TOPOLOGICAL FIGURES, OR NOBLE SHAPES by Lucinda Cook

 Topological Figures, Or Noble Shapes/p>

In the photos above I am holding this Cook Twist Ring at the same spot! The second photo is a quarter turn to the left.

Below is the same Cook Twist, with three rounds of blue added along the one continuous edge.  It is a topological figure with only one side and one edge.  It has only one core gap hole, but effectively and visually it has two core gap holes.

My arm is going through the same hole as the hole hanging off the side. Impossible?

True.

It is an actual topological object.

If you search "Topological Figures" on a search engine, all you will see is computer-generated images of imaginary topological objects.  So quantum physicists typically use one-D to draw, represent, and understand an object that is 4- or 5-D.  Hmm, is there something amiss there?

How much easier would their comprehension be if they actually got their hands on real 4- or 5-D objects? Or better yet, grew one from scratch themselves?

I call Topological figures "Noble Shapes", because as you grow them on around the edge, they fold themselves into beautiful and distinct shapes.  In order to access the next adjacent gap, you will have to pull/push the edge four times for each row as you stitch the edge.  This results in different Shapes.  I call them Noble because they are symmetrical in the further dimensions, and are pleasing to the eye, yet defy description.  As well as during each row, the topological body-of-work will make new/different Noble Shapes when it gets bigger.

Below is a photo of a different Noble Shape made by the same Cook Twist.  The middle photo is a Noble Shape  with justeleven stitches of blue on Row 4.  (Row 0 is dark green). 

Above. The Cook Twist Noble Shape at Row Four complete.

Below, more Noble Shapes of the same Cook Twist.

I am wearing my phone inside

The edge in this photo is deceptive. It is orange edge completed only halfway around on blue edge "below" it.  The only way to see that is to actually hold it in your hands!

Other Topological Figures and Noble Shapes

               A plethora of possibilities

Above a different kind of Cook Twist.  The twist disappears from the edge after a few rounds.  I call it a Bowl on Two Holes.

I believe this is 5 half twists, not 4 because the twist does not disappear when I grew it on:

If you found this blog helpful, and/ or still cannot see real topological figures on Google Search, please help me. :  Go oogle are censoring my posts, the reason they give is that my posts are "unintelligable, unoriginal  and derivative".

You could complain to Google, share this post, and/or follow me.

Thanks, Lucinda Cook. 7 Feb 2023