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Comments on Lecture 10 "Topology-Disturbing Objects"

Comment 1. Decomposition of the crossing three circles

The counter part consists of three co-centric circles, and so we have to decompose the crossing three circles into three elements with the same widths as the associated circles. For that purpose we can decompose as shown in the left diagram, where we displaced the touching vertices in the vertical direction so that each component becomes clear.

Comment 2. Unfolded surface of a topology-disturbing two cylinders for paper crafting

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The diagram of the unfolded surface is placed here.

Reference on the topology-disturbing objects

K. Sugihara: Topology-disturbing objects: A new class of 3D optical illusion. Journal of Mathematics and the Arts, vol. 12 (2018), issue 1, pp. 2-18.
(This paper was selected as one of the Best Writing on Mathematics 2019, and is included in: Mircea Pitici (Ed.), The Best Writing on Mathematics 2019, Princeton University Press.)

Comment 4. For those who want to construct a topology-disturbing object from a kit


Illusion Trick Kit (in Japanese) (Gento-Sha Publisher)
It contains five objects, one of which is a topoloty-disturbing object. It appears to be a separated pair of rectangular cylinders in one view, and appears to be an intersecting pair in the other view.