#### Event Type

Research Presentation

#### Academic Department

Mathematics and Statistics

#### Start Date

25-4-2022 12:00 AM

#### End Date

25-4-2022 12:00 AM

#### Description

The goal of exploring mathematical forms through crochet is to produce and explain mathematical objects and concepts to a general audience by allowing them to interact with a variety of crocheted items. Crochet was chosen as the method for representing the objects due to the sturdiness of crocheted surfaces and the ability to manipulate the crocheted objects in a way computer graphics cannot be manipulated. By crocheting different variations of a hyperbolic plane, with varying stitch ratios, one can observe how a hyperbolic plane is affected by exponential growth rate. One can observe that the less stitches a hyperbolic crochet pattern has between stitch increases, the more pronounced a hyperbolic plane’s “curls”. By having two crocheted mobius bands that are mirror-imaged, one can also illustrate the concept of how a Klein bottle is formed. Where one might have difficulty imagining a surface that has no distinction between inside and outside, by providing a craft-based visual representation, one can highlight the mathematical properties that go into composing the object.

Hyperbolic Geometry and Exploration of Mathematical Topology Through Crochet

The goal of exploring mathematical forms through crochet is to produce and explain mathematical objects and concepts to a general audience by allowing them to interact with a variety of crocheted items. Crochet was chosen as the method for representing the objects due to the sturdiness of crocheted surfaces and the ability to manipulate the crocheted objects in a way computer graphics cannot be manipulated. By crocheting different variations of a hyperbolic plane, with varying stitch ratios, one can observe how a hyperbolic plane is affected by exponential growth rate. One can observe that the less stitches a hyperbolic crochet pattern has between stitch increases, the more pronounced a hyperbolic plane’s “curls”. By having two crocheted mobius bands that are mirror-imaged, one can also illustrate the concept of how a Klein bottle is formed. Where one might have difficulty imagining a surface that has no distinction between inside and outside, by providing a craft-based visual representation, one can highlight the mathematical properties that go into composing the object.

## Comments

Under the direction of Dr. Molly Lynch.