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== Thread Geometry == | == Thread Geometry == | ||
We explored what kind of geometric constructions we can do with thread, chalk and the help of several people... | We explored what kind of geometric constructions we can do with thread, chalk and the help of several people... | ||
=== We found out... === | === We found out... === | ||
* how to draw a line | * how to draw a line | ||
* how to draw a circle ( d = const.) | * how to draw a circle ( d = const.) | ||
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* how to measure the circumference of a circle | * how to measure the circumference of a circle | ||
* how to calcualte pi using only thread (See also [https://twitter.com/astonishedstag/status/720114478768070658 here]) | * how to calcualte pi using only thread (See also [https://twitter.com/astonishedstag/status/720114478768070658 here]) | ||
=== 3D thread geometry === | === 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 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 discovered the 3d ellipsoid (a + b = const.) | ||
* We found that multifocal 3d ellipsoids have a doughnut-topology. | * We found that multifocal 3d ellipsoids have a doughnut-topology. | ||
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** the polygon method, where the thread forms a polygon going through the focal points and the drawing point | ** 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 | ** the star method where the thread is alternately visiting each focal point and the drawing point | ||
=== Observations === | === Observations === | ||
* Geometric knowledge from school only got us so far ... | * Geometric knowledge from school only got us so far ... | ||
* There is a whole universe of "new" shapes and forms | * There is a whole universe of "new" shapes and forms | ||
=== Questions raised === | === Questions raised === | ||
* Questions regarding surface of different shapes popped up | * Questions regarding surface of different shapes popped up | ||
* We discussed different methods of measuring the surfaces using thread | * We discussed different methods of measuring the surfaces using thread | ||
=== Homework === | === Homework === | ||
* What could an Experimentier-Baukasten / a kit / a sandbox for computing with thread look like?<br>Do some research on other kinds of kits! | * What could an Experimentier-Baukasten / a kit / a sandbox for computing with thread look like?<br>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 | * 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 | * Document your thread-art in the wiki | ||
=== Links === | === Links === | ||
=== Geometry === | === Geometry === | ||
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Create a nice framework for displaying knots.<br> | Create a nice framework for displaying knots.<br> | ||
The framework can be physical, graphical or computational in nature | The framework can be physical, graphical or computational in nature | ||
=== Links === | === Links === | ||
==== How are threads made? ==== | ==== How are threads made? ==== | ||
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* [https://www.youtube.com/watch?v=aqyyhhnGraw&list=PLt5AfwLFPxWLyfD4nhZCX_3UZdSSpkBTs&index=1 Knot Theory Videos] by Numberphile | * [https://www.youtube.com/watch?v=aqyyhhnGraw&list=PLt5AfwLFPxWLyfD4nhZCX_3UZdSSpkBTs&index=1 Knot Theory Videos] by Numberphile | ||
* [https://www.youtube.com/watch?v=co78AEqsv3s How Mathematics gets into Knots] | * [https://www.youtube.com/watch?v=co78AEqsv3s How Mathematics gets into Knots] | ||
* Alexei Sossinsky, ''Mathematik der Knoten: Wie eine Theorie entsteht'' ISBN 978-3499609305 | * Alexei Sossinsky, ''Mathematik der Knoten: Wie eine Theorie entsteht'', ISBN 978-3499609305 | ||
* [http://katlas.org The Knot Atlas] | * [http://katlas.org The Knot Atlas] | ||
* [http://katlas.org/wiki/Other_Knot_Tables Historic Knot Tables] | * [http://katlas.org/wiki/Other_Knot_Tables Historic Knot Tables] | ||
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* [http://www.ritsumei.ac.jp/se/~hirai/research/linearobjectmanipulation-e.html Manipulation of Deformable Linear Objects] feat. [https://www.youtube.com/watch?v=UZfpFkIdhl0 Un-Knotting Bot] | * [http://www.ritsumei.ac.jp/se/~hirai/research/linearobjectmanipulation-e.html Manipulation of Deformable Linear Objects] feat. [https://www.youtube.com/watch?v=UZfpFkIdhl0 Un-Knotting Bot] | ||
* [http://ijr.sagepub.com/content/25/4/371.full.pdf Knotting/Unknotting: Manipulation of Deformable Linear Objects] | * [http://ijr.sagepub.com/content/25/4/371.full.pdf Knotting/Unknotting: Manipulation of Deformable Linear Objects] | ||
== Braids == | == Braids == | ||
In this class we identified the basic elements of braids, and explored the intersection of braiding and sorting algorithms. | |||
In this class we | === 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 | |||
