Le silence a régné dans la cour du château en 2020 en raison des contraintes sanitaires.
Espérons que la fête de Mézerville aura lieu en 2021 et que l’Association NAMUKA pourra nous proposer un spectacle !

The Golden Number

Let AB be a segment divided at the C point, we speak about the “divine proportion” when

 

If AC = a and CB = b, the Golden Number is defined as the ratio a/b called phi

 

The divine proportion can be written:

 

Multiplying all terms by phi gives the equation

This equation comes out as a positive solution

which is the Golden Number :
1,61803398 ...

From the previous equation, two interesting properties of the Golden Number are revealed:

-> It is the only number which added to one is its own square, and subtracted from one is its own inverse.

Other noteworthy properties

These numbers define a “sequence” called “Fibonacci sequence”

1, 1, 2, 3, 5, 8, 13, 21, .....

Golden Number and unities of measurement

Golden Number and unities of measurement

In the Middle Ages, the cathedral builders used 5 units of measurement related to the human body:

  • the “paume” (the palm) = 34 lignes = 7,64 cm
  • the “palme” = 55 lignes = 12,36 cm
    (distance between the forefinger and the little finger, hand opened)
  • the “empan” = 89 lignes = 20 cm
    (distance from the thumb to the little finger)
  • the “pied” (the foot) = 144 lignes = 32,36 cm
  • the “coudée” (the cubit) = 233 lignes = 52,36 cm
With a base unity : the line = 2,247 mm

 

The result is two surprising truths:

To go from one measure to another you multiply it by the golden number.

  • the “palme” = the “paume” * 1,618 (7,64 * 1,618) = 12,36 cm
  • the foot = the “empan” * 1,618 (20 * 1,618) = 32,36 cm
  • the cubit = the foot * 1,618 (32,36 * 1,618) = 52,36 cm

A unit of measurement is equal to the sum of the two previous units

  • “empan” = “palme” + “paume” (12,36 + 7,64) = 20 cm
  • foot = “empan” + “paume” (20 + 12,36) = 32,36 cm
  • cubit = “empan” + foot (20 + 32,36) = 52,36 cm

Following page: Golden Number and Geometry

 

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