Oftentimes, students don't realize that
mathematics can be used in creative ways. In this
workshop, they get to experience first-hand the process of
designing an original mathematical artwork. Based on an
understanding of geometric principles, they will propose a
design which satisfies mathematical constraints while also being
aesthetically pleasing. We have found that when students
are given the opportunity to take ownership of their work, they
become more confident and more fully invested in the learning
process.

- The
*Autumn*sculpture

- One copy of this rhombus
template per student on regular paper

- Pencils
- Card stock
- Access to photocopier

- Clear tape

- Scissors

1. We assume students have already built theAutumnsculpture, so are familiar with its structure and how its parts connect.

2. Allow time to make photocopies in the middle of this workshop.

3. The design and assembly can be naturally split over two days, giving students more design time.

5. Hand out the paper template sheets. Project or draw the image above of

6. Ask students to sketch the

7. Now students can start thinking of their own shape to build a sculpture from. Instruct them to first draw (darken in) their choice of segments where the pieces join. Give students the following constraints when choosing their segments:

- Each of the four rhombus edges must contain a segment.
- The left and the right sides must match.

- Each of their segments should be at least 30% (three ticks) of the rhombus edge so there is enough contact area for strength.

8. Students can then draw their own curves that connect the
segments. Suggest that they shade in the part to make clear
which regions, if any, are holes. Guide them to visualize
what their finished sculpture would look like if assembled from
sixty copies of the piece they designed. Point out that
there is also an engineering issue: the shape can not be too thin
or the part will flex and sculpture will not be rigid.

1. Ask students to display their designs and then choose one design which the class will make into a paper sculpture.

2. Using a photocopier, make sixty copies of the chosen template onto card stock.

3. Hand out the printed card stock, scissors, and tape. Ask students to cut out several copies each, so there are sixty pieces altogether for the class.

4. Direct students to tape the pieces together in the same manner as Autumn, first making three-part modules using the segments in the top half of the rhombus, then joining the modules in cycles of five using the segments in the bottom half of the rhombus. The result will be a unique original design.

5. Here is a student design in which the parts are shaped like a curvy letter H. The top of this page shows a student design in which the parts are shaped like the letter "Y". Note that this has mirror symmetry while Autumn does not.