How an Architectural Intention Was Embodied in the Pyramids of Giza: A Relationship Between the Building and Geometry

Today the Pyramids of Giza continue to be a mystery to researchers and admirers of ancient Egyptian architecture. One of these great pyramids, Cheops, is among the Seven Wonders of the World and is renowned for its geometric eccentricities. They were built around 4500 years ago and are located on the western bank of the Nile River in Al-Jizah, Egypt. These buildings took on original construction that was sought after an Egyptian sophistication of a concept called a "mastaba." A mastaba is a term that means "platform." These platforms were built over royal tombs and eventually acquired numerous additions. Several stacked mastabas were incorporated together and tapered to form the pyramid shape. It is believed that this process took place over a 20 year time span. To begin, once the construction site was cleared and prepared, the blocks were transported into place. These blocks however, were made of stone and weigh around 2 tons each. Without the equipment and technology that we have today, one may ponder on how these massive building blocks were transported and set into place. There are several theories describing methods that may have been used such as ramps and counterweights.

Afterlife and respect for deceased pharaohs were important aspects in the Egyptian lifestyle. This was shown in the Pyramids of Giza by the use of various burial chambers, elaborate tombs, and human preservation for each pharaoh. Evidence of the importance of afterlife is provided by researchers' discoveries of artifacts including articles of clothing and various items found in the tombs. It was believed that death was not an important event in life. It was just a transition from one life to another. Egyptians also had to perform many rituals before entering the pyramids. The great importance of these aspects is backed up by the grandeur of the pyramids and the amount of time it must have taken to build them.

It challenges my mind to think of how these great buildings were constructed by the Egyptians so long ago. The use of precise measurements and careful architecture is outstanding for a civilization to practice in that period of time. I felt that I needed to look into these ancient landmarks more deeply and research as much is I could about them. Writing this paper is a good way for me to better appreciate and understand the relationship between building structure and the use of geometry in the ancient Egyptian Pyramids of Giza.

Geometry is probably one of the most important aspects in designing a building. When architects sit down at the drawing board, they must execute their knowledge and style of geometry in order to express their ideas. Architects formulate in their minds what they think a building should look like before it is drawn out. The use of straight edges, measuring tools, and even computers help architects layout their designs very easily today. But around 2500 B.C., what did the architects and project planners use to design such a magnificent building such as a pyramid? The pyramids obviously take on a shape that most people are familiar with. Beginning with a square base, the pyramids have triangular sides which converge together forming a point at the very top of the building. These simple shapes may look average to a normal person but research has shown that they possess much more underlying meaning than one would think.

To give a more in depth, yet still basic description of the Pyramids of Giza, I will describe the Great Pyramid of Khufu, also known as Cheops. When this pyramid was built, it stood approximately 481 feet tall. As time went by, it lost about 30 feet off of the top due to natural weathering processes. At one time, this pyramid was deemed the tallest structure on earth until the 19th century. This pyramid was covered with stone casings which were used to smooth the outer surface. Some of these casings can be seen on the top of Khefre's Pyramid today. The sides of the pyramid are each sloped at an angle of 51 degrees and 51 minutes. Each side also faces one of the four cardinal points of the compass: north, south, east, and west. If a horizontal cross-section of the pyramid was taken, the plan view would reveal a perfect square at any level. These sides were each about 751 feet long at the base. Amazingly accurate for that time period, the average error between side lengths is less than 0.1%. The Cheops used about 2 million blocks of stone for construction. Each one of these stones weighs about two tons a piece. It is said that with the amount of stones in all three pyramids, a 10' x 1' wall could be built around France. The area of the pyramid could contain St. Peter's, the cathedrals of Florence and Milan, Westminster, and St. Paul's combined.

The interior detail of the Cheops will be described to portray what it must have looked like inside. The entrance is located on the north face. There are numerous corridors, galleries, and escape shafts leading to the King's burial chamber and other secret locations. In order to access the King's chamber, one must enter through the Great Gallery and an ascending corridor. This chamber is located in the heart or center of the pyramid. The King's sarcophagus or coffin is made of red granite as well as the interior walls of the chamber room. The stones outlining the doorway have sharp edges that allow for minimal space between each adjoining stone. It is said that a playing card will not even fit between the stones because they are fit so well. This doorway was 10 feet long and 8 feet tall. The sarcophagus is aligned according to the compass directions, similar to the sides of the pyramid. This coffin is only 1 centimeter smaller in dimensions than the doorway to the chamber. These building aspects indicate the intelligence of the ancient Egyptian civilization's builders. A more in depth description of the geometry will be discussed emphasizing this knowledge of how to relate buildings and geometry.

The "royal master builder" was in charge of directing the planning that went into the construction prior to the actual building. This included physical orientation and the layout of the pyramid. These responsibilities ultimately fell on the "vizier" who is the head of all royal works. The first step of the process was to draw up the plans for the pyramid. These steps were completed by specialists on papyrus paper. It seems that the complete plans were not drawn out completely before commencement of construction. As the project went on, additional plans were drawn on papyri or flat slabs of limestone. Models of the pyramids were also made by the planners. These miniature limestone artifacts have been discovered in various Egyptian sites. After the planning stage was completed, each step of the pyramid construction was