Hi Hermoine ,,, and thank you.

Here is one of the key discoveries I feel I have made.

"The distance from the eye to the center of a clenched fist is none other than 20.62 inches... THE CUBIT !!!"

The more I think about this the more amazed I am for now you always had your surveying equioment with you. You simply need a stick of some sort longer than 20.62 and inches and simply holding it up to your face you could mark it with your hand.

I further suggest that perhaps they called it "The Royal Cubit" because it equalled the distance of none other than Sneferu himself or perhaps even predated that to Djoser. Or maybe Imhotep used his length of eye to hand.

The second major discovery is that The Ancient Egytians used fractions because, unlike us who got our system from The Arab world and use decimals and thus are base 10 and unlike Ancient Sumeria who used base 6, The Ancient Egyptians USED BASE 7 ! This has enormous ramifications and also limitations. Using this system IT IS IMPOSSIBLE to find any of the "irrational" numbers. So in that category would include Pi, phi, square root of 2 and of course square root of 3. However this also means that any rational number and here is the definiton of a rational number "In mathematics, a rational number is any number that can be expressed as the quotient or fraction p/q of two integers, p and q, with the denominator q not equal to zero. Since q may be equal to 1, every integer is a rational number." can be found in Egytian mathematics.

However 7 is an amazing nubmer in it's own right. Firstly and interstingly it is THE ONLY NUMBER OF THE FIRST 10 THAT CAN NOT BE DIVIDED INTO THE 360 DEGREES OF A CIRCLE ! What does this mean ? Well simply that using 360 would for the ancient Egyitans be a little more difficult because every graduations or "degree" would be a fraction. For example 360 / 7 equals 51.428571428571428571428571428571 or more easily shown as 51 and 3/7ths.

It is now my studied opinion that The Ancient Egyptians did not know square root of 2. They arrived at what appears to be square root of 2 by dividing 99 by 70 (base 7 x 10) to get a value of 1.414285714 which when squared gives us 2.0002 and checking to square root of 2 to about 0.999898. A similar phenomenon occurs with the square root of 3 which when 10,000,000 is divided by 280 (70 x 4) we get 35714.2857 and when we divide this by the accepted standard of the cubit at 20.62 inches we get 1732.0216 or 1732 and some fraction I can't for the life of me figure out.

So as I hAve been told a thouSand and one timEs, the Ancient Egyptians, in their surveying DID NOT USE CIRCLES OR PI OR ANGLES !!!!!!! They did not have to and now really neither do we. The Ancient Egyptians perhaps knew as I do that the the circle really does not exist and also interestingly except for a very few special cases angles can not really be defined and drawn in the real world either. As an example take the simple 3, 4 and 5 sided right angled triangle. tan of angle "a" equals 4/5 or 0.8. all well and good until we go to try to figure out the angle and we get tan 0.8 equals 38.659808254090090604005862335173 ... degrees. Could you or anyone mark that on a protractor ? It is an imaginary angle however using The Egyptian method we mwould get this:

Image to follow.

Cheers
Don

"There is nothing as impenetrable as a closed mind"
and ..." if everything is a coincidence what is the point of studying or measuring or analyzing anything ?" db