Khufu, a giant in desert

By definition, a pyramid is a great monument on a rectangular base with four triangular faces. For historians, it is a sepulcher, a royal tomb of ancient Egypt. For all humanity, the three pyramids of Khufu (Cheops), Chephren and Mykerinos, that stand on the Giza plateau at the gates of Cairo in Egypt, are both a treasure and a mystery.

We do know that these pyramids were designed to house the remains of three pharaohs, nearly three thousand years before the Common Era. The most impressive of these colossal stone structures, the Pyramid of Khufu, has been contemplated and photographed innumerable times, but its heart still remains a mystery, evoking tales of fabulous treasures and legendary curses.

The last of the Seven Wonders of the World

The Great Pyramid is said to be the last of the Seven Wonders of the Ancient World, the only one that has to this day survived the follies of humanity and the violence of the elements. Standing 146 m high, it was the tallest monument in history until the Eiffel Tower was built. And yet we know neither how it was built nor how long it took to build by men who had no knowledge of iron, or the wheel or pulleys. And we have no idea what astonishing secrets may still lie hidden within its walls of stone.

A witness to 4,500 years of history, the Pyramid of Khufu has seen many of the world's most powerful people come and go - people who have admired the boundlessness of all it symbolizes, who have dreamt of infinite conquests or of immortality. Ephemeral potentates or passing travelers over the centuries have walked on its stones. Some, intoxicated with the extraordinary feeling of the place, have said that such excess could not have been made by man and that only an alien civilization from far away could have produced such a marvel.

The theory in images

The summit is reached. Finishing work is about to start, from the top down. The recesses are being filled in, the last roughly cut facing blocks are being surfaced.

5th year of the reign

The two-lane external ramp is used to supply massive amounts of stone for the construction of the first courses of the pyramid. The ramp remains in use during the building of the first 43 meters of the edifice.

14th year of the reign

The external ramp has reached its maximum level. The interior ramp already has three flights of stairs, but because of its geometry, it does not interfere with supply to the site. The ceiling rafters in the King's Chamber are raised to this level by means of the counterweight operating in the Great Gallery.

15th year of the reign

The granite rafters that form the King's Chamber are raised by means of the counterweight and are positioned definitively in each of the ceilings. Floor by floor, the King's Chamber is constructed using the counterweight, which considerably reduces the number of workers required.

19th year of the reign

The King's Chamber has been finished for some time. The pyramid is being constructed with materials recovered from the demolition of the external ramp. The blocks are now transported to their final positions via the internal ramp .

Stone blocks rotation system

In particular, the scientific 3D made it possible to validate the theory about the how the stone blocks were rotated on the recessed platforms, taking into account the mechanical aspects as well as the human factor. Using this system, rotation of a block would take approximately one minute.

20th year of the reign

The summit is reached. Finishing work is about to start, from the top down. The recesses are being filled in, the outside gangway is being dismantled and the last roughly cut facing blocks are being surfaced.

23rd year of the reign

The funeral of Khufu has taken place. The King's mummy now lies in the sarcophagus in his Chamber. Construction work had been completed at the end of the 21st year of his reign with the filling in of the recesses, the dismantling of the outside gangway and the surfacing of the last blocks of stone.

Scientific 3D simulation in support of the theory

Modeling: the vital first stage

Modeling takes place in three stages. The aim is to obtain a virtual double of the pyramid that will behave identically to the real pyramid with regard to the laws of physics.

Geometric modeling:

This involves recreating the pyramid in 3 dimensions, with all its available measurements and with the complete layout of the interior corridors and funeral chambers. The geometrical model can then be manipulated at will: it can be turned in any direction and examined from any angle, cross sections can be defined, the layout of the internal corridors and funeral chambers can be visualized transparently , etc. Such manipulations of the 3D model, which are utterly impossible on the real pyramid, allow a vast range of observations to be carried out very rapidly. In particular, the 3D model enabled Jean-Pierre Houdin to acquire a deeper understanding of the monument and to establish relations between certain measurements .(The distance between any two points on the model can be obtained instantaneously). The ability to compare certain gradients with the length of the different internal structures of the pyramid provided the architect with both insights and evidence for the development of his theory.

Physical modeling:

As the geometrical model cannot be used to simulate events, physical modeling is used to enrich the geometry with the physical characteristics of the materials used in the pyramid. Using Dassault Systèmes’ software which integrates laws of physics, it was possible to simulate the behavior of the virtual pyramid as if it were the real thing, for example the resistance of the materials or the effect of the weight of the pyramid on itself etc. It was therefore easy to identify the location of limestone or granite elements, but also to get their physical parameters (density, elasticity etc.). This data is then integrated to the geometrical model, which thus increasingly resembles the real thing.

Functional modeling:

Jean-Pierre Houdin’s theory integrates a certain number of mechanical systems such as sleds or carriages running on wooden roller beds. The characteristics and disparities of such systems are well known in mechanics (e.g. the friction generated by a skid sliding on a rail is not the same as that of a load being moved on a roller). These characteristics were integrated into the 3D model in order to obtain a total model with the same dimensions, and the same physical and functional parameters, as the real pyramid.

