WO2014033491A1

WO2014033491A1 - Building blocks of creation

Info

Publication number: WO2014033491A1
Application number: PCT/IB2012/001655
Authority: WO
Inventors: Frédéric MANSUY
Original assignee: Mansuy Frederic
Priority date: 2012-08-28
Filing date: 2012-08-28
Publication date: 2014-03-06

Abstract

The invention relates to a geometric method that can be used to tile the plane with a symmetry of order 5 and in a quasi-periodic manner, using only three basic building blocks, of which one (a regular pentagon) has three different states depending on how it is traversed or not traversed by the primordial array of straight construction lines, i.e. the α (Alpha) array. Only Roger Penrose achieved an equivalent result, in 1972, using two types of lozenges.

Description

The creative squads

Description:

It is a geometrical process that allows to plane the plane with a symmetry of order five and almost periodically, with only three building blocks of which one, (a regular pentagon), has three different states depending on how it is traversed or not by the primordial network of lines of network constructions a (Alpha).

Only Roger Penrose in 1972 had achieved an equivalent result with two types of diamonds.

Graphic construction:

We draw a network of parallel lines of which both

spacings are worth:

called S. = φ and L. = φ ²

Such as :

Starting from a central space [SL] worth φ ³ and

developing in the two opposite directions from this space, a right-hand sequence whose intervals follow one another by obeying the progression rules of the Fibonacci sequence, etc. SLSLLSLSLLSLLSLSLLSL [] LSLLSLSLLSLLSLSLLSLS etc.

that this network is rotated around an axis placed at 2 at an angle of 36 °; then 72 °; then 108 ° and 144 °, one obtains a primordial network "supersymmetric" with respect to an equator, which one will call: network a (Alpha) whose irrational values equilibrate perfectly on all the network.

In the center of the figure, there is a regular decagon worth φ ³ between two opposite sides; then around, a horizon (starry with 10 branches); around the horizon, regular pentagons

These pentagons are of three natures according to which they are crossed not by the network of lines of constructions. We will call:

• PO virgin pentagons

• PI pentagons crossed by a straight line

• P2 pentagons crossed by two straight lines

These pentagons (P0, P1, P2) are always in contact only by their points. Around the horizon of the central decagon

find: 1 PO; then 4 PI in contact; then 1 P2 and 4 PI in contact. If we draw a line crossing PO and P2 in their height, (which we will call equator) we see that the symmetry is perfect between the north pole and the south pole, and this, as far as one can can extend the network to (Alpha).

Beyond the horizon and the first circle of pentagons PO, PI and P2 are positioned so that two of the same nature are never in contact and:

• PI always in contact with three others.

• P2 always in contact with two others.

• PO always in contact with five others.

The gaps between the pentagons have only three different forms, and can be filled with only two bricks and this over the entire network, which implies that we can pave the whole plan with three "bricks" of bases (one of which pentagon which has three different states), in symmetry five and almost periodically.

Claims

Claims:

Hitherto deemed impossible, it is the only method which allows, so simply, to obtain a "supersymmetry" of order five with respect to an equator, and which extends indefinitely with only three basic bricks . The technical effect thus obtained can have many applications as well thanks to its aesthetic and ornamental aspect, as in the fields of architecture, crystallography, nanotechnologies and elementary particle physics chemistry.