# Cardboard Catenary Arch

The cardboard catenary arch is a fun project for any classroom.  It is appropriate for students of all levels and provides an enjoyable construction challenge that is a vehicle for the exploration of mathematical ideas.  Students will enjoy having this beautiful sculptural creation in their classroom which will engage them continuously as they repeatedly rebuild it.

With middle school and older students, we recommend first doing the paper catenary arch in order to give them a detailed understanding of the structure and assembly process.  After that, very little instruction is needed for the cardboard version.

With younger students, we suggest that the teacher prepares ahead of time by doing the paper catenary workshop themselves, both to internalize the details and to have a finished paper version for students to play with.  Once students are familiar with how the paper catenary goes together, they will have a better sense of what they will make in cardboard and why, as well as an understanding of the importance of accuracy and teamwork.

Time Required for Assembly:  1 Hour

Materials:
• A model of the paper catenary arch
• Corrugated cardboard, cut using this template.  (e.g., http://www.uline.com/BL_1851/Large-Corrugated-Pads) Four each are required of Triangles B-G.  Two each of parts A0, A1, A2, B0, B1, B2, C0, C1, C2, D0, D1, D2, E0, E1, E2, F0, F1, F2, Triangle A.  One each of parts G0, G1, G2.
• Several rolls of packing tape
Notes:

1.  This is the second of a series of three catenary arch workshops.  If you want to create a three-part lesson, use the Minds-On and Conclusion from the paper arch workshop.
2.  The parts can be sawed or laser-cut ahead of time by the teacher or by students in a shop environment. A utility knife could be used instead, but we don't recommend that for students. The template is scaled so that the larger parts just fit on a 12-by-24 inch sheet of cardboard.  You will want to arrange the parts to pack well on your laser-cutter bed size.  If using a laser-cutter, be aware that laser-cut cardboard can sometimes have sharp edges, which can be dulled if necessary with a piece of sand paper.
3.  It is much easier to apply the tape if you use a dispenser.

Detailed Instructions

1. If students haven't made their own catenary arch, let them play with the one you made.  They will discover how the thirteen parts balance and lean on each other to make a stable structure.

2. There are thirteen modules to be assembled.  Divide the class into groups so that everyone can participate.  Hand out the proper pieces to each group.  The parts are labeled with the same system as for the paper arch.  For example, module C requires five parts: C0, C1, C2, triangle C and triangle D, as shown above.

3. Instruct students to tape together their parts 0, 1, and 2 in that order, with the writing on the lower left of each part.  Leave some space between the parts to allow for folding.  Tell students that rubbing the tape into the cardboard with their fingernails makes for stronger adhesion.

4. Fold the parts into a triangular prism with the writing on the outside.  Tape the third edge.

5. Use tape to attach the triangles to the ends.  The larger triangle goes on the end with the writing.

6.  If students have done the paper arch workshop, they will know what to do without further instruction.  Allow them time to organize themselves and play.  If the students are new to this arch design, guide them in properly lining up the modules.  Remind students that the spacing between the base pieces is crucial.

7.  Students will work together to balance the pieces for the exciting result.