Making Math

Four Geometric Sculptures

Geometric sculpture showcases the beauty of mathematics in a permanent way.  It captures the essence of math as a creative artform and makes it inviting and accessible to the general public.  Working as a group on the assembly of a sculpture becomes a metaphor for the collaborative process of solving mathematical problems.  Professional mathematicians often take great pleasure in working together to solve challenging puzzles.  The following sculpture activities immerse students in enjoyable collaborations that create an emotional connection to mathematics.

Sculpture differs from other art forms because it is the most tangible and has a strong physical presence.  Many sculptors encourage their audiences to touch the work in order to understand it at a more fundamental level.  Geometric sculpture allows this deeper interaction, which communicates mathematical concepts of pattern and structure in a tactile manner.  When students take part in a geometric sculpture build, they not only gain deeper understanding from the construction, but they also become personally invested in the final result.  This leads them to take ownership of the work, to ask meaningful questions, and to explain the process and ideas to others.

The following four activities provide teachers with templates and instructions for a progressively more challenging tetraptych of sculptural ways to make math visible in the classroom.  The four designs can be spread out over the school year following the four seasons.  Each design consists of sixty identical laser-cut pieces that assemble with cable ties to make a sculpture 25 inches in diameter. To prepare the parts, you need access to a laser cutter, plus three of the four require a sander to bevel edges.  In all four cases, the underlying symmetry relates to the icosahedron and dodecahedron, which gives students the opportunity to recognize patterns and discover recurring mathematical ideas.  And together, they make for a beautiful sculptural display.  If desired, the cable ties can be snipped at the end of the year and the parts can be reassembled by the following class.

Autumn.  Start your school year with this sculpture assembly activity.  You can choose either to make it monochromatic or with a color pattern.  After building this, students are ready for the design-your-own-sculpture activity below.

Winter.  In this design, all the pieces sit at the surface of a sphere, making for an elegant orb.  This one is particularly easy to make because the edges do not require beveling, so the parts can be prepared without a sander. 

Spring.  This sculpture involves a challenging assembly process because of the way the parts weave in and out through each other, alternating between two layers.  We've given it a two-color pattern here, with each part green on one side and yellow on the other.

Summer.  Your students will be proud to complete the set of four with this intricate puzzle which is a satisfying challenge to assemble.

In addition, we offer a fifth related activity in which students design and make an original sculpture with similar mathematical foundations.  This develops variations on the ideas from Autumn, above, which should be done beforehand:

Design Your Own Sculpture.  In this activity, students learn how the above sculptures combine mathematical constraints with the freedom to creatively choose certain portions of the design.  Each participant will sketch their own design, then the class chooses one to produce in paper.  It can optionally be produced by laser cutting afterward.

For general background on laser-cut wood sculpture, see this paper:
     G. Hart, "Laser-Cut Plywood and Cable-Tie Sculpture," Proceedings of Bridges 2015, (online copy)

The four were exhibited together for the first time at the 2017 National Math Festival in Washington, DC.