We finished the first assignment of this course, and I have to say: it was more fun and less stressful than I thought it would be! I would like to give a special thank-you to Leon and TsáKtalay’pa for providing something unique to the project. To describe what each of us did, Leon was instrumental (pun not intended) in making the tensegrity table and coordinating the interactive activity where we gave groups of 3-4 the chance to make a da Vinci popsicle stick bridge with prizes, and TsáKtalay’pa provided his expertise on the history of bridges, vector forces and mathematical interpretations, running the activity timer, and answering questions. I also have to credit myself for providing the inspiration and diagrams for the mathematical and artistic extensions segment of the project, as well as conducting the extension experiment that can be seen on the last slide. The slide deck was made in an afternoon with contributions from all three of us. All in all, everyone contributed greatly and our project wouldn't have felt as good as it did if even one person was missing.
Pictured: The original tensegrity table math art by Owen Rohm, and Leon's duct tape cardboard tensegrity table which took 2.5 hours to make (according to him)
Pictured: The step-by-step visual guide on how to assemble the popsicle stick bridges for our interactive activity
Pictured: The theoretical diagram of our proposed extension of the tensegrity table - the Extended Tensegrity Arch
As for my experiences with working on and presenting the project, I have to say it went a little differently from what I expected. After working on the slide deck about four days before the actual presentation, the Extended Tensegrity Arch diagram (as shown above) bothered me a lot. Initially, I wanted to take that afternoon to assemble the ETA, but after Leon mentioned the sheer length of time it took to assemble even one tensegrity table unit, I decided to cut my losses. However, I had time on the weekend, so I took it upon myself to make a toy model of 5 smaller tensegrity table units.
Even making one unit was very challenging. That, or I lacked the dexterity.
After scrambling to get one unit assembled, I instantly flipped it on its side in accordance to the ETA diagram that I drew in order to learn more... and voila! It was staying still despite being sideways, which was in line with my hypothesis. I was inspired by spaghetti bridges made for my high school physics classes. The spaghetti bridges would have weights incrementally added underneath, and oftentimes the first snapping point was actually at the top where the compressive forces made the bridges buckle. As such, I thought: since the tensegrity table's main draw is its ability to resist compression while maintaining its form, why not use that same principle in a bridge? That was the hypothesis, and it felt great when it was proven true. Even better, I got to understand the need for the non-central threads to hold the tensegrity table together by snipping it with a scissor (as seen in the last slide's video).
On presentation day, I think my biggest surprise was how hard it was for someone to make a popsicle bridge if they had no prior experience with it. None of the groups could form the 9 popsicle (3 middle segments) stick bridge within 5 minutes, and the longest bridge category was won by a bridge with only 2 middle segments. Other than that, the positive reception felt really good, and the payoff for my inquiry into my diagram's hypothesis was equally great. We were able to make an impromptu discussion on what should be done to the top of the middle unit and whether the arch was plausible or not, and in the end I was able to shed a bit of light on my findings! I still think it is unfortunate that we weren't able to make the full ETA, but I am still proud nonetheless for taking it as far as I did.
I also want to apologize to every group that came after us, considering how distracting the popsicle sticks were. If I ever hold any activities related to popsicle sticks, I will be sure to collect them back before starting something new.
As for the potential of this project in my own teaching, I feel that due to the foundation of physics that holds up the art piece, there is an inherent parallel with physics that would manifest. I found that the ETA diagram was a major inspiration for integrating the project into teaching, and one would notice that it resembles a complex free-body diagram which is a key element of understanding physics. Not only that, but due to the ambiguous yet plausible nature of the diagram, it raises a whole slew of questions that we can get students discussing! Even during the presentation, we've had people questioning whether the arch can really hold up against gravity and itself, questioning the placements of the strings, and theorizing about what would be needed in order for the top unit to stay in equilibrium -- all things that we can get students to think about in a case study fashion in order to build their spatial reasoning skills (I want to credit Leon for bringing up this skill to our group, which I also think is great for general relational mathematics). It would also be cool to get students to draw their own free-body diagrams as part of a debating process in order to defend their own tension-based construct designs, which would serve to exercise their critical thinking, visual and verbal communication skills. If we want to get wild, perhaps encouraging students to experiment with toy models to verify their diagrams like I did, which could increase the amount of "play" happening! There's also a tie-in to the historical aspects of the physics and the contextual premise as well; bridges come as part of humanity's long history, as well as being a long-used subject of applied mathematics (think of how much bridges are brought up in the field of engineering, and not just the Tacoma Narrows Bridge collapse). It would also be useful to promote elements of the history of mathematics through this extension. I could also see myself asking students on how they could further extend the ETA, using the same principles that allowed the ETA to be plausible. Could we make it 3-dimensional and create a super-extended tensegrity DOME? Maybe we could create a leaning tower of tensegrity tables -- the possibilities are endless.
In terms of what couldn't be used: I'm going to go with having students constructing their own tensegrity tables, at least within a short timeframe. It is a far more challenging task than making popsicle stick da Vinci bridges, which is saying something considering how difficult it was for many people to make da Vinci bridges (though da Vinci bridges may be more in the realm of possibility). It may also be challenging to find a curricular unit to naturally segway from and to this art piece depending on the course, but it could be possible to bring up tension-based art and structures during miscellaneous instructional time as a fun brain teaser (for example).
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