Thread Geometry

We explored what kind of geometric constructions we can do with thread, chalk and the help of several people...

We found out...

  • how to draw a line
  • how to draw a circle ( d = const.)
  • how to draw an ellipse ( a + b = const.)
  • how to draw multifocal ellipses (a + b + c = const.)
  • how to draw egg-shaped curves (3 * a + b = const.)
  • how to measure the circumference of a circle
  • how to calcualte pi using only thread (See also here)

3D thread geometry

We explored how our thread-based drawing tools could be used to identify points on the surface of shapes in 3 dimensions.

  • We discovered the 3d ellipsoid (a + b = const.)
  • We found that multifocal 3d ellipsoids have a doughnut-topology.
  • We found two different ways to create ellipsoid shapes:
    • the polygon method, where the thread forms a polygon going through the focal points and the drawing point
    • the star method where the thread is alternately visiting each focal point and the drawing point


  • Geometric knowledge from school only got us so far ...
  • There is a whole universe of "new" shapes and forms

Questions raised

  • Questions regarding surface of different shapes popped up
  • We discussed different methods of measuring the surfaces using thread


  • What could an Experimentier-Baukasten / a kit / a sandbox for computing with thread look like?
    Do some research on other kinds of kits!
  • Do some thread-based geometry at home. Pick a parameter such as the thread-length and vary it systematically
  • Document your thread-art in the wiki



Some links to classics of compass + straightedge geometry
as well as the thread-based geometry we explored in our class.



Compass and Straightedge


Here are some links to all kinds of kits.
May they serve as inspiration for creating your own textile computing kits.

Educational Kits

Sewing Boxes

Tool Boxes

Portable Textile tools

Knots and Splices

Knot History

  • various knot books online and offline
  • We learned how ropes are made in a "Seilerei" on the "Reeperbahn"
  • We learned about a rope inspection machine, that travels along a the cable of a "Seilbahn"

Knot Theory

  • We learned the basics of knot theory
  • Minimum number of crossings
  • Knot-Invariants and Knot-Polynomials

Knot Classification Game

We played a knot identification game.
It goes like this:

  • Student A creates two knots using thread.
  • Student B tries to figure out whether or not the two knots are the same


Create a nice framework for displaying knots.
The framework can be physical, graphical or computational in nature


How are threads made?

Thread Games



Unknotting with Force and Magic


Knot Theory

Tie Knotting


Knot Robot


In this class we identified the basic elements of braids, and explored the intersection of braiding and sorting algorithms.

Communication game

  • We developed and discussed different notations for braiding
  • We played a game involving three persons
    • The first person creates a braid
    • The second person describes the structure or construction of the braid using words only
    • The third person recreates the braids accordingly


  • There are different ways to describe the structure of a braid
    • structure vs construction
    • position-based vs thread-based
  • Some instructions will not result in a braid
  • Some systems are simpler than others, but may not be universal in the sense that they can describe every possible braid

Sorting Braids

  • We discussed why sorting is an important topic in computer science
  • We got to know the concept of computational complexity and the big-o notation
  • We re-enacted several sorting algorithms using threads and chalk
  • We developed collaborative sorting algorithms resulting in braids


  • Bubblesort is a fun collaborative activity
  • The mapping from sorting operations to operations of textile construction is important
  • If the mapping is bad the result may not be a stable (overs and unders)
  • If the mapping is bad the result may not be dense (no-ops vs crossings)
  • Sorting networks allow for parallel sorting / braiding




Computational Complexity

Braiding + Card Weaving

Braiding Techniques

Braiding Tools

Rope Weaving



In this class we had a look at graphs and networks, both in the textile and the social domain.

Network Analysis

We had a look at knotted networks and discussed possible representations

  • We discussed which properties of the textile net are important, and which properties can be abstracted away
  • We looked at different ways of creating a network from single pieces of thread or a single continuous piece of thread
  • We found that a graph representation may not be a suitable model for textile networks
    • If we care about the network structure, nodes of degree two (a node with two edges) may not be meaningful
    • However nodes of degree two could serve to represent a knots in a single thread
    • We could encode the distance between knots (weight of an edge)
    • If we follow a thread through the network, direction might play a role as well (directed edges)

Network Construction

We wondered how networks can be constructed from a single thread.

  • We found that some networks can't possibly be constructed from a single thread
  • We had a look at the Seven Bridges of Königsberg, and tried to figure out which conditions need to be met, to find a path that crosses all bridges exactly once (Eulerian path)
  • We found there is a complementary graph for people who use a boat and try to cross under all bridges exactly once
  • We learned about the classic problems of graph theory
    • Visiting each places / node exactly once in a single tour (Hamiltonian Path)
    • visiting each bridge / edge exactly once in a single tour (Eulerian Path)
    • The Travelling Salesman Problem (TSP)

Regular Networks

We explored various tilings, and the networks that result from their edges.

  • We had a look at regular tilings of the plane, and the node degrees of the resulting networks
  • We discussed which of the tilings can be turned into networks using a single continuous thread and how to do it
  • We had a look at pentagonal tilings of the plane, and the kind of networks that they would yield

Random Networks

  • We discussed how we can create networks in a random but controlled manner
    • Using a dice to randomly decide which knots to connect
    • Modify knotting probability based on the degree of a knot
  • We learned about the history of small world and scale free networks and their properties

Network Topology

  • We learned about graph embeddings, and that some graphs cannot be embedded in the flat plane without edges crossing
  • Accordingly some networks cannot be laid out without threads crossing
  • Networks may be filled with inflatables to create interesting 3D shapes. (see also: Knitflatables)


  • Find personal, autobiographic or social relations, that are important to you
  • Can you represent those as a knotted network?
  • Consider the use of knotted networks to store and communicate the flow of resources, family relations etc.


We talked with Katrin Steiger to discuss the inclusion of our experiments in the upcoming future vintage exhibition.


Travelling Salesman Problem

Paths in Graphs

Sorting Networks



Random Networks