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Applying solar geometry to understand the foundation rituals of 'Old Kingdom' Egyptian Pyramids.

Article Excerpt
Abstract: The republication of the interesting book by Rossi (2003, 2007) has provoked questions about the orientation of Egyptian pyramids from the architectural science point of view. The main concern of this paper is to explain several hypothetical possibilities for orientation of the first step Egyptian pyramid. The oldest monumental step pyramid complex, at Saqqara, was built by Imhotep in the 3rd millennium BC, 3rd Dynasty of the 'Old Kingdom'. Pre-construction involved a foundation ritual, during which the pyramid's south orientation and plan were determined by 'stretching the cords', a site design procedure partially illustrated on stone engravings. Though helpful, these illustrations incompletely depict the method of pyramid plan design and orientation. Due to rhombic signs on mastaba foundation stones, some Egyptologists claim that geometry was the primary method used for pyramid plan design and orientation. However, due to the solar equinox festive day and the pharaoh's presence at the festival, it is possible that the solar equinox was the day chosen for the ceremony. During the equinox, the gnomon shadow would directly indicate the E-W cardinal points. It is plausible, therefore, that solar geometry, at the equinox, was chosen to establish the primary orientation of the pyramid complex. Sundials based on the equinox sun-shadow were commonly used during the 3rd century BC. This paper discusses methods that could have been available to determine the orientation of pyramids.

Keywords: Cardinal points, Gnomon, Orientation, Pyramids, Solar geometry

Introduction

Studies of the relationship of architecture and mathematics to the design of Old Kingdom pyramids commonly refer to a pre-construction planning and design ceremony or foundation ritual. The ceremony of Old Kingdom pyramids involved a procedure called "the Stretching of the Cords". However, the method used to set the orientation of the first stepped pyramid remains speculative. Nevertheless, there are several clues that suggest the use of methods based on solar geometry. Vitruvius (13 BC, 1970), in his first of ten textbooks for architects, documents a philosophy on building orientation and thus reinforces the case for the ancient application of solar geometry to understanding the planning and orientation of the great pyramids.

Historical Background and Developments in Determining Time and Orientation

Since the dawn of civilisation, daytime activities have needed nighttime rest. Annual periods of gathering fruit or raising and harvesting crops have depended on diurnal and annual sunlight changes. There is no record of who first realized that there are two equinox days within a year, when the lengths of day and night are the same, exactly twelve hours each. In the equinox days, the sunrise precisely indicates the East cardinal point, the sun zenith is South, while the sunset determines the West cardinal point. These directions are especially valuable for orientation in desert regions where there may be no other orientation points or objects in view.

In two-dimensional geometry, it is quick and simple to draw a circle in sand, using a tent peg at its centre and a 'cord' or rope with another peg to move it around with respect and proportional to its centre. However, it is much more difficult even to imagine even the two-dimensional result of tracking the shadow thrown by the three-dimensional sun path intercepted by a vertical pole inserted at the centre of a circle. Such a 'solar time and geometry' based orientation and clock would mark sunrise and sunset and, when exactly 90[degrees] from the noon sun zenith, define equal time intervals on its primitive clock face. The sun zenith occurs at noon and, at that instant, the basic N-S cardinal points in any northern location, and the shortest sun shadow indicates north.

Mesopotamian and Egyptian priests conducted relatively simple geometric experiments with cords and pegs, or gnomon sticks, (1) with defined right triangles to acquire knowledge and build practical tools. The first wooden rectangular forms to manufacture clay bricks, and wooden triangles with a...

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