A series of geometric constructions seem reasonably to account for the locations of chambers and passages within Khufu. It will be seen that root two is an essential element.

Legon put forward an anaysis defining the positions of the King's and Queen's chambers -



- pyramid height 280, divided by root two = 198 = floor of King's Chamber below apex, or 82 above base.
Queen's Chamber floor is half this 41.
Axis of Queen's chamber on the centreline of the pyramid.
South wall of King's chamber from north base 246 = 6 X 41.
Descending passage south end horizontally to north base 205 = 5 X 41.

Meanwhile Gantenbrink explored the KC shafts and discovered a fascinating interplay on the factors 7 and 11 defining the pyramid profile -



- KC south shaft implies a square 44 below base. The black rectangle has dimensions 280 X 198, reducing to 99/70, again root two.

As to the Grand Gallery, its north wall is 79 horizontally from centre. A simple geometric construction on the diagonal of the double square intersects pyramid side 79 above base (or 3 below KC floor 82) and the total horizontal length of gallery (including the Great Step) is 82 -



280 - 79 = 201 = 67 + 134 - the former locates the junction of the descending and ascending passages. (These numbers are met elsewhere at Giza - for example Khafre granite base is 134 above Butler's reference datum, or 'sea level').

Looking at the passages in more detail, whereas the descending passage is laid out fairly precisely on the diagonal of the double square, the upper passages have slightly different slopes - it is evident the design has been 'tweaked'. Legon proposed that the upper passages were laid out using ratios of height to slope - for the Grand Gallery 39/88 and ascending passage 33/75, so total height = 72. (And height of entrance over passage junction is 24 = 72/3). I notice also that the mean of the passage lines intersects the south wall of the KC at ceiling height so the line of the upper passages to this point measures 192 = 8 X 24 -



Others have put forward yet more complex schemes for the details of Khufu design (the exact intended height of the KC and the proportions of the Antechamber for example) but uncertainties (due to possible building errors or subsidence) make such propositions difficult to assess. But the overall design criteria seem plain enough.

Many have commented on the possible significance of the particularly-thick 35th course. Petrie and Goyon independently measured the top of this course as 57.6 above base - level 57.7 divides the pyramid into two equal volumes.
The bottom of this course is 55 above pavement level. The line of the KC shaft intersects pyramid axis 55 cubits above base.

If we now consider the pyramid passages with reference to Butler's proposition (408 from sea level to Khafre apex) we find that the line of the descending passage intersects sea level 99 south of centre, while the line of the upper passages (their mean slope) intersects sea level at 396 = 4 X 99 north of centre -



- it will be seen that level 55 above pyramid base divides total height in the ratio 169/239, or root two. This was probably derived from the simple series - later attributed to Theon of Smyrna - which converges on root two at infinity -

1 3 7 17 41 99 239 577 1393 ...
1 2 5 12 29 70 169 408 985 ...

- this may be derived in a number of ways, most simply by the addition of squares -





Using this as a basis we may now examine the putative trans-generational plan.