We make things out of wood, stone, plastic, fabric, and … numbers. Professional designers first describe things as a set of points, distances, and angles on a computer. Then machines read these numbers as they turn virtual plans into physical objects. In this workshop, students will see the digital design and fabrication process first-hand as you create a vinyl sticker of your very own. Students will dream up a mathematical design, code it up in a programming language, and send the output to a programmable cutting tool.

Pixar animation and the maths that make them work. This is a video intended to pique their interest; you do not need to show the full 7.5 minutes. See here.

After a welcome, an introduction of facilitators, and a brief introduction to computer science, students will engage in two design activities. First, they will draw a composite shape out of rectangles and circles on graph paper, identify its mathematical properties, and code it up in a special geometric programming language developed by the instructor. Second, as time allows, they will draw a polygonal design and learn how to round off its corners using Bézier curves. The workshop will conclude with a reflection and a discussion of ways to continue learning at the intersection of mathematics and computer science. Students will leave the workshop with a vinyl sticker of their own design in hand.

Students will apply concepts related to spatial thinking, especially the Cartesian coordinate system, linear and angular measures, and the properties of circles, rectangles, and polygons. Students should feel comfortable drawing imaginatively. We will do our initial mathematical thinking on graph paper and not on the computer. Coding will be treated as a secondary translation of ideas about the physical world into a digital form.

• Mathematics - Students will navigate the Cartesian coordinate system; describe shapes in terms of their positions and dimensions; and learn how organic forms are modeled using quadratic and cubic functions via Bézier curves.
• Mechanical and Industrial Engineering - Modern structures and appliances are designed with digital modeling tools. The products, just like vinyl stickers, must be designed to withstand physical stresses and must satisfy many spatial and material constraints.

The ideas students encounter in this workshop are the same ones that Dr. Johnson encounters on a daily basis in computer graphics, web design, and game development. In a program, there is no nature arranging objects in space and giving them color and shape. That’s his job!

Paper artists design ornaments and sculptures and sell them using sites like Etsy. The final art form is often fragile and expensive to ship. Using the same concepts that we’ll discuss in the workshop, these artists can alternatively design their art in flat pieces that can be shipped more easily and assembled by the customer.

Industrial designers dream up the objects of our daily lives, from clocks to blenders to  cars. They first consider the space in which the objects will be placed and the physical properties of the materials used to manufacture them. Then they describe the shapes of these objects to a computer using mathematics and code, just as you will do in this workshop. See examples here and here.

The activities of this workshop are adapted from the opening day of a fabrication summer camp that we have held several times. A manuscript of that lesson is available here.