The Sun line

On the previous page (page E3) the Sun line was shown to be the defining geometry line from which the architecture of the gabled roof of the main chamber was constructed and you can zoom in on the main chamber area to see that section in more detail.

Connecting the Sun line to the main chamber roof

After the surveying of the internal architecture of the pyramid is corrected on the CAD drawing the vertical center line of the main chamber of the pyramid falls exactly 20 cubits to the south (left) of the vertical Y-axis axis of the geometry (this is one of the features that further confirms that the correction to the surveying is robust). So, because the Sun line has been drawn to the Y-axis of the system, then its upper end must be 20 cubits from the vertical center line of the main chamber.

You will recall from the calibration of the building that the architects have repetitively used the primitive triangle with sides of 200 and 221 units and in the gallery used various sizes of this triangle in various places. The exact same system has been used to define the location of the apex of the main chamber gable, starting from the top end of the Sun line and applying a transformation based on a triangle with sides 20.0 cubits and 22.1 cubits as can be seen by clicking here.

The lower internal apex of the main chamber's gabled roof is positioned by using the triangle construction and the length 'A' on the drawing is the length of the other side of the triangle, which is 9.4027 cubits. The upper apex of the chamber can also be determined because the Sun line is at exactly 1 radian from the vertical, so through trigonometry the length 'B' can be calculated as being 20/Tan(1)-A = 3.4392 cubits.

So the upper apex of the gabled rood is positioned by using two transformations

1. The hypotenuse of the triangle
2. A vertical offset

and this same system is used again in the gallery.