Hans Walser, [20130821]

Tribar Spirals

1        The Tribar

Figure 1 shows the usual tribar.

Fig. 1: The Tribar

The tribar is an impossible structure, it cannot be realized in the three dimensional world.

2        Spirals

Now we try to extend the tribar into spirals.

2.1      Archimedean Tribar Spiral

Figure 2 shows the Archimedean tribar spiral.

Fig. 2: Archimedean Tribar Spiral

We have a real end in the center. All branches of the spiral have he same width. This figure shows a not an impossible structure.

We explain this in a smaller version (Fig. 3). (The indicated numbers give the total lengths of the edges, if the structure is built from unit cubes. The edge lengths are multiples of three. )

Fig. 3: Smaller Version

In Figure 4 we have another view of the same structure. Clearly we see that this is possible in the three dimensional world.

Fig. 4: Other View

2.2      Logarithmic Tribar Spiral

In Figure 5 we have a logarithmic tribar spiral. We have a point at infinity in the center.

Fig. 5: Logarithmic Tribar Spiral

Can you imagine that this Spiral is constructible in the three dimensional world?

Figure 6 gives another version. It goes down and down.

Fig. 6: Another Logarithmic Tribar Spiral

But the perspective in Figure 6 is not correct.

Figure 7 gives a better, but still not correct version.

Fig. 7: Staircase to Hell