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Crochet Hyperbolic Forest

The Hyperbolic Forest will be an exhibition at the next Festival of the Mind, from the 14th to the 25th September 2016 in Sheffield.

Our goal is to re-create a forest floor via knitting and crochet. We will emphasize crocheted mushrooms, leaves, flowers, etc, that have hyperbolic shapes, showing how those shapes appear everywhere in nature. We use this opportunity to demonstrate the beauty of geometry, and of hyperbolic geometry in particular: Explanatory videos and posters will be prepared jointly with a Summer research student and show-cased here and on the exhibition site.
Anybody can contribute and send us knitted or crochet reproductions of forest fauna and flora! (See below for more information on how to contribute.)

A little bit of Mathematics...

For 2000 years, since the publication of Euclid's elements around 300 BC, many geometers made attempts to prove the parallel postulate, which states that in a plane, given a line and a point not on it, exactly one line parallel to the given line can be drawn through the point. Their attempts failed because the parallel postulate is not provable from the other postulates, but their efforts led to the discovery of Hyperbolic Geometry: Bolyai, Gauss and Lobachevsky constructed in the early 19th century a new consistent geometry in which the parallel postulate does not hold.
Our goal here is to describe Hyperbolic Geometry, and what it means that "Hyperbolic Geometry is the geometry of a space of constant negative curvature".
In the following short videos, you will learn about...

... Euclidean Geometry (video by Fionntan Roukema).


... the curvature of a plane curve (video by Madeleine Jotz Lean).

... the curvature of a surface.

In further videos to appear later, we will describe the "straight lines", angles and areas on the pseudosphere, and we will talk about the models for hyperbolic geometry, which should be understood as maps of the pseudosphere, just as you would use a map of Sheffield to represent a part of the city on a piece of paper.

Here are some further videos by international colleagues, if you have become interested in the Hyperbolic Space:

Credits and inspiration

This project is inspired by Daina Taimina's idea to make models of the hyperbolic spaces via crochet. Here is her original article on the subject, jointly with David Henderson . An updated version was published in the Mathematical Intelligencer . Both David Henderson and Daina Taimina are professors of Pure Mathematics at Cornell University. Daina Taimina published a book "Crocheting Adventures with Hyperbolic Planes" that we warmly recommend reading. See here for her TEDxRiga talk on hyperbolic crochet. We are very thankful to Daina Taimina for kindly encouraging us to use her ideas for this project.
Note that Daina Taimina's ideas were previously used by Christine and Margaret Wertheim in their Crochet Coral Reef project.

Patterns and some pictures of already existing pieces

We will post here, as soon as they are ready, some patterns that are being developed by Kerry Rose, by our pattern makers and our research student Rosie Shewell-Brockway. We will also regularly upload pictures of incoming pieces of a particular hyperbolic flavour.

Trametes versicolor, photography
  by Nichola Denton

Information for crafters

You are free to reproduce via crochet or knitting any mushroom, leaf, flower, snail, etc, that you can find in nature. Of course, we would like to have as many pieces as possible that are shaped, if even only locally, like a hyperbolic surface. See
here for many pictures of hyperbolic crochet. You can also join our Facebook group if you would like to find, discuss or share ideas.
Please send your pieces by the 31st of August 2016 to
  Madeleine Jotz Lean
  School of Mathematics and Statistics
  The University of Sheffield
  Hicks building, Hounsfield road
  S3 7RH Sheffield
  UK
  
or alternatively, bring them in person to the porter of the Hicks building, at the main entrance.
Make sure to give us, alongside the piece, the name under which you would like to appear on our list of contributors on the exhibition site and here. You will not be remunerated for your work, but we will make donations to charities in the name of the crafters. We ask you to vote here for a charity.
Do not hesitate to contact us if you have any question.

About us...

Mike Futcher Mike Futcher is a digital animator with an interest in Mathematics and an interest in using animation for education: using the medium to explain complex concepts. Kerry Rose Kerry Rose is the initiator and leader of the project. After seeing an article on hyperbolic crochet, Kerry began to think of other ways to present the idea of hyperbolics as a learning tool within an exhibit and came up with the Hyperbolic Forest. As an artist, crafter, designer and seamstress/pattern maker she has a keen interest in mathematics and geometry and its application to the skilled arts and crafts. She loves foraging and the forest floor and hopes to present a visually stunning piece that will introduce people to the world of Hyperbolic Geometry and how it exists in nature. Madeleine Jotz Lean Madeleine Jotz Lean is a senior research fellow in Differential Geometry in the School of Mathematics and Statistics. Hyperbolic Geometry is a special branch of Differential Geometry, and can be best learned in a study of curves and surfaces, something that Madeleine has been teaching at undergraduate level for several years. She looks forward to exploring new ways of teaching some of the basic ideas to a wider audience, and especially to children.
Fionntan Roukema Fionntan Roukema is a research and teaching fellow in the School of Mathematics and Statistics. He is a great communicator and has years of experience in making Mathematics available to a wider audience, especially to secondary school students. Rosie Shewell Brockway Rosie Shewell-Brockway is a third year undergraduate in the School of Mathematics and Statistics. She is interested in many areas of Pure Mathematics and is yet to pick a favorite. She loves to knit and crochet, and really enjoys thinking about how they can be used to express mathematical ideas. Sarah Whitehouse Sarah Whitehouse is a Professor of Pure Mathematics in the School of Mathematics and Statistics. She is active in research in an area called algebraic topology and she very much enjoys teaching at all levels. This project is an exciting opportunity for her to be involved in introducing some mathematical ideas to a wider audience.

Sponsors

This project is funded by The University of Sheffield via the Festival of the Mind and via a SURE studentship .

May 2016 by M. Jotz Lean; background picture by Sarah Jotz.