ABSTRACT
In the land of the pharaohs in ancient Egypt, the builders of the majestic pyramids and temples that adorn the surroundings of the Nile river made use of an amazing lowtech, biodegradable, zero-radiation, inexpensive, and low-maintenance computer to nd solutions to a variety of geometric problems that they encountered in their daily lives: the knotted rope. As the name suggests, this computer consists of a rope of suitable length tied together at the ends, and interspersed with a preselected xed number of equally spaced knots. ere is evidence that one popular model of this computer comprised 12 knots as shown in Figure 25.1, in two congurations: loose (le ) and taut (center). e users of this computer knew from experience in the eld that if three people holding the rope at the knots numbered one, ve, and eight walked away from each other until all three strands of rope between them were taut, the nal shape of the rope would be a triangle.* Furthermore, and this is the crucial point, they were condent that the triangle would be a right-triangle: the angle made between the two short sides of lengths three and four is 90° angle. One of the most useful applications of this computer was, therefore, the construction of 90° angles in architecture. To illustrate this application, assume, for example, that the workers had to build a new wall that made a 90° angle with another wall already built, and refer to
Figure 25.1 (right), where the old wall is shown in the horizontal position. Assume further that this new wall is required to meet the old wall at the point marked A. First, one worker holds the rope at the h knot and stands at position A. e second worker then takes knot number one, and walks away from the rst worker along the old wall until the rope between them is taut, ending at position B. Finally, the third worker takes knot number eight, and walks away from the other two workers adjusting his or her position until both strands are taut. e engineers were convinced that if the new wall was built in a straight line from A to C, the angle BAC would be a 90° angle.
