Construction of Orderly Tangles
At Moravian College

Prof. George Hart

In February 2008, I visited Moravian College in Bethlehem Pennsylvania to give a lecture and give two workshops at their annual Student Mathematics Conference.   This web page shows one of the workshop activities I led during the visit.

In this workshop, we make Orderly Tangles from paper triangles. The theory is explained here.

The template looks like this. The triangular hole has half the edge length of the outside.

Start by cutting out the four equilateral triangles and their holes.

Start to put them together. Every pair is linked, so two start out like a chain and the third links each of the first two.

Some head-scratching is required to get the fourth one in position.

Extra hands are helpful to hold the parts in position, so it is good to work in pairs.

In the background you can see a computer animation I showed explaining the underlying concept.

It is much trickier than it looks, so we are pleased when it is completed.

In the lobby, I displayed a series of geometric models and puzzles.

For workshop instructions and more templates, see this paper.
Thank you Kevin Hartshorn for making all the arrangements.