Making Math

Wooden Catenary Arch

This seven-foot tall wooden catenary arch is a sculptural object and mathematical conversation piece that can be displayed in the classroom or the school.  It provides a wonderful culminating activity after students have constructed and experienced the paper catenary arch or the cardboard catenary arch.  It is appropriate for students at the middle- and high-school levels, however connecting the cable ties may be too challenging for younger students.  Everyone will enjoy having this beautiful sculptural creation in their classroom and will want to explain the concepts to others. 

We recommend first doing the paper catenary arch in order to give students a detailed understanding of the structure and the assembly process.  After that, relatively little instruction is needed for this wood version. 

If you want to try this workshop with younger students, we suggest that you prepare ahead of time by first doing the paper catenary workshop yourself, 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 modules go together, they will understand the structure to be made in wood.  Younger students will be able to position the pieces properly, but you may need to help them insert the cable ties.

Time Required for Assembly:  1 to 1.5 Hours


1.  This is the third 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. The template is scaled so that the larger parts just fit on a 12-by-24 inch sheet of wood.  If using a laser-cutter, you will want to arrange the parts to pack well on your laser-cutter bed. If sawing, use a drill to make the cable-tie holes.
3. For safety, the completed arch needs to be affixed to a base, a wall, or the ceiling, so it can not fall over.

Detailed Instructions

1. If students haven't made their own catenary arch, let them play with the paper modules you made.  Explain that the wood arch has the same 13-part triangular structure, but is different in that the modules are joined together without the doubled triangles.  They will be making a display object, not a balancing puzzle.

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.  Here, module F requires three parts: F0, F1, and F2, as shown above.  (The triangles will be added later.)  Instruct students to use cable ties to connect their parts 0, 1, and 2 in that order, with the writing on the lower left of each part.  Leave the cable ties loose initially to allow for flexing.

3. Flex the parts into a triangular prism module with the writing on the outside.  Use cable ties to join the third edge.  Tighten all the cable ties and clip their tails.

4. For the A modules only, you can attach the A triangle under it as a base.  Weaving the ties through all the holes is a little tricky and requires patience.  Encourage your students to take their time and not get frustrated.

5.  Make sure students understand that wherever two modules come together, there is a single triangle piece in between.  Each cable tie has to go through four holes to connect the pieces.  Students will come up with their own method and sequence for building the arch.  Consider laying out all the pieces in order on the floor.


6.  An option is to stain the parts.  Here, they are blue on the exterior and green on the interior.

7. When finished, you can stand it up and affix it to a base, a wall, or the ceiling.  Or take it to the beach...