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

Please observe the different factors:

·       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

kvadratrod2storpng



Section 3.2.4

√2 is an irrational number, which has been known in thousands of years.

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




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.

egyptiskebrkerjpg

Source: https://en.wikipedia.org/wiki/Ancient_Egyptian_mathematics

 

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:

1 1 trekantpng


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
a b trekantpng

a _ bPNG

then

b _ aPNG

if

x seked 7  a_bPNG

then


x seked 7  1_TAN APNG

or


x seked 7_TAN APNG

and the angle A is:

arc tanPNG