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Carved Wood and Geometrical Drawings

The fascinating world of geometry of tessellations, of coating the surface with a plane geometrical figures that do not overlap and do not leave blanks.

Tesselletions

The fascinating world of geometry of tessellations, of coating the surface with a plane geometrical figures that do not overlap and do not leave blanks.
I have often wondered why not to coat the surfaces with wood, and even more specifically, with wooden floors that were inspired to periodic or non periodic tessellation with the use of different shapes and sizes different from those used today or in the past as the Versailles
Research has proved itself a fascinating journey uphill because of my lack of familiarity with the topic, that is mathematics, and even more specifically the plane geometry, but the desire to know, learn, explore, threw me into a truly engaging world without boundaries.

The Girih

Below, I’ve replicated a picture of a wooden flooring that is inspired by the Girih, in my opinion, a world of geometry that is intriguing and truly without boundaries, so there is still much to explore. The result obtained in my example, is based on the use of wooden elements and exactly five tiles that have been used to create models of tessellation for the decoration of buildings in Islamic architecture around the year 1200.

pavimento con tassellatura-girih

The study on Girih stems from the discovery by Peter J. Lu of Harvard and Paul J. Steinhardt of Princeton.
If their assumption was correct, it would mean that Islamic architects came close to discovering the aperiodic tessellation long before Western mathematicians. In any case, there is no indication of how deep their knowledge of the mathematics of tessellations was.
The term Girih specifically refers to the lines, ie in this case, the engravings made ​​in the wood in bas relief.

The five plane geometrical shapes are:

  • A regular decagon;
  • an enlengthened hexagon;
  • an enlengthened hexagon;
  • a rombhus;
  • a regular pentagon.

All sides of these figures have the same length, and all angles are multiples of 36 °.
Islamic architecture has mainly used a periodic Girih tessellation . Some had traces that cannot be extended to the tessellation of the whole plane. Tessellations Girih with traces that can be extended to the whole plane only a-periodically are not known..
The use of algorithms, the aesthetic taste that drives the choice of the wood/s to be used in the five sizes opens up incredible expressive possibilities for those who design, live, work, visit rooms designed with this “new” approach to the wooden floor and that enables a tessellation, a coating of the plan in a tailored way.

esempio-algorito-girih-aperiodico-non-chiude
The first picture shows the use of two woods, one of which as a field and the other as an edge, insert, Greek fret that runs on the surface in a pentagonal shape.
The picture shows a representation of a-periodic that not “closing” requires the use of other plane geometrical figures, in addition to the five basic ones ,to be able to cover the floor.. This is because wishing to surround an area of ​​the floor to create an area in which to include part of the furniture and algorithmically mark an area such as the living room with its furniture, it is not possible without creating cuts in the five basic pieces. This is to have the internal broken lines obtained by continuous and uninterrupted engravings.

The internal field is obtained using a single geometric shape such as, in this case, the pentagon highlighted with the use of a different wood compared to the internal field and to what will be the external field. The broken lines run free, drawing the surface and the drawing geometric figures obtained by the five Girih.

Algoritmo Girih Chiusura Anello

You can carry out the fields without cuts, with the five Girih elements, then placing them in the desired context and, through algorithmic verification and a lot of patience, hope that the external field gets upholstered with the only use of the five elements without interruption, but we must always check… and hope.

Tassellazione campo interno

Once maybe they carried out the plane study in this way… free hand .

Girih: disegno a mano libera

You may use the modularity and not the algorithm thus avoiding headaches and insomnia. We can therefore make drawings with some of the five Girih figures, creating endless variables as tessellation of the plane and as a continuity of the lines that will… then create other figures… so maybe and I say maybe… with metal or marble…

Variables without end; formats, sizes, types of wood, surfaces, designs and workmanship at low or high relief, patinas inserts in different materials of the past and today…
The wooden elements belong to the collection and Patterns arise from the Elite Charme collection by Quadrolegno. This is to realize large wooden elements with the noble part obtained by book matching sawn jointing for the reconstruction of the trunk, but with a thickness suitable for floor and possible realizations open spot.
But that’s another blog post… I’ll let all lovers of geometry and challenges create for themselves or for others…