Units

Section 3.2.1

In the Ancient Egypt for approx. 4500 years ago they had following lengths:

 Lengths Metric system, meters 1 Shet 20.9440 1 Cubit 0.5236 1 Remen 0.3702 1 Foot 0.2618 1 Hand* 0.0740 1 Finger 0.0185

Section 3.2.2

The correlation between the Ancient lengths are:

 Shet Cubit Remen Foot Hand* Finger 1 40 56 80 280 1120 1 √2 or 1.4142 2 7 28 1 √2 or 1.4142 5 20 1 3.5 14 1 4 1

·       1 Khet = 100 Cubits

·       1 Shet = 40 Cubits

·       1 Cubit = √2 Remen, 1 Remen = √2 Foot

·       1 Cubit = 2 Foots

·       1 Cubit = 7 Hands*

·       1 Hand = 4 Fingers      ( 2 x 2 )

·       1 Foot = 14 Fingers    ( 7 x 2 )

·       1 Cubit = 28 Fingers  ( 7 x 2 x 2 )

·       1 Shet = 56 Remens ( 7 x 2 x 2 x 2 )

·       1 Remen = 5 Hands*

* Some sources call the length "hand" for a "palm", it is exactly the same size. I prefer to use the word "hand".

Section 3.2.3

### Square root of 2

Section 3.2.4

If a square measure 1 x 1, then the diagonal length (the hypotenuse) is √2.

However, √2 is an irrational number, which was not known in the ancient Egypt. Instead they invented two different lengths:

1. Cubit
2. Remen

If the above right triangle had two legs of 1 remen each then the hypotenuse is  √2 remens = 1,414213562 remens, a number which was totally unknown in ancient Egypt.
Instead they defined that length as 1 cubit, so √2 remens = 1 cubit.

Section 3.2.5

### Other measures

Area:

1 Setat = 1 square Khet

Section 3.2.6

Pi:

Pi (π) is a mathematical constant defined as the ratio of the circumference of a circle to its diameter.

There is no evidence that the ancient Egyptians knew or used the irrational number Pi (=3.14159 or fractions like 22/7). They did not even need it, when they calculated the measures inside and outside the pyramid.

They used fractions in general as 1/x, x is ( x = 2,3,4,5 ...) - exception is the fraction 2/3.

Section 3.2.7

Volume:

1 Hekat = 4,8 litres

1 Hin = 0,48 litres

Section 3.2.8

Angle or slope:

The ancient Egyptians did not calculate angles. They calculated the decrease or increase of steepness.

1 Seked = The horizontal length measured in hands  / The vertically length measured in cubits.

The slope of the Khufu pyramid is 5 1/2 sekeds calculated as:

220 cubits horizontally x 7 hands/cubits / 280 cubits vertically = 5 1/2 sekeds.

There is a connection between a seked and an angle.

Imagine a right triangle with each side of 1 cubit as an example:

The horizontal is 1 cubit equal to 7 hands.

7 hands horizontal / 1 cubit vertical  = 7 seked which is an angle of 45°

In general we can deduct following:

The  cotangent to the angle is the adjacent side / the opposite side

then

if

then

or

and the angle A is:

Section 3.2.9

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