This single, fundamental design principle: 11 : 7 Base to Height Ratio  generates ALL amazing mathematical properties of the Great Pyramid:

• the Golden Ratio Phi=1.618 (the Great Pyramid is a Golden Pyramid: length of the slope side (356) divided by half of the side (440/2 = 220) height is equal to 1.6181818… which is the Golden Ratio Phi
• squaring the circle ratio 1.571 (base/height = 44/28 = 1.571)
• pi=3.14159… (2 x base/height = 2 x 44/28 = 3.14286 which is very close approximation of “pi” = 3.14159…)
• Perimeter of the square base, 4×440=1760, is the same as circumference of the circle with radius = height: 2x ”pi” x height (2x 22/7 x 280=1760)
• The ratio of the perimeter to height of 1760/280 cubits equates to 2x pi
  to an accuracy of better than 0.05%
• Side of the base (440) plus double height (2x 280=560) = 1,000
• Perimeter of the square base is equal 4×440=1760 RC = 0.5 nautical mile = 1/7,200th of the radius length of the earth
• the slop angle 51°.843
• The Pyramid exhibits in the design both pi and by Phi,  given the similarity
  of 2/ sqrt(phi) (2 divided by the square root of Phi) with pi/2 :

• 11/ 7 equal 1.5714
• 2/ sqrt(89/55) equal 1.5722
• 2/ sqrt(Phi) equal 1.5723
• pi/ 2 equal 1.5708

• Royal Cubit = 0.5236 m,  pi – Phi² = 0.5231

1¹ + 2¹ + 3¹ + 4¹ = 10

  1!+2!+3!+4! =33

1 + 2 + 3 + 4 + … + 36 = 666

For penulum with length L= 1 MY = 0.83 m,
the pendulum period T= 1.827 seconds
666/1.827 = 364.5

PS 1 Titus-Bode Law and Pascal’s Triangle

In 1768, Bode published his popular book, “Anleitung zur Kenntnis des gestirnten Himmels” [Instruction for the Knowledge of the Starry Heavens]. In this book, he described an empirical law on planetary distances, originally found by J.D. Titius (1729-96), now called “Bode’s Law” or “Titius-Bode Law”.

The original formula was:

  a = ( n + 4 ) / 10 
where n=0,  3,  6,  12,  24,  48,  96,  192, 384, …

To find the mean distances of the planets, begin with the following simple sequence of numbers:
0     3     6     12     24     48     96     192     384   …
These numbers (after 0) derive from the Pascal’s triangle as the sum of a row added to the sum of the previous row:

Row 1:  2+1=3
Row 2:  4+2=6
Row 3:  8+4=12
Row 4:  16+8=24
Row 5:  32+16=48
Row 6:  64+32=96
Row 7:  128+64=192
Row 8:  256+128=384

Next, add 4 to each number and you will get:
4     7     10     16     28     52     100     196     388
Then divide it by 10:
0.4     0.7     1.0     1.6     2.8     5.2     10.0     19.6     38.8

The resulting sequence is very close to the distribution of mean distances of the planets from the Sun
expressed in Astronomical Units (AU): 

1 AU is approximately the mean Earth–Sun distance equal AU = 149.597 *10⁶ km

All planets (and asteroid belt) fit Titus-Bode Law except for Neptune!

Here is another way to connect Bode’s Law with Pascal’s Triangle
(Source: http://milan.milanovic.org/math/english/titius/titius.html)

The modern formulation of the Titus-Bode law is that the mean distance a of the planet from the Sun in astronomical units ( AU = 149.597 *10⁶ km ) is:

   a = 0.4 + 0.3 x k  

where ”k’=0,1,2,4,8,16,32,64,128 (sequence of powers of two – from Pascal’s Triangle)

PS2 Spiral Solaris

.. For these reasons and from such constituents, four in number, the body of the universe was brought into being, coming into concord by means of proportion, and from these it acquired Amity, so that coming into unity with itself it became indissoluble by any other save him who bound it together. (Timaeus, 31b-32c, Plato’s Cosmology: The Timaeus of Plato, Trans. Francis MacDonald Cornford, Bobbs-Merrill, Indianapolis, 1975:44, emphases supplied)

“The three-fold number is present in all things whatsoever; nor did we ourselves discover this number, but rather nature teaches it to us”  – quotation from Ovid provided by Nicole Oresme in his major work, Le livre du ciel et du monde.

