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 !

Golden Number and Geometry

The geometric construction of the Golden Number

 

• Let ABCD be a square

• O centre of AD

• An arc centered at O and radius OC intersects the prolongation of AD at F

• The segment AF represents the golden number


AF calculation

In the right angled triangle OCD:

If : AD =AB = BC = 1

So :

So :

The rectangle ABEF is called a “golden rectangle” because its sides are in the ratio of the golden number

Golden number and pentagon

The regular pentagon is a regular polygon with 5 sides inscribed in a circle and for which all the sides and all the angles have the same measuresments.

The angle between two consecutive sides equals 108°

Let ADC, ADF and AFC be the triangles

FD calculation

If DC = AD sin 18° + AC sin 18°

If DC = AD x 2sin 18°

DC = AD x 0,618

The ratio between a diagonal and one side of the pentagon is equal to the golden number.

The triangles AED and ADC are called “golden triangles” because their sides are in the ratio of the golden number

Another remarkable relationship:

Golden spiral

Golden spiral

The sides of squares are a sequence of Fibonacci

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

 

The face can be made from golden rectangles

 

Following page : The Quadrature of the circle

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