Week 10 Reading Reflection on
Highly Unlikely Triangles and Other Impossible Figures in Bead Weaving
by
Gwen L. Fisher
In this paper, Gwen L. Fisher describes how impossible triangles are used to create sculptures with beads and thread, using a technique called "cubic right angle weave"(CRAW). "The impossible triangle, also called the Penrose triangle, is a two-dimensional drawing that represents three straight beams with square cross sections, and the beams appear to meet at right angles"(p.100).
The impossible triangle
The impossible triangle was independently discovered by the mathematician Roger Penrose, and a graphic designer M.C. Escher, who, in turn, used it in his art. The beaded version of an impossible triangle is quite possible and it is not very intuitive. The twist in the beadwork allows the impossible triangle to be constructed in 3D.
Here is the link for mathematical beading by Gwen L. Fisher,
I have found this video of making ear studs by beading
"A highly unlikely polygon is a beaded polygon whose edges are rectangular beams with a quarter twist. For a highly unlikely polygon with an odd number of beams (e.g., the triangle), there is a single path on the face that travels around the polygon four times. When the polygon is a square, the path on the faces separates into four, distinct paths that each travel all the way around the polygon only once. Similarly, there are four paths for the edges."(p.102)
Stop
"To resolve the paradox of the impossible triangle, a highly unlikely triangle exhibits a quarter twist on each beam. The twist in the beadwork allows the impossible triangle to be constructed in 3D. The twist in the beaded version also destroys the optical illusion due to the curvature it introduces to the edges that appear straight in the 2D drawing."(p.100)
The author's reaction to making an impossible triangle struck me because we may feel that everything is impossible when we first see it. When we see an impossible triangle we may feel like creating it is a difficult task because it is how our brains interpret shapes. It seems like a puzzle that makes you confused about what is real and what is not where to start and where to end. When we relate it with art we get a solution.
Question
What makes the highly unlikely triangle different from regular triangles, and how does it mess with our brains?Do you feel it like easy to make?
Reference
Fisher, G. L. (2015). Highly Unlikely Triangles and Other Impossible Figures in Bead Weaving. In Proceedings of Bridges 2015: Mathematics, Music, Art, Architecture, Culture. Sunnyvale, CA, USA: beAd Infinitum.
I believe that the "unlikely triangle" is different from a regular triangle because of the optical illusion it creates. The way it is constructed gives the impression that the edges do not touch and the surfaces invert, similar to a mobius strip where the interior becomes the exterior. I think it would be challenging to create this triangle without knowing the proper technique, similar to making a mobius strip.
ReplyDeleteThe unlikely triangles diverges from regular triangles by appearing to form a continuous three-dimensional loop that defies conventional spatial logic, thus creating a compelling optical illusion. Our brains, accustomed to processing visual information based on the physical world, are intrigued and puzzled by this impossible figure because it suggests a structure that cannot exist in three-dimensional space. While drawing this triangle might seem straightforward to those experienced with optical illusions, constructing it in three dimensions to preserve the illusion from specific viewpoints requires a clever manipulation of perspective and design, making it an engaging yet complex task.
ReplyDeleteThe Penrose triangle differs from regular triangles due to its optical illusion of a three-dimensional object with a seemingly continuous looping of its sides, defying the rules of Euclidean geometry. This illusion tricks our brains by suggesting a spatial structure that cannot exist in three-dimensional space, challenging our understanding of perspective and depth. Creating a Penrose triangle on paper or as a 2D illustration is pretty easy, involving careful drawing to achieve the desired optical illusion. However, I feel constructing a 3D model would require more effort to maintain the illusion from all viewing angles.
ReplyDelete