Senior Project Advisor

Dr. Jessica Cohen

Document Type


Publication Date

Spring 2020


knitting, mathematics, mathematical knitting, geometric shapes, knitting patterns, Honors Capstone


When knitting 3-D objects such as hats or socks, the knitter is using geometry and mathematics to make the 2-dimensional string into 3-dimensional shapes. In this project, I will be creating mathematically accurate, geometric shapes, to directly show the relationship between the mathematical formulas, knitting patterns, and the knitted objects. There is more than one way to understand and perceive math, one of which is knitting. Past mathematical knitters have shown the relationship between algebra and complex shapes (such as a Klein bottle or Möbius strip) and knitting. In an effort to explore how more accessible mathematical shapes and concepts relate to knitted objects, I created patterns for knitted cones and paraboloids.

In doing this, I created versions of the patterns that allow knitters to solve formulas and use Excel spreadsheets to develop a pattern for a cone or paraboloid that is consistent with the mathematical formulas of the shape. Additionally, I created patterns three specific sized cones and paraboloids so that anyone, regardless of their mathematical background or experience, could create a mathematically accurate cone or paraboloid.

This project explored how a fixed rate of decrease differed from a changing rate of decrease, the relationship between the absolute world of knitting (0 or 1; no decimals) and the infinite world of mathematics, and the accessibility of mathematical concepts across multiple platforms.



Subjects - Topical (LCSH)

Knitting--Mathematical models; Geometrical models


presentations (communicative events)




Copying of this document in whole or in part is allowable only for scholarly purposes. It is understood, however, that any copying or publication of this document for commercial purposes, or for financial gain, shall not be allowed without the author’s written permission.





Included in

Mathematics Commons