The Surveying of Egypt - The Geometry of it re-visited

[Don Barone]

Hi all ... tough to complete a topic when I keep side tracking myself but here we go again on this topic. ...

This should be in a Mathematics forum but this is as good as place as any as it will slowly and eventually lead toward my solution in it's completeness of my thesis on how The Ancient Egyptians surveyed their fields and their lands.

The first thing to note is to step out of the box and realize that there is a different and unique way of calculating Pythagorean's theorem. We have all always been taught that it is "a" sqrd + "b" sqrd = "c" sqrd and that I am afraid may have held us back for there is a very simple second way of doing it ... and I will teach it too you. It simply involves two squares or instead of a circle inside a square we will have a square inside another square with each corner touching the side of the outer square as shown in the diagram below.

The thing to note is that this solution is to be solved on a flat plain and involves no height or angles or really anything but straight distances and straight lines ... here is a diagram of the end result. Note that a new measurement has been instituted .. that of "d" which is the total of a + b ... So as an example in the famous 3, 4, 5 triangle with a = 3, b=4, c=5 ... d = (a + b) or 7

So in my new system you would start with a square of a + b and we get a square of 7 units (I used 14 small squares)



But by definition that includes a + b or 3 and 4 so let's draw those squares in ...



So now let's draw in our square using the meeting place of the "3" point and the "4" point as our corner of the inner square and we get this ...



A proof is very easy as we get four 4 x 3 triangles which translate into four 4 x3 squares which equal 4 x 12 or 48 and the single unit in the middle for 49 thus solving the equation





Or maybe easier we start with 7 x 7 or 49 units and we subtract [(4 x 3) x 4] / 2 = 24 to get 49 - 24 to get 25 and sq rt = 5

Note that in this solution no angles have been needed !

So a formula could read:

(a+b)² - [(a x b) x 4] / 2 = c²

so now what do we do with this ? Well we know that using this we do indeed get some angles ... I have shown them in the diagram below ...



So in this diagram angle "a" is simply the ratio of 3 divided by 4 or 0.75 ... whatevers. We call it angle 36.87 but it could be anything we want it to be but the ratio will always remain 0.75 !

so to end this particular post I have to emphasize that everything above the line is not needed ... all we need is the ratio of 3 to 4 or 0.75 and everything in this diagram becomes known .. so for example if I drew the simple line below:



We know that the square is 5 from our (a+b)² - [(a x b) x 4] / 2 = c² equation.

We also know that the angles are 3/4. and 4/3 ... for 3/4's or 1 and 1/3rd

For now that is all but in the next post I swill show how this became important to The Ancient Egyptians and how it was the only possible way they could have done a variety of things.

Cheers
Don Barone

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[Don Barone]

Okay let's return to Egypt and bring in those alleged tombs (but I still would bet on Geodetic Survey Monuments) and see how they can help my thesis.

Thesis:
1.
a statement or theory that is put forward as a premise to be maintained or proved.
"his central thesis is that psychological life is not part of the material world"
synonyms: theory, contention, argument, line of argument, proposal, proposition, idea, claim, premise, assumption, hypothesis, postulation, supposition
"the central thesis of his lecture"

(in Hegelian philosophy) a proposition forming the first stage in the process of dialectical reasoning.

2.
a long essay or dissertation involving personal research, written by a candidate for a college degree.
"a doctoral thesis"
synonyms: dissertation, essay, paper, treatise, disquisition, composition, monograph, study
"a doctoral thesis"

As a prelude I would like to post a few pictures of the various pyramids and how they look from varying sides:









Okay so now let us look at these pictures of the pyramids using my system ...

Let's start with this one ...



What can it tell us ? Can it ell us how far away we are ? No. Can it tell us anything about the pyramid itself ? No. Well then what can it tell us ... Well it tells us what angle we are off of 90 degrees. Well I measured the lines and it isn't quite bang on but I will call the red line = to the blue line. But how would we measure those lines ? Aw that is for a later lesson ! All we need to know for now is that a = b and of course that gives us seked of 7 (really 1 as we would have 1 cubit by 1 cubit) or angle or ratio of 1 and that as we all know is of course the tan of 45 degrees.

Let's try another ....



Here we have the ratio of the line = 0 since red = 7 blue = 0 and if blue = 7 red = 0 and thus we know that the tan of 90 degrees is undefined or infinite or 0 ... or facing either true north or south !

And finally just one more ...



This one scales to red = 1.1666 and blue = 5.833333

So this seked is 5.0 or 0.2 and tan is also 5 and thus the angle is 78.69 OR 11.31

So thus we have shown how using the simply square method to finding a solution to a right angled triangle has allowed us to very easily find the correct angle we are in relation to true north TO ANY OF THE PYRAMIDS !!!!!!!

The one thing missing of course is what are we using to measure the red and blue lines ? Patience please it will be coming.

cheers
Don Barone

[spaceyhippie]

(x+1)(x-1) = x^2 - 1
and imagine this on graph paper if you like
but say x is 7
(x+1)(x-1) = x^2 - 1
6 x 8 = 48
48 = x^2 - 1
49 = x^2
x = 7
and this works on any (real number) x

[Charlotte]

May 22, 2017 12:07:31 GMT -5 spaceyhippie said:

(x+1)(x-1) = x^2 - 1
and imagine this on graph paper if you like
but say x is 7
(x+1)(x-1) = x^2 - 1
6 x 8 = 48
48 = x^2 - 1
49 = x^2
x = 7
and this works on any (real number) x

Nice to see you, spaceyhippie, it's been a long time since you were here, I do hope all is good in your life.