It All Started with Hyperbolics..

A group of us are studying Textiles Installation as an elective at university and for our final project we must create a model representing hyperbolic space. Furthermore its context must be derived from a concept of our choice.

What is hyperbolic space?

Hyperbolic space: A space described by hyperbolic rather than cartesian coordinates. (Farlex 2010)

The distinguishing characteristic of hyperbolic space is that as you move further away from a point the space around it expands exponentially. (Taimina 2010)

Another property that differentiate it from a normal plane is that here are infinitely many lines passing throguh a given point parallel to a given line in a hyperbolic plane.

From the brief there are two methods we may use to represent hyperbolic space, these are sewing a series of geometric shapes or using crochet.

Woodcut by M.C Esher

1. Geometric Shapes

Using coloured cardboard and a paper template we explored the possibility of using a combination of triangles and regular heptagons repeatedly to create a hyperbolic model.

Here are some photos of the process..

Cut up cardboard shapes ready to be assembled

assembling

taking shape

final mock up model

2. Crochet

For most of us this was our first time learning how to crochet initially there were some issues but once we mastered the technique it became a simply and repetitive process which is somewhat therapeutic.

Here are some of our first attempts at crochets..

lost a few loops resulted in this..

A added a 2nd stitch a bit late and ended up with a hat shape

Learning from our mistakes our second attempt was much more successful.

first few rows..

you can finally see the wool crenulating

Final practise

After practise we were able to create the desired shapes.