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Scott Sherman’s approach to flexagons – the big picture

In this article, Dr Yossi Elran describes Scott Sherman’s approach to flexagons from a birds-eye view.
Scott Sherman (center)  at the Neil Shore Recreational Math Workshop in Israel in 2019
© Davidson Institute of Science Education, Weizmann Institute of Science

The big picture

Scott Sherman’s flexagonator program and his approach to flexagons in general has made a significant impact on the study of flexagons.

Coming from the perspective of a computer scientist, his approach is focused on the structural change of flexagons when manipulated by hand. Pat notation is a great way to describe the inner structure of flexagons, and when combined with flex notation we can accurately describe, and predict, the structure of the flexagon after every move. This way, flexagons can be built up, flex by flex, as we did in the second week of this course.

Scott has now moved on to “atomic flex notation”, where every flex is broken down into several independent movements. This is a great way to discover new flexes without even having to make a physical model of the flexagon, and indeed, Scott has discovered many new slot flexes using this notation, yet to be published.

Scott’s method, which is based on a “computational thinking” approach, does have its drawbacks though. For one, although in theory, it can be used for all flexagons, at the moment it only tackles edge flexagons with triangular leaves. There are many other kinds of flexagons, including all the point flexagons and some more complex flexagons – of the kind we’ll see when we get to Les Pook’s approach. Also, the methodology of building flexagons by searching for structures that support certain flexes, immediately restricts them to the set of the flexes you start out with, which cannot be exhaustive (although atomic flex notation should at least partially solve this problem).

Discussion

Can you think of any more pros and cons of Scott Sherman’s approach? If so, please post below so that we can answer!

© Davidson Institute of Science Education, Weizmann Institute of Science
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