The Pyramids of EgyptThe Secrets RevealedPart IVSurveying The fields of egypt .

The Pyramids of Egypt
The Secrets Revealed

Part VI

Surveying The fields of egypt ... Circa 4500 years ago

Hi all. With the discovery of the simple angles and ratios of The Egyptian Pyramids I became convinced that they had been built that way to make it easy for the ancient surveyors to lay out the fields, that had washed away, quickly and acccurately. Today we use trigonometry to help solve geometric problems and back then they used a form of trig .. called Seked. Here is what is known of "Seked" :

The seked (or seqed) was an ancient Egyptian unit for the measurement of the reciprocal of the slope of an inclined surface.^[¹ ^] The system was based on the Egyptian's linear measure known as the royal cubit. The royal cubit was subdivided into seven palms and each palm was further divided into four digits. The inclination of measured slopes (Author's Note: we call this tan) was therefore expressed as the number of palms and digits moved horizontally for each royal cubit rise.

Information on the use of the seked in the design of pyramids has been obtained from two mathematical papyri; the Rhind Mathematical Papyrus in the British Museum and the Moscow Mathematical Papyrus in the Museum of Fine Arts.^[² ^] Although there is no direct evidence of its application from the archaeology of the Old Kingdom, there are a number of examples from the two mathematical papyrii, which date to the Middle Kingdom that show the use of this system for defining the slopes of the sides of pyramids, based on their height and base dimensions. The most widely quoted example is perhaps problem 56 from the Rhind Mathematical Papyrus.

However most people think only in height or rise but there is another application for this formula and that is ON THE GROUND ! For an example I am going to use The Red Pyramid althought I really could use any of them. It is not often thought about but as you approach any of the pyrmaids you can tell what angle you are approaching form IF you had the tools to measure certain things. Today's lesson is what to measure and possibly how to do it. For example if you were appraoching The Red Pyramid directly from the cardinal points (east, west, north or south) here is what you would see:

If we wanted to use trig language we could say we were approaching this at 0 degrees and that facing the base at 0 or 90 degrees is 1 or in this case 420.00 cubits while the other side is non existent and so has a value of 0 of no cubits.	In this image above (it is supposed to be looking at it edge on but this is the best picture I could find) we have now rotated 45 degrees and the base is 594 or 1/2 base of 297 and each side is now 297 with the hypoteneuse 420 and the angle of 45 degrees . To the side is an image of what I mean. The angle is 45 degrees. As you appraoch this pyrmaid the ratio will always be between 0 and 1 (sounds like tan) and the side you can see will vary from 297 to 420 and the samller side will vary from 297 to 0. And the overall measurent of what you can see will vary from 420 to 594 Simple basic trigonometry.	So basically you could tell what azimuth you are approaching from simply by knowing the difference in the short and long side that you can see. In the above image you can see 297 and 297 You would know that is 1 (side a or 297 divided by side b or 297) or tan of 45.0 degrees. So you are approaching from the precise SW or SE

In this above image we are approaching from an angle or azimuth of 26.5651 (this is a 1, 2 and sq rt of 5 triangle) The person approaching would know this if they had a tool or were able to measure the left side of what they see and were able to compare it to the size of the right part that they see. they would meausre both sides and then divide the two results and they would see that "side a" was twice as large as side "b" and so they would know it was 0.5 ratio and they would know the angle or at least what the triangle was since it became so common in the Giza Pyramids. To the right is an iamge of the pyrmaid viewed from this angle (approx)	So from this picture you would be approaching the pyramid from the SSW at 26.5651 degrees azimuth. Here is an image that show this: