The Egyptian great-pyramids are built of large blocks of limestone piled in an orderly way on a cut-level limestone surface. In map view the pyramids are perfectly square with two sides exactly north-south and two east-west.

Many have pondered the question: How was it possible for the pyramids to be so well oriented? The ancient Egyptians I suspect would have been amazed to know this for the technique of exactly laying out a north-south line on a level surface is easily done with a vertical stick, which casts a shadow on a cloudless day (common in the desert), a piece of chalk, and string. Once a north-south line is drawn, this can be carried forward (or backward) by two workers using three vertical sticks that can be moved. Exact right angle corners of a square can be laid out with a loop of rope that has knots marking out three lengths of it in the well known ratios (3:4:5), and stretching this into a triangle holding the knots (and this was certainly common knowledge to the ancients, as it is to any present-day construction worker).

For your essay (to be handed in at our next class meeting Wednesday May 12):

1) Describe, with a diagram to which you make reference, how we were able to draw an exact north-south line on a level surface using the shadow of a gnomon, a length of rope, and chalk.

2) Describe, with a diagram to which you make reference, how a surveyed straight line can be continued in the same direction indefinitely using two workers and three movable vertical sticks.

3) Describe how to know when it is local noon.

During the morning I marked positions of the end of the shadow that a vertical stick cast at several times (see below). I added the last point in the afternoon when we arrived and used this as a radius length from the gnomon to draw a circle that intersected the path of the morning shadow curve. We then bisected the distance between the last afternoon point and the drawn circle's intersection point of the path of the morning shadow curve. That construction gave us a true North and South line. (Note: It would be better to draw the circle using the first point in the morning and then simply wait until in the afternoon the gnomon-shadow end meets the drawn circle. Mark that as the second point and then bisect the true E-W line that joins between the first and second points.)

For large image, click on the picture: