Chapter V — Temple, Micro

CHAPTER V

TEMPLE

ANIBAL

AMIOT

The Peace of the House by which the Male is recognized as masculine...

019

POINT AND CENTRAL "MASCULINE" SYMMETRY

YANG (EXPLOSION)

ODD NUMBERS

020

HOT MATRIX

PRESENTATION OF ODD NUMBERS

21 16 22 7 11 17 23 4 8 6 12 18 24 1 5 9 1 7 13 19 25 2 6 2 8 14 20 3 3 9 15 4 10 5

CATEGORY:

ODD

Self-filling method attributed to Claude Gaspard Bachet de Méziriac.

PROPERTIES:

Over-presence of the center

11 17 23 4 8 12 18 5 7 13 19 2 6 8 14 3 9 15 43 36 29 37 22 30 15 23 31 8 16 24 1 9 17 25 2 10 18 3 11 19 4 12 5 13 6 7

1. PREPARATION

Draw an odd-numbered square whose cells align at the vertices. Fill it in according to the order of the natural numbers.

2. DELIMITATION OF THE AREA

22 30 23 31 16 24 17 25 10 18 11 19 4 12 44 45 38 46 39 47 32 40 33 41 26 34 27 35 20 28 21 14

Then, starting from the center of these preparations, isolate the inner horizontal square. (Thick gray lines)

38 46 39 32 40 33 26 34 27 20 28 48 49 42 021

9 3 7 1

3. IMPLEMENTATION

4 10 24 5 6 25 1 20 21 2 16 22 21 16 22 7 11 4 17 10 23 4 3 8 6 24 12 5 18 6 24 1 9 5 1 9 1 7 25 13 1 19 25 1 2 7 6 2 20 8 21 14 2 20 3 3 16 9 22 15 4 10 5

ANIBAL

AMIOT

Move the outer squares inside the frame and away from the center.

21 16 22 7 4 10 3 6 24 5 6 24 1 9 1 9 1 25 1 25 1 7 2 20 21 2 20 3 16 22 4 10 5 43 36 44 29 37 45 22 5 30 13 38 21 46 15 47 23 6 31 14 39 15 47 8 16 48 24 7 32 8 40 48 9 41 17 49 25 1 33 9 41 49 2 10 42 18 43 26 2 34 42 3 35 11 36 19 44 27 3 35 4 29 12 37 20 45 28 5 13 21 6 14 7 5 13 21 47 41 35 48 42 6 49 36 7 43 14 1 44 8 2 15 9 3

EDELBERTO

022 29 37 45 43 36 44 29 37 45 5 13 21 15 47 6 14 15 47 8 48 7 8 48 9 41 49 1 9 41 49 2 42 43 2 42 3 35 36 44 3 35 29 37 45 5 13 21 6 14 7

22 5 30 13 38 21 46

4. RÉSULTATS

4 3 8 9 5 1 2 7 6 Order 3 11 4 17 24 12 5 10 18 6 23 7 25 13 1 19 20 8 21 14 2 47 23 6 31 14 39 15 Order 5 16 48 24 7 32 8 40 41 17 49 25 1 33 9 10 42 18 43 26 2 34 Order 7 3 16 9 22 15 35 11 36 19 44 27 3 4 29 12 37 20 45 28 +

n2 + 1 = 10

n2 + 1 = 26

n2 + 1 = 50

5. OBSERVATIONS

COURTESY OF ANIBAL EDELBERTO AMIOT

023 -

n2 + 1 / 2 = 5

n2 + 1 / 2 = 13

n2 + 1 / 2 = 25

6. REPRÉSENTATIONS

Superposition Superposition Superposition

CHAPTER V

MICRO

ANIBAL

AMIOT

“Let the waters swarm with living creatures, and let birds fly above the earth in the firmament of the sky...” Genesis 1:20

V X XV XX

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SYMBOLISM OF THE FIFTH NUMBER

Pentagram: A pentacle in the shape of a five-pointed star-shaped polygon. It symbolizes the Microcosm because its shape suggests that of a human being with arms outstretched and legs apart.

The five appears as a pivot from the square of Saturn; on the Pythagorean triangle, it faces the right angle.

5 1 d 2

For a temple built according to Vitruvius or Solomon, five is the value of the square of the diagonal: "The width of the temple must equal half its length."

d / c = ( d + c ) / d =

c

Golden ratio ( ), golden section, Divine proportion or division of a line segment into mean and extreme ratio: Value of the proportion that results from dividing a line segment in a way that is both asymmetrical and harmonious.

c d

On the pentagon and the golden ratio

"Three aligned points, determining two segments, form a golden section, if there is the same ratio of the smallest part to the largest as the large part to the whole."

( = (1 + √5) / 2) 1,618034

The structure on the left is made up of three intertwined golden rectangles, allowing you to easily construct an icosahedron. (By connecting the vertices of the golden rectangles with a wire.)

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THE FIVE PLATONIC BODIES

This page and the one opposite are entirely made from Extracts from "Geometry of the Golden Ratio" by Robert Vincent. Chalagam Editions.)-

Regular convex polyhedra inscribed in a sphere (Platonic bodies):

In the fifth century BC, Plato demonstrated the existence of closed solid bodies bounded by regular and equal polygonal faces and angles with equal vertices.

4 FACES 4 SOMMETS 6 ARÊTES

These bodies, called regular polyhedra, are said to be convex if they remain entirely on one side of the plane of any of their faces.

He counted five of them, each inscribed in an inscribed sphere, tangent to all their faces. Euclid, Archimedes, and Apollonius, mathematicians of antiquity, were interested in them, as were Albert Durer in the Middle Ages, Leonardo da Vinci during the Renaissance, and later, in the 16th, 17th, and 18th centuries, Kepler, Euler, Poinsot, Cauchy, Catalan, and Joseph Bertrand.

8 FACES 6 SOMMETS 12 ARÊTES

12 FACES 20 SOMMETS 30 ARÊTES

“The even is always imperfect and lacks something.

The odd number, on the contrary, is full and complete; united with the even, it retains its character since the result is odd (...); united with itself, that is to say with any odd number, it produces the even, thereby showing its fertility. It cannot be divided into two parts without there being a remainder.

TETRAHEDRON

Regular polyhedron whose faces are four equilateral triangles.

OCTAHEDRON

Regular polyhedron whose faces are eight equilateral triangles.

DODECAHEDRON

Regular polyhedron whose faces are twelve pentagons.

Conversely, the even number united to itself proves incapable of procreating the odd, and it allows itself to be easily divided. Homer was not unaware of this. (P.53 Mysteries of Numbers, Lucien Gérardin)

6 FACES 8 SOMMETS 12 ARÊTES

HEXAHEDRON OR CUBEP-

Regular polyhedron whose faces are six squares.s.

20 FACES 12 SOMMETS 30 ARÊTES

ICOSAHEDRON

Regular polyhedron whose faces are twenty equilateral triangles.

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