Math + Making

A student blog for Math 189AH: Making Mathematics at Harvey Mudd College

Parabolic Curve String Art

Tia Tounesi

For the final project, I designed and constructed a string art pyramid using parabolic curve stitching techniques. I aimed to reimagine traditional “nail, hammer, and a plank of wood” string art to a smoother way that utilizes makerspace resources in a three-dimensional form.

I first designed the sides of the pyramid using Adobe Illustrator. My initial vision was to create a flat, flush base for the pyramid. To achieve this, I calculated that the internal angles at the tip of each side needed to be 30 degrees. This design ensures that when two sides connect, they form a 60-degree angle, creating an equilateral triangle.

Figure 1: Design of the Pyramid’s Based

In traditional string art, nails are hammered into a wooden surface and strings are then wrapped around these nails to create an image. However, given the smaller scale of my pyramid, using nails would have made the artwork appear overly bulky. Instead, I marked 21 equidistant points along each side and designed lines through these points for laser-cut notches. This adjustment allowed me to replicate the string art effect without the bulkiness of nails. I created three identical sides to form the base of the equilateral triangle.

 Figure 2: Laser Cutting the Sides + Notches and the Finished Pyramid Base

After constructing the base, the next step was to design three protruding sides that would come together at the top to form a triangle. The connecting angles at the base were set at 60 degrees, whereas the apex angles were 30 degrees. Similar to the base, these sides featured equidistant notches that were precisely cut with a laser. The pieces were then assembled using super glue and painted black to conceal any residue from the laser cutting process.

With the structural elements complete, I turned my attention to designing the string art. Initially, I experimented with string patterns on square bases to understand how they could be adapted to triangular forms. I drew two perpendicular lines, marked an equal number of equidistant points on each, and then connected these points in a way that resembled an xy-axis. This method was replicated across all three sides, resulting in the creation of a unique parabolic curve pattern.

Figure 3: Parabolic Curve Stitching Design on perpendicular lines.

Once adapted to the triangular form, the design was applied uniformly to all three sides, culminating in the visual depicted in Figure 4.

Figure 4:  Parabolic Curve Stitching Design on a triangle.

To finalize the project, I selected colorful and sparkly thread to contrast strikingly against the jet-black pyramid structure. This design element was consistently applied to all three corners of each face, resulting in a total of nine intricately decorated corners.


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