Mathematical Knitting — 3D Objects

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. Past mathematical knitters have shown the relationship between knitting and algebra or highly complex shapes (such as a Klein bottle or Möbius strip). Knitting is a wonderful and interesting tool to understand how math works in our tangible world. One of my favorite types of math is calculus — specifically how we use calculus to describe geometric shapes we see all around us.

This interest led me to create patterns for mathematically accurate knitted cones and paraboloids. We see these shapes in our world often which makes the concepts more tangible and introduces mathematical concepts we can relate to our everyday experience. In this project, I created patterns for mathematically accurate geometric shapes, to directly show the relationship between the mathematical formulas, knitting patterns, and knitted objects. There are infinite ways to understand and perceive math, one of which is knitting.

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. With these patterns, you can create any size cone or paraboloid!

If you want to make some mathematical shapes without doing the calculations, my patterns for three specific-sized cones and paraboloids are for you! I want anyone, regardless of their mathematical background or experience, to be able to explore these concepts and create a mathematically accurate cone or paraboloid.

The Primary Mathematical Focuses of These Patterns:

• Exploration of 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

• The accessibility of mathematical concepts across multiple teaching/learning methods.

For More Information…

• Mathematical Knitting

  • dr. sarah-marie belcastro is one of the leading experts on mathematical knitting. Her website has a wealth of knowledge including many patterns (most available on Ravelry), her published books about the topic, and much more! There are also links to mathematics in other fiber arts, not just knitting.

• About These Patterns

  • Please reach out to me with any questions! You can use the Contact form or send me an email at hello.cmw.create@gmail.com. Please include “Mathematical Knitting“ in the subject.

  • Visit my Ravelry designer page. You can message me or add me as a friend on Ravelry if that is preferred!