This week's activity engaged me in a predictable struggle lol. I have difficulties with orienting the paper correctly. I wish the people in such videos didn’t hold up their paper and turn it all around for us to see until they are done. Simply, fold then flip or rotate in the most efficient way possible. This would leave me guessing less. Although I did get the Miura Ora Origami folds after the third attempt. Interesting math here might be how efficient the new structure is at compacting the surface area.
I read Highly Unlikely Triangles and Other Impossible Figures in Bead Weaving by Fisher, G. (2015). Gwen’s inspiration for her woven beaded sculptures came from Oscar Reutersvard’s 1934 Impossible Triangle. Impossible triangles are a “two-dimensional drawing that represents three straight beams with square cross sections, and the beams appear to meet at right angles.” (p. 99) Impossible polygons are a natural extension of this optical illusion.
(Fisher, 2015, p. 99)
Gwen notes that the flexibility of weaving beads removes the optical illusion of the 2D drawings. This is why she refers to her creations as unlikely triangles and polygons instead of impossible. The beading medium allows for techniques like turns and twists or varying sizes and directions. As well as curvature which removes the straight edges of the 2D drawings. Other techniques with this medium include strategic use of bead size, colors, and placements. Bead color can be used to show paths, lines, faces, and vertices.
(Fisher, 2015, p. 102)
A stop that came to me was caused by the uniqueness of the medium and the techniques which allowed for a different take on the impossible triangle versus the 2D paper. As well, as when Gwen mentioned how graphic designer M.C. Escher used the impossible triangle in some of his drawings. The contrast between 2D paper and 3D woven bead sculptures cause me to think of Marshall McLuhan's “the medium is the message”. “Each medium, independent of the content it mediates, has its own intrinsic effects which are its unique message.” (McLuhan, E) The beading medium allows for a new take on what paper says are impossible constructions.
This kind of flows to Gwen’s desire to make a highly unlikely dodecahedron that shows the ten distinct paths (loops) that occur when moving through the twists and turns of the medium. She referred to this as passing through levels of hierarchy.
(Fisher, 2015, p. 105)
I also was drawn to the uniqueness of the mediums, and the possible messages that come from each, when I watched the videos. In particular Yackel, who said “wallpaper patterns are realized through the dyeing process”. I appreciated the uniqueness of techniques and limitations that come with the medium, 2D paper is not infinite like the patterns it is trying to capture. Her use of the words constraints and resists - the tightness/clamping of the cloth prevents the dye from entering the cloth - both highlight the uniqueness of the medium. It is also fun to think of the folds as allowing a 2D paper to briefly enter the 3D world, which was similar to Gwen’s mention of passing through levels of hierarchy.
(Yackel, 2020)
References:
McLuhan, E. (2024). Commonly asked questions about McLuhan – the estate of Marshall McLuhan. Ginkgo Press. https://www.marshallmcluhan.com/common-questions/
I greatly admire your willingness to take on the paper folding activity! My experiences with origami have mostly left me with nothing to show for it but crumpled paper. I love the orange design and how you were able to create repeating triangular patterns; it inspired me to look at the activity after all and consider trying it with my students!
ReplyDeleteI never connected traditional beading techniques with this level of geometry! It reminded me a lot of the Salish artist I wrote about a few weeks ago who uses geometric shapes and repeating patterns to create traditional Indigenous art. The collision of new and old makes for a very thought-provoking piece of artwork, and also highlights that these mathematical ideas have existed in art long before they were explicit.
Hi Shawn,
ReplyDeleteThe beadwork is quite striking to look at as well as demonstrates complex mathematical ideas. I have been so amazed at how intricately all the artistic models demonstrate the concepts they are based on. When I used to hear the term "using alternative ways to represent/express understanding" I couldn't see how math could be expressed in other ways. This course certainly has shown us multiple ways this can be done. it is certainly not an easier alternative, it requires deep thinking and deep knowledge of a topic to be able to express it in another medium.
I think it's been important that we got to read in depth about the mathematics behind the artistic works, even though I am often finding myself having to research the concepts such as the Klein bottle. It's been a mental workout for me at times. It's really driven home the point that the "art" is simply not alongside the math, the math often actually drives the model and how it is created.
I am impressed with your final chevron folding...you made out better than I did!