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13 juillet 1970 1 13 /07 /juillet /1970 10:46



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La Ora Stelo
(the golden star), dedicated to Jean-Pierre Puisais-Hée, is a puzzle whose pieces are polymultiforms  (more precisely polyores).
The polyores are polymultiforms obtained by juxtaposition of several triangles as the 2 triangles below :

undefined

These 2 triangles are isoceles : their sides measure respectively 1, 1  and undefined  for the first and 1, undefined and undefined for the second.
undefined is the golden number (the golden ratio, the golden proportion) :
      undefined
These 2 triangles are called "golden triangles" (someones speaks about "golden triangle" for the second and "golden gnomon" for the first).

Their angles measure respectively 36°, 36° et 108° for the first and 72°, 72° et 36° for the second.

But what really matters is that, if we take the area of the first as unit area (so its area is 1), the area of the second is undefined.

The polyores below are arranged in order of area (their area is red pointed) :












The 32 polyores above are the 32 pieces of La Ora Stelo.
They cover area of 42undefined + 42 ; if we add 5 little triangles, we obtain area of 44undefined + 43 : it's the area of a regular pentagon with side undefined + 4.

 

The first goal of this puzzle is to realize a golden star by 22 of its pieces. Here is a possible weft for this star which have area 36undefined + 22 :

undefined

There is a vast number of possible wefts ( to see an example of transformation of the weft, click here ).

I have not solution and I don't know if one exists.
(solution of Robin King)

On the other hand, the pieces of La Ora Stelo allow realize many figures with different sizes :
pentagons, diamondstrapeziums, starsdecagons, kites, "dunce's caps", "mushrooms", "darts", "witche's hats", "diaboloes", "pantaloons", "shirts", "fans", "flowers", hexagons, "tents", parallelogramstriangles, "wheels", "cooking-pots", "mountains", "norias", "butterflies", "foxes", "barrels", "apple trees", "crowns",  octagons, "shuttles", and so on ...

 

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