Building the Great Pyramid by Levering. A Mathematical Model

Abstract

A review of the extensive literature on the building of the Egyptian pyramids reveals that so far this problem has not been treated in a systematic, quantitative way. The present study aims at filling this gap by means of an integrated mathematical model, taking into account the interaction between various activities involved, such as quarrying, transportation and building. I focus my attention on the largest pyramid, the one built by Khufu.

The model simulates an efficient project co-ordination by balancing supply and demand of the building material, with all activities related to the growth of the pyramid and assuming a constant total workforce. This makes it possible to determine the effect of different building methods and of the productivity of the workers on the workforce required for the various tasks. In this paper only one building method has been considered, namely levering. Calculations have been carried out for two sets of input data, indicated as base case and maximum case.

Assuming a project duration of 20 years with 2624 working hours per year, the workforce for this building method is estimated to range from 4 000 to 10 000 men directly involved in the building of the pyramid and the supply of the necessary material.