Geometry
Plentiful documentation mentions a four sides pyramid of 230.30 m length and 146.36 m height. The sides slope is in a ratio of the vertical on the horizontal one of 14:11, so an angle of 51°51' 33''; the angle could hypothetically have been represented in a ratio 5:4, so an angle of 51°20' 24'' for a theoretical height of 143.75 m, 2.61 m less than what is currently assumed.
For estimation purpose, supposing that a block measures one cubic meter (1 m3), one needed approximately 3 000 000 blocks, including a loss of 30%, weighing on average 2,5 metric tons (t) to build the pyramid; certain blocks could however weigh up to 60 t. Actually, the bottom lines have until approximately 1.5 m height and the number of lines is about 180.
At the construction time, the center on each side was bent towards the interior of approximately 60 cm at the base to be null at the top, thus creating two plans separated by a valley, the apothem. The plans on the same side are slightly more abrupt than only one continuous plan; the apothem has the same continuous angle from bottom to top 51°59' 30''. This comes down saying that the facing blocks, corner and valley have all the same shape for their specific use; these three typical shapes will remain the models for the twenties and a few years of construction.
Although many speculations surround the dimensions of the pyramidion, our interest is limited to its approximate size and on two other aspects. What was its structure, granit, limestone, electrum, or limestone covered with electrum? What was its shape, pyramidal square, conical, pointed or truncated? Was-it a square base bevelled pyramidion with its perimeter to be used as anchoring for an electrum covering. A pyramidion of 1,5 m wide by 1 m height weighs approximately 2 t with the additional weight of electrum which one estimates at 56 kg/mm. If the apothem was present on all the height of the pyramid, it would be reasonable to find it starting from the bottom of the pyramidion which should be bent down of 6 mm and finish to zero at the top. Was it the case?
Dessin : Dany Lavoie