Commentaries of Proclus on the Timeus of Plato:

    The figure of the spiral likewise, is no vain, fortuitous things, but gives completion to the media between bodies that move in right lines, and those that are moved in a circle. For the circle alone, as we have said, is in the inerratic sphere, but the right line in generation. And the spiral is in the planetary region, as having a co-mixture of the periphery and the right line. The motions also according to breadth and according to depth, viz. of the upward and downward, and the oblique motions. Perhaps likewise, the theurgist [Julian] in celebrating time as a spiral form, as both young and old, directed his attention to this, conceiving that the temporal periods, were especially to be known through the motions of the planets. [Trans. Thomas Taylor, Vol. II, Book IV, p.239]

    With these things however, not only Plato as we have observed, but theurgists likewise accord. For they celebrate time as a mundane God, eternal, boundless, young and old, and of a spiral form. And besides this also, as having its essence in eternity, as abiding always the same, and as possessing infinite power. For how could it otherwise comprehend the infinity of apparent time, and circularly lead all things to their former condition, and renovate them, and also recall things which become old through it, to their proper measure, as being at once comprehensive both of things that are moved in a circle, and according to a right line. For a spiral is a thing of this kind; and hence, as I have before observed, time is celebrated by theurgists, as having a spiral form. [trans. Thomas Taylor, Vol. II, Book IV, pp.207-8, emphasis supplied]

Without going into the finer details we may nevertheless take an initial cue from the information provided by Archimedes that :

“the area bounded by the spiral in the first revolution is a sixth part of that added in the second revolution”.

Simply stated, if the first area is 1 (i.e.,unity) then the second area will be 6, the third 12, the fourth 18, and so on, for according to Archimedes:

“generally the areas added in the later revolutions will be multiples of that added in the second revolution according to the successive numbers”,

thus the areas expand by successive multiples of 6.

But what does this have to do with the equiangular period spiral as derived in the previous section which concerns time and successive heliocentric revolutions?

Since the revolutions in the latter also proceed according to a fixed increment, i.e., by the fundamental period constant associated with the equiangular square and the construction of the spiral itself – Phi ²- we can also obtain successive “areas” from the corresponding periods (as “radii”) from the Phi-series planetary framework. And as it so happens, the “areas” pertaining to the planetary positions also expand in a uniform manner – not by 6 as given by Archimedes – but by a constant factor of 6.854101966 (Phi ⁴) instead, and thus 6 may (or may not) be considered a simplified approximation for the latter.

But however one looks at it, the number “6″ is undoubtedly of importance in Pythagorean contexts while a similar weight appears to have been placed – either directly or indirectly – on the numbers 6, 12 and 18 by Plato in the Epinomis, in the Timaeus, and elsewhere. And here we might also recall that with respect to the equiangular period spiral (with notable exceptions) that the heliocentric distances occur at the 60 and 300-degree points, thus a six-fold division is also a feature of the basic configuration.

So what indeed is Archimedes referring to here? One can hardly be certain at this stage, but from what we have seen so far, one might begin to suspect that these seemingly simple operations are neither numerology nor primitive mathematics, but something quite different. It may well be that it is not common practice to treat time in radial form per se, but then again, we are not used to working with such an all-encompassing, complex entity as this particular equiangular spiral either. But if we are not dealing with numerology and elementary mathematics in this context, then what are dealing with? It may be too early to be definitive, but it is beginning to look more and more like highly condensed, competent methodology clothed in disarmingly simple terms.

Source: http://www.spirasolaris.ca/sbb4d2.html