Math Challenge Corner

Jessica Korth's Spiral and Quilt Designs MAT Paper
Jessica Korth's Spiral and Quilt Designs MAT Paper

Spirals and Quilt Designs: featuring the work of Jessica Korth, OPS Math in the Middle Cohort 1.

Have you ever looked at a quilt and thought about the math behind it? Have you ever sat in class and drawn a spiral to consider its mathematical features? This paper looks at the history and mathematics behind a variety of spirals, focusing mainly on two, and includes step-by-step instructions for building a spiral and incorporating them into quilts. (It also includes some really cool photos of spirals which occur in architecture and nature!)

Jessica begins by introducing the history and mathematical features of two types of spirals: the logarithmic spiral and the Archimedean spiral. In the logarithmic spiral, the radius increases exponentially with the angle; in the Archimedean spiral, the radius increases at a rate that is proportional to the angle. Based on these descriptions, which of the spirals shown in the first row of the image is logarithmic and which is Archimedean?

While we believe it highly likely that readers of this newsletter will quickly identify the spiral types, we encourage a visit to to verify answers and to check out Jessica’s complete paper.

Jessica also examines the mathematics behind what is referred to as "Spiraling Squares," which can be used to form designs like the one shown in the quilt in the second row of the image.

Step-by-step instructions for reproducing several of the spirals are also included in the paper. Of special interest is the construction of the "Wheel of Theodorus," which requires the use of only a ruler, a note-card and a pencil (second row, second column of image).

In short, readers with an eye for geometric design, both in nature and on paper, will find much to enjoy.

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