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  Prof. Urban
Materialien für Mathematik, Physik, Informatik
 
 
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The impossible Tribar

We start with a sketch of three equilateral triangles, sides differing by some equal amount.
To gain practice we try to connect the intersection points to get a view of a simple true 3D-triangle, each side and each edge viewed from top right.

We end with a nice coloured picture like this

 

But now we change visibility: we draw the left corner as seen lying flat, the right one rising up, the top one in mid-air pointing towards us.

Each corner seems ok seems ok for itself. Whenever one corner is hid, the remaining figure is possible. But observe its orientation in space!

So we get the famous impossible tribar like

 

In 1934 the swedish artist Oscar Reutersvärd painted a similar tribar consisting of small cubes. To reveal the trick, you get the 'real' tribar first, the 'impossible' one next to it. Where's the difference? We will use the same trick later, when re-building the impossible Penrose staircase.

(I did these two pictures with a little Python-Script, the other ones using Micrografx PicturePublisher.)


--- © Wolfgang.Urban@schule.at ---