<< Page of Cups | Home

One knot like the Other

The Texture of Heidegger's Being and Time

The trefoil knot is shown from two angles (0.a/b) and is the boundary of the mobius band.

Figure 0-a Figure 0-b


One knot like this page's theme is defined by the joining of two ruled surfaces upon the trefoil edge.

Figure 1-a/b

 The left figure (1.a) shows how the mobius strip fits in the gap which produces the knot, and the right figure (1.b) shows the other strip that encloses the knot entirely.  As the two rulers seem in some sense to mate upon their edge, I tend to think of the outer (right) one as female and the other (left, inner) as male.  

The offspring figure bears a similarity to the parent in that they are toroids, and so the child then also admits a quality of divisiblity wherein a second mobius strip is formed within the knot.

Figure 2-a/b

 The left figure (2.a) shows the strip that fits inside the knot, and the right figure (2.b), although difficult to see with the transparency, shows the two together.  To better perceive the imposition, the reader might find helpful the streamlines along the surfaces in order to follow the design.

Finally, the two bands are shown intertwined from two different viewing angles (3.a & 3.b).  Whether or not the second band within is a mobius and not just a loop is something I haven't yet worked out, but I suspect that given an extra turn, then either could fit in the space.

Figure 3-a/b

 Here's another intertwined band, and in this case the two shapes are more readily discernible as mobius bands.

Export this post as PDF document  Export this post to PDF document

Add a comment Send a TrackBack