Geometry of the great Pyramid (cont.)
By Nick Kollerstrom Phd
Half of the Base Area
The King's chamber, as William Petrie pointed out in 1883, 'was placed at the height in the Great Pyramid at which the area of the horizontal section is equal to one-half the area of the base'. (9) That height implies use of the square root of two - how exact was that?
In the figure,
√2 = AB / BC
Where the height of the pyramid AB is 280 cubits = 146.64 metres (its theoretical height, as if it still had the capstone), and the height of the floor of the King's Chamber floor AC is 82.09 cubits = 42.99 metres (10). That equation would then be exact to 99.8%. That has to be intentional. Experts have surmised that the King's Chamber floor height was intended to be just 82 cubits, (11) which would make this ratio exact to four figures! Thus the scale chosen for the building made the units of measure used chime in with this 'irrational' ratio, 1.414...
The Victorian astronomer Richard Proctor wrote a book proposing that the Great Pyramid was first only half-built, up as far as what became the King's Chamber floor. So, this has been regarded as quite an important juncture. (It was then used as an observatory, he argued). He did not comment upon its exact mathematical placement. The yellow square in the diagram represents this floor at the King's Chamber level, and this may be a good visual method of 'seeing' the root two relationship, whereby it is half the area of the outer square, which represents the base. (12)
* Half of an Angle
The Ascending Passage leading up to the 'King's Chamber' has a slope angle of 26° 2' (13). This angle bisects that of the Great Pyramid's outer slope angle, within arcminutes. Therefore, this slope angle represents a one-fourteenth division of a circle. This mysteriously re-emphasises the number seven, within the Great Pyramid. The lovely star-heptagon (see figure) has this angle at its corners.
If those who built this pyramid were able to bisect a one-seventh angle within arcminutes, that would tend to indicate their use of angular measure.