged - and even the best 'bitmap' image is no substitute for an accurate 'vector' image.

Conclusion
Please let me confirm that I am quite convinced that the use of what we now call 'sacred geometry' was employed when laying out the ground plan (or plans) on the Giza Plateau - and elsewhere in the ancient world.

However I cannot accept that all of the possible alignments that have been (and will be) found at this site are anywhere near accurate enough to be taken seriously. Far too many 'discoverers' use expressions like, "It neally crosses..." - "It passes close to..." - "It is within the thickness of the line..." - and "It seems to align with...".

None of this is good science and none of it will help us get even close to learning what the Ancient Egyptians actually did when designing their Grand Plan.

NB:
See also A Cautionary Tale to understand why even accurate alignments cannot be automatically assumed as being the result of the intentions of the Ancient Egyptians.

Nobody said that this search was going to be easy...

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