Pantheon of collective memory
The universal language of spacial shapes are inscribed within the plan of a circle
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3 The equilateral triangle is the simplest surface. It is defined by 3 angles, 3 sides and one dimension.
4 The square : 4 angles, 4 sides and one dimension
5 The pentagon : 5 angles, 5 sides and one dimension
6 The hexagon : 6 angles 6 sides and one dimension
The regular polygons which are in the plan of a circle are in an infinite number. The more the number of their sides increases, the more they get closer to the circumference. (they approach to the circumscribed circle.)
Five
solids of Plato inside
the volume of a sphere
The pythagoricians imagine that in
the space of a sphere, the regular polyhedrons, the faces of which are regular
polygons are exclusively 5 in all of the universe.
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The tetrahedron (4 faces as equilateral triangle) |
...4,
3
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The
cube ( 6 square faces)
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...6, 4
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...8,
3, 4
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Dodecahedron
(12 faces in regular pentagons)
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...12,
5
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Isocahedron
: 20 faces in isocametric equilateral triangles.
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....20, 3 Figures in bold type are highlighted to show the importance of numbers in the construction of matter |
The tetrahedron is the most elementary volume in three dimensional space since it has as a base the equilateral triangle which is the most elementary closed geometrical figure given by a single dimension of the side.
The tetrahedron has all its importance in organic history along with carbon and silicon.
Silicon has a chemistry rather similar to that of carbon:
1. Silicon is the most abundant element in the Earth's crust and a constituent of many occuring rocks combined with other elements principally as silicates.
Silicates : the crystalline building of silicates consists of a stacking of tetrahedrons having at each top an oxygen atom and a silicon atom in the centre. The natural state of these minerals is the hexagonal volumetric shape.
2. carbon 6 (4+2 é)
Carbon is found in all organic matter and in all living beings.
1. Diamond is a very pure form of carbon cristallizing in the cubic system. It is the hardest mineral made of carbon atoms connected to each other. Each atom is linked to 4 others which form together a pyramidal structure or tetrahedron.
2. Graphitic carbon cristallizing in the hexagonal system. It has the same chemical formula as diamond but the atoms of carbon are laid out in thin strips that are weakly bounded.
3. Carbon is one of the most fondamental elements of life. Associated to hydrogen, oxygen and nitrogen, it is part of the cycle which connects the living world to the inanimate world. It can bind four atoms or chemical groups according to the configuration of a tetrahedron.
The regular tetrahedron
The carbon atom presents 4 bonds. When it is related to 4 identic atoms or 4 identical chemical groups, the unit forms a geometrical figure like the tetrahedron, of which carbon is the centre. This is the case for methane (CH4), the first molecule of the organic cycle. The carbon atom is connected to four atoms of hydrogen in a regular tetrahedral configuration.
When the four atoms or chemical groups are different, the space composition becomes asymmetrical. This is the case for many compounds of living organisms.
The
irregular tetrahedron
Proteins are built from 20 amino acids. The spatial arrangement (the spatial combination) of the amino-acid molecule which forms the proteins is the asymmetrical tetrahedon.
As in most organic molecules the amino acids are asymmetrical but the arrangement always presents the same chirality.
This pecularity is the prerogative of living molecules. Many scientific studies have been curently undertaken on chirality.
We can state that NOCH, which is the most primitive formula of organics is involve in the simplest spatial volume in the Universe. This preferential volume of organics is the tetrahedron built on the equilateral triangle which is the first simplest surface (3 sides and one dimension). And yet, organics are the most complex state of matter compared to solids, liquids and gas states.