Week 8 (Mathematics & fibre arts, fashion arts and culinary arts )

 Reading Reflection:

 Gwen Fisher (Bridges 2015) Highly unlikely triangles bead weaving

In this paper Gwen Fisher has described their work on using impossible triangles and its variations to create a series of sculptures with beads using a bead weaving technique. The beaded art objects generated surfaces that twist like Mobius bands around the objects. 

STOP - What are impossible triangles

This is an unfamiliar subject to me, So I took some time to understand the concept of impossible triangles. As per Fisher(2015), impossible triangles are two dimensional drawings that represent three straight beams with square cross sections and the beams appear to meet at right angle. An impossible triangle is only impossible to be constructed in 3d (assuming edges are straight and connections are right angles. While in two dimensional drawing, they are not actually impossible, they just seem to twist in an impossible way. Below is an image for impossible triangles:

STOP - Beading the highly unlikely triangle

Fisher states that a beaded version of an impossible triangle is very much possible because of flexibility of beadwork. In the beadwork, the twist allows the impossible triangle to be constructed in 3d. 

This was very interesting to me as it doesnot appear very intuitive. The figure below shoes the highly unlikely triangles in three sizes:

Fisher showed in detail about how to convert an impossible triangle into a beaded version. As depicted in the image below, they talked about imagining the beams as little cubes. And then place beads on each line segment of the cube so that the hole of the bead is aligned with the line segment. 

Then beads are woven together with the beaded cubic right angle weave (I didn't fully understand this technique just by looking at the images)

Overall, the work as described in the article at first glance was very confusing and beyond comprehension for me. Upon reading multiple times and deeper analysis, I got some basic idea of the complex beading technique that was involved in creating beaded versions of impossible triangles.

In my teaching practice, I have only used beading in making bracelets to show repeated patterns in terms of repeated rows and columns and have also used beading for helping to learn area and perimeter. 

I have not used beading for anything more complex or anything remotely similar to constructing impossible triangles.

Question - In what context have you used beading in mathematics classrooms? 

Activity

 

For the activity this week, I tried shoe lacing activity. I chose this activity as  lately I have observed that I am not very good at tying my daughter’s skating shoe laces. My toddlers have been wearing the Velcro shoes, and my older one recently started her skating lessons, and I have been helping her tie the shoelaces  but I have noticed that in the just rush of getting her ready of skating lessons, I have been ending up with either uneven length of laces ends or too short of ends. This morning I tried to tie her laces with a different method, but in the end I had to come back to criss cross tying as that's the only technique I have ever used myself and seems very intuitive. Any other method seems very confusing. I would definitely be going back to the video as this is something I would like to improve on especially to make the lace tying more clean and neat looking.