Fahmina Ahmed
sqrt(x^2 - y^2 - z^2)
Sculpture
November 2012

I was taught two different ways of thinking about design; starting either at the top with pure geometric ideas, or at the bottom by teasing out the inherent logic of materials.

As architects, we often start the design process with sketches and computer renderings based on the pricipals of point, line, and plane. As we get further along the design process, we begin to asign thickness and scale to our ideas. Further down the process, our ideas take on a life of their own, as we begin to determine the construction materials and methods. For this sculpture, I wanted to create a pure and abstract form that demonstrates all stages of this process and the ways in which they interact.

I explored the tension between the two approaches to design that I was taught by approximating a pure platonic form through a distinctly handmade material process.

Design Phase

I decided to build a sculpture based on the following mathematical question, as it came to me in class one day:

Picture a sphere circumscribed in a cube. Now imagine a grid of lines that intersects this shape from top to bottom. For each line, determine which points, if any, intersect the sphere.

To figure it out, I wrote a script in python that calculated the height at which each line began to intersect the sphere. I used this script to model my sculpture in rhino. Based on my renderings, I continued to tweak the spacing between each line in order to create the best illusion of a sphere drawn onto the strings. I realized that in places where the sphere curves steepest, I need lines to be closer together in order for the human eye to read them as part of the sphere.

Construction Phase


During the construction phase, we begin to choose our materials and hammer out our construction methods. This phase is when our ideas begin to come to life. Unlike in the theoretical design phase, the construction phase is full of decisions that have tactile and material consequences. One must begin to consider the grain of wood, the warping of twine, and be guided by the inherint logic of each material.

I chose to build a plywood structure that held two 4' by 4' pieces of wood exactly 4' apart from each other. This structure had to support my weight and be elevated far enough off the ground so that I could crawl under it to tie my strings. I chose twine because of the way its expressive, handmade quality contrasted with the abstract and perfect mathematical equation I was working with.

I began by drilling holes in the appropriate coordinates on each plane of wood. I then strung the twine row by row by crawling under and sitting inside my structure. After each comleted row, I painted each line of twine according to the calculations from my python script.

In this way, string by string, I created a 3D drawing, translating my python script into a physical object.