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:
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.
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 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 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 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 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 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 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.