King students design and build the Quadrics Mobile

JC Fredette '21, Ronnie Harvey '22, Sammy Hillenmeyer '21, Nick Jiang '22, Nadia Kucher '21, and Joaquin Silvani '21 are all studying multivariable calculus with Mathematics Faculty Dr. Laura Toniolo. Recently, these six students had an opportunity to collaborate together to transform the theoretical material they learned in class into an actual product.

Guided by Dr. Toniolo and by Elisa Shapiro, Innovation Lab Director, the students worked in the Innovation Lab to use Tinkercad as a software product and to learn from the sites https://www.yeggi.com/q/quadric/https://cults3d.com/en/3d-model/various/quadric-surfaces-set, and thingiverse.com, to design, print and assemble a special mobile. Dr Toniolo explains that her students were excited to pursue this initiative in order to deepen their understanding of multivariable equations and to problem solve issues that inevitably come up in real-life applications.

To the untrained eye, this might look like a geometric mobile of undefined shapes.  Looking at it more deeply however, one would recognize ellipsoids, paraboloids, elliptic cones, and even hyperboloids, which are the extension to 3-dimensions (called quadrics, hence the name) of the conics these students studied at the beginning of their mathematical journey in high school.  

The students describe the experience of designing and creating the mobile, sharing: 

  • "Graphing quadrics in 3D is much more challenging than you would think, so by printing them, we were able to visualize what we had learned. Not only were we able to visualize our quadrics in a physical object, but we had to overcome several obstacles to ultimately balance our quadrics and create a functional mobile." - Nadia Kucher
  • "It was a great way to apply what we learned in the classroom to a real-life situation." - Sam Hillenmeyer
  • "It was cool to use what we learnt in Math class in a project and apply the knowledge on it. The project made the knowledge learnt in Math class more clear as we can see it in real life." - Nick Jiang
  • "It was a great challenge to overcome our early mistakes and build a balanced mobile. I think we all learned a lot about perseverance."- Ronnie Harvey
  • "3 iterations were necessary, but in the end, it was the struggle that lent itself to the final product." - JC Fredette
  • "It was cool to use something we learned in physics and apply it to the designing phase of this project."  - Joaquin Silvani

Dr. Toniolo adds that she "hopes that other students who see the Quadrics Mobile will become interested in investigating the meaning of these different shapes."  

Learn more about the King Upper School, about the STEM program and about how King students put their science research skills into practice.