The demand for mechanical precision, particularly in the areas of time keeping and the measurement of angular displacement, originated in Europe's astronomical observatories and first showed to good effect there . . . or so we were told.
Some 2,500 years ago the Greek historian Herodotus visited Egypt and reported that the Great Pyramid, one of seven wonders of the ancient world, was used as a celestial observatory during the course of its construction. We’ll take the man from Halicarnassus at his word. Because we find these features true today, it must have been important to the pyramid’s builders that the growing mound of limestone blocks be aligned precisely to true north, that its base be level and square, that the entry or “descending” passageway parallel the Earth’s axis, that the “ascending” passageway be reflected from the former and, finally, that the top of the pyramid be centered directly over the intersection of the diagonals of its base. A tall order it would seem, but was it really?
Let's give it a go, relying only on tools nature provides.
Steps 1 and 2—pick a construction site that is reasonably flat with clear site lines to the north; lay out a true north-south line.
For this exercise we’ll use an available field near Las Vegas’s McCarran International Airport. Fortunately, we have a reference for true north, the North or Pole Star, Polaris, readily identified in the night sky. (The two stars that form the lip of the cup of the Big Dipper constellation point to Polaris, itself the last star in the handle of the Little Dipper.) If Polaris were not almost perfectly situated along a projection of Earth’s spin axis, it would describe a small circle in the sky as the heavens wheel. A bisection of that circle—or the circle described by any other neighboring star—does lay on Earth’s spin axis. Drive a stake into the ground at what will become our pyramid’s northeast corner. Drive a second stake into the ground a little beyond what will become our southeast corner such that the two stakes line up with yonder Pole Star. Stretch a string between the two stakes and, behold, in one act, a true north-south reference line and one boundary of our structure.
Steps 3 and 4—lay out a square base and level it.
Roughly stretch a second string at right angles to the first, passing the base of the northeast corner stake. Since it has been known from ancient times that a triangle with legs in the ratio 3:4:5 forms a right triangle—three squared plus four squared equals five squared—adjust the second string so the rule prevails and fix it in place. Now measure off two equal sides of the pyramid starting at the northeast corner. Translate both strings and lengths to their opposite sides and “square up” the construction boundaries by comparing diagonal measurements. The diagonals should be—must be—equal. Trench around the boundaries of our construction site then within the boundaries on a grid of, say, three feet by three feet. Temporarily fill the connected trenches with water. Dig out the trench bottoms until the bottoms are everywhere equally flooded. Drain the trench system and plane the surface of the construction site to meet that datum. We are now aligned, squared and level, with nothing but nature’s bounty—Polaris, gravity and the properties of a taught line.
Steps 5 and 6—construct an entry or “descending” passageway parallel to the Earth’s axis; at some point along that passageway, reflect its orientation and construct an ascending passageway.
There are two points we must determine and preserve on the square surface that is to be the base of our pyramid. One is the intersection of the square’s two diagonals—done—and the other lies somewhere on a true north-south line that passes through the first point. Let’s choose a spot roughly halfway between the first point and the north edge of the square. Precision in this placement is not important to this exercise. (Doubtless, the ancient Egyptians chose purposely.) At both locations carefully center stone basins designed to hold a few inches of water with centers marked by fine bronze pins. Lay up a few courses of limestone block—or Styrofoam block if time is pressing—leaving open a shaft to the north that allows light from the Pole Star to strike the head of the pin in basin two. Roll something flat and pliable, a piece of papyrus paper perhaps, into a straw-like tube and poke it through a curtain limiting the rays from Polaris to only those that strike the head of the pin. Fill the basin with water to just cover the pin. Backing up from the basin while facing north and adjusting height-of-eye, there is one alignment and only one that reveals Polaris reflected off the basin’s surface, and that alignment guides construction of the ascending passage. More blocks, now, being careful to maintain vertical access to the first basin so that it may serve its intended purpose.
Great Pyramid Passageways
All this trouble might strike the novice astronomer as odd until the novice is informed that most telescopes are mounted “equatorially,” taking into account the latitude of the observation site. The angle between the base plane of our laboratory pyramid and the ray of light connecting Polaris and the pin in our second basin is equal to—yes, equal to—our site’s latitude, in this case the latitude of McCarran International Airport or 36°-04'-47" N.
Step 7—center the top of the pyramid directly over the intersection of the diagonals of its base.
After each course of blocks is laid, a new square, smaller and higher, may be established with the intersection of its diagonals falling precisely over the intersection of the base diagonals. This is achieved by suspending a plumb bob over the bronze pin in the first basin. (Filling the basin with water will help dampen the bob in its swings, and a shout of “Mark!” will tell fellow workers the bob’s nether-most point is directly above the centering pin.) With a final course of blocks squared and trued, the pyramidion cap piece may be sky-craned into place. Job done.
Among other interesting tidbits, Herodotus reported that the Great Pyramid’s pyramidion was made of solid gold. Solid gold or just gold clad, it must have been a magnificent sight. Suppose the priests in charge of the finished complex linked the pyramidion with an insulated gold wire dropped down through the plumb bob shaft and anchored to ground—what a lightning rod! Throw in a switch in a basement control room, no telling what miracles might be pulled off.
Herodotus (c. 484-425 BCE)
Hotel Luxor in Las Vegas
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