Simulation

Once the 3D model had been completed, the full range of Dassault Systèmes software solutions was used to simulate the construction processes suggested by Jean-Pierre Houdin’s theory and check their validity and coherence. These software applications are normally used by industrialists to simulate every aspect of the production process, from plant design to the operation of the production chain (location and programming of robots, verification of work station ergonomics by means of virtual dummies, etc.) These tools were then applied to the construction hypothesis advanced by Jean-Pierre Houdin. They revealed no incoherence or impossibility in the theory. Better still, the complete simulation of the construction processes validated the theory by allowing the duration of the building work to be estimated at around twenty years (the length of the reign of Khufu). A critical aspect of the Dassault Systèmes software used was that it took into account the vitally important parameter of time. Today, manufacturers are desperate to shorten what is known as ‘the cycle time’. Products must be designed and produced more and more quickly in order to get products to the market before the competition. Dassault Systèmes software facilitates the optimization of tasks at all levels by integrating this vital time factor.From the virtual to the real. Without replacing field-developed observations, analysis of the 3D model and simulation of its behavior can be used to prepare observation missions more effectively. Any scientific approach always comprises three stages, always in the same order:

• Intuition, leading to the development of theory: ‘the pyramid was constructed from the inside’
• Painstaking demonstration of the theory
• Experimental proof

3D modeling and simulation had provided the demonstration; now it was time to test the theory on the ground and verify the presence of the internal ramp experimentally. At this stage, the 3D model would still be useful in helping in the positioning of detection and measurement devices in order to obtain results under the best conditions without damaging the monument.

Real time 3D

Real time 3D consists of displaying images of an environment on a screen in three dimensions while adding to the sense of depth the possibility of interacting in real time. As in a 3D video game, the user is free to move about at will and can interact virtually with the 3D objects that surround him. Real-time 3D thus differs from the 3D normally used in animated movies where everything the spectator sees is pre-calculated and must be watched passively. The spectator of a normal 3D animated movie cannot, for example, interact with the script or change his viewpoint. The quality of display of real-time 3D depends on the power of the hardware and the 3D graphic boards implemented. These boards are increasingly widespread and are evolving rapidly, so the quality of both the graphics and the rendering of real-time 3D environments is likely to improve rapidly to rival that of the pre-ordained traditional 3D of the animation studios.

The birth of a theory, one man's intuition
By Jean-Pierre Houdin

I was born in Paris in 1951, but I grew up in Abidjan, in Africa, where my father was the director of a construction company. As a small boy, I spent my spare time on construction sites while my mother, who was a doctor, cared for her patients in a bush dispensary. My interest in building and construction no doubt grew out of this first period of my life. Back in Paris, after the baccalauréat, I naturally enrolled in the Ecole des Beaux-Arts, in the architecture section. After obtaining my diploma in 1976, I set up as an independent architect, a profession that I would follow for twenty years. I participated in the construction of a large number of residential and office buildings in and around Paris. At the same time, with my wife Michelle and our friend Laurent, I opened an avant-garde art gallery cum salon (“Les Enfants Gâtés”), which over a period of ten years supported scores of young artists, and which became a centre for the arts in Paris at the turn of the 1980s and 1990s. In 1996, Michelle convinced me to move on and we decided to take a year out in New York! I went with no specific plans but with a thousand ideas in mind: I was eager to start learning again and excited to be able to work in freedom, without constraints but with passion. It was the perfect moment for such an approach, because the 1990s saw the remarkable development of the Internet. This new communications medium presented a universe of new perspectives for every field of activity, including for my work . I learned how to use the Internet and how to use the first digital design tools. I got involved in website design , first in New York and then in France when I returned to Paris in 1998, with a new career and a world of new experience.

On January 2, 1999, while I was once again away in New York, my father, a retired engineer, saw a television program about the construction of the pyramids presented by François de Closets. With his civil engineer’s eye he took a critical look at theories in vogue at that time. He thought they just didn’t stand up to logic. And then suddenly an idea dawned: what if the pyramids had been built from within – from the inside out as it were? This was a revolutionary concept that swept away all the other hypotheses that had been put forward until then. As an architect with experience in three-dimensional graphics, I was called in to assist him in his research. During 2000, we met with members of the team who, in 1986, had worked on the mystery of the Pyramid of Khufu under the aegis of the EDF Foundationj. They showed us plans on which we discovered a construction anomaly, a detail in the drawings that none of the hypotheses could account for. This anomaly, baptized “the spiral structure”, looked exactly like a ramp built inside the pyramid ,which could have played a part in its construction! "This revolutionary idea swept away all the other hypotheses put forward up to now. "

In 2003, my father created the Association of the Construction of the Great Pyramid (ACGP) in order to promote the project. This association enabled me to meet a number of experts.
In 2005, Dassault Systèmes welcomed me enthusiastically into its brand new sponsorship program “Passion for Innovation”. Together, we decided to examine the theory in the light of Dassault Systèmes’ industrial and scientific 3D solutions. I would finally be able to analyze and confirm my theory in the virtual 3D world, which enables today’s industrial corporations to produce in the real world. Using these software applications to reconstitute the site of this gigantic construction in three dimensions allowed us to test in real-time whether such an approach was plausible.
We would be able to see whether the human and material organization that the theory implied was optimal and coherent and whether it conformed to the unchanging laws of physics and mechanics. Hundreds of calculations and algorithms were used to gauge the soundness of our premise, to check whether our models and hypotheses defied the laws of gravity or operated contrary to the forces and the materials being manipulated. Simulations were used to back up and enrich the theory, continually inciting me to ask new questions to ensure that no doubt would remain concerning the mystery of the construction of the Great Pyramid.

But it was not enough just to confirm the theory. We had to explain it and communicate it: we had to share the secret of the construction of the sole survivor of the Seven Wonders of the World with the public. With Dassault Systèmes, we decided to push the challenge even further by using 3D technology as a teaching medium and to propose the first interactive voyage through time in three dimensions, on the giant screen of the Géode . This would be a world premiere that would precede the field-based scientific exploration that would enable us to probe the actual pyramid in order to find proof to confirm the existence of the internal ramp.