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## The entrance passage

The geometry of the entrance passage is based on the creation of an ellipse inside the structure that has already been developed on the previous pages and its geometry relates directly to the upper shafts of the building. The ellipse that is highlighted on the drawing has the two faces of the pyramid as tangent lines, and the face tangent points on this ellipse are exactly the same points as the upper shaft exit points that were created in a completely different manner on the previous page (page B3). The algebraic proof of this fact is contained in this PDF file which I wrote when I was at an early stage in the analysis of the building's architecture in 2002.

This ellipse is formed in a specific manner which will become important in the more advanced section of this work - it is defined by the following four bounding lines (which will be highlighted as you mouse over the descriptions)

• The base of the pyramid
• The southern face
• The line connecting the principal tangent points
• The northern face

An analysis of the method used in the formation of this geometry is described in an article by Chris Jones and I based the programming code required to create the 'entrance ellipse' on his wonderfully useful analysis.

• Once the ellipse is created its major and minor diameters are defined.
• The final part of the construction is easier to visualise than it is to describe. The major and minor diameters of the ellipse are formed into a 'T' shape and pivoted from the 'top' of the ellipse until the north end of the minor axis is coincidental with the northern face line of the pyramid.

Bring up the object information panel for the entrance passage by clicking here and you can see that the angle of the geometric line varies from Petrie's surveyed value of the passage by 0° 4' 31.43". The positioning of the geometric line appears to be slightly lower than the entrance passage as you can see by zooming in on it , and the reason for this discrepancy is identified in the more advanced section of this work.

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Last edited: 3rd July 2019
Last code/graphics edit: 29th March 2021