==== Observations ==== | |||
* 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 | |||
==== Observations ==== | |||
* 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 | |||
=== Links === | === Links === | ||
==== Braiding ==== | ==== Braiding ==== | ||
* [https://www.flickr.com/photos/taffeta/8201660840/in/album-72157632050570535/ French Children's book] feat. Maypole Dance + Track Diagram | * [https://www.flickr.com/photos/taffeta/8201660840/in/album-72157632050570535/ French Children's book] feat. Maypole Dance + Track Diagram | ||
* [https://issuu.com/thepetflakesproject/docs/petflakesthebook Pet Flakes] Architecture inspired by Maypole braiding | * [https://issuu.com/thepetflakesproject/docs/petflakesthebook Pet Flakes] Architecture inspired by Maypole braiding | ||
* [http://weeklyweaves.blogspot.de/2014/08/bobbin-dancing-yan-tan-tethera-part-1.html Bobbin Dance] by Shane Waltener | * [http://weeklyweaves.blogspot.de/2014/08/bobbin-dancing-yan-tan-tethera-part-1.html Bobbin Dance] by Shane Waltener | ||
==== Sorting ==== | ==== Sorting ==== | ||
* [https://www.youtube.com/watch?v=LOxfdsBBjKI Sorting Networks] by Computer Science Unplugged | * [https://www.youtube.com/watch?v=LOxfdsBBjKI Sorting Networks] by Computer Science Unplugged | ||
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* [https://www.youtube.com/watch?v=DFG-XuyPYUQ Insertion Sort] | * [https://www.youtube.com/watch?v=DFG-XuyPYUQ Insertion Sort] | ||
* [https://www.youtube.com/watch?v=aQiWF4E8flQ Quick Sort] | * [https://www.youtube.com/watch?v=aQiWF4E8flQ Quick Sort] | ||
==== Computational Complexity ==== | |||
* [https://www.youtube.com/watch?v=-Eiw_-v__Vo Big-O-Notation] | |||
* [http://bigocheatsheet.com/ Big-O-Cheatsheet] | |||
* [https://xkcd.com/399/ XKCD Cartoon on TSP] | |||
* [https://www.youtube.com/watch?v=YX40hbAHx3s P vs NP] | |||
==== Braiding + Card Weaving ==== | ==== Braiding + Card Weaving ==== | ||
* [https://www.cs.arizona.edu/patterns/weaving/topic_braiding.html Braiding] in Griswold's Weaving Archive | * [https://www.cs.arizona.edu/patterns/weaving/topic_braiding.html Braiding] in Griswold's Weaving Archive | ||
* [https://www.cs.arizona.edu/patterns/weaving/topic_tabletweaving.html Tablet Weaving] in Griswold's Weaving Archive | * [https://www.cs.arizona.edu/patterns/weaving/topic_tabletweaving.html Tablet Weaving] in Griswold's Weaving Archive | ||
==== Braiding Techniques ==== | ==== Braiding Techniques ==== | ||
* [https://loopbraider.com/ Loop Braiding] | * [https://loopbraider.com/ Loop Braiding] | ||
* [https://www.schleich-s.com/en/US/horses/braiding-techniques/ Braiding Techniques] for horses | * [https://www.schleich-s.com/en/US/horses/braiding-techniques/ Braiding Techniques] for horses | ||
==== Braiding Tools ==== | ==== Braiding Tools ==== | ||
* [http://craftdesignonline.com/ Online Braiding Tools] | * [http://craftdesignonline.com/ Online Braiding Tools] | ||
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* [http://www.guntram.co.za/tabletweaving/gtt.htm Guntram's Tablet Weaving Thingie] | * [http://www.guntram.co.za/tabletweaving/gtt.htm Guntram's Tablet Weaving Thingie] | ||
* [https://archive.org/details/AtariComputerDesignBandWeaving ATARI band weaving] book + disk | * [https://archive.org/details/AtariComputerDesignBandWeaving ATARI band weaving] book + disk | ||
==== Rope Weaving ==== | ==== Rope Weaving ==== | ||
* [https://www.youtube.com/watch?v=uX9DJp_pfgM How to weave a Rope Mat] | * [https://www.youtube.com/watch?v=uX9DJp_pfgM How to weave a Rope Mat] | ||
* [https://www.youtube.com/watch?v=_VdOId9jmN8 Rope Weaving Clinic] | * [https://www.youtube.com/watch?v=_VdOId9jmN8 Rope Weaving Clinic] | ||
=== Books === | === Books === | ||
* Y. Kyosev, ''Braiding Technology for Textiles'', ISBN 978-0857091352 + [http://www.sciencedirect.com/science/book/9780857091352 ebook version] | |||
== Nets == | |||
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) | |||
=== Homework === | |||
* 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. | |||
== Meetup == | |||
We talked with Katrin Steiger to discuss the inclusion of our experiments in the upcoming future vintage exhibition. | |||
* | === Links === | ||
==== Travelling Salesman Problem ==== | |||
* [https://www.youtube.com/watch?v=-cLsEHP0qt0 Travelling Salesman Problem] with Thread | |||
* [http://www.cgl.uwaterloo.ca/csk/projects/tsp/ TSP-Art] | |||
* [http://blog.ninapaley.com/2013/08/30/the-traveling-horse-salesman/ TSP-Animation] | |||
==== Paths in Graphs ==== | |||
* [[wikipedia:Eulerian_path|Eulerian Path]] | |||
* [[wikipedia:Hamiltonian_path|Hamiltonian Path]] | |||
==== Sorting Networks ==== | |||
* [https://www.youtube.com/watch?v=LOxfdsBBjKI CS-Unplugged] | |||
* [[wikipedia:Sorting_network|Sorting Network]] | |||
==== Tilings ==== | |||
* [[wikipedia:Euclidean_tilings_by_convex_regular_polygons|Tilings by Convex Regular Polygons]] | |||
* [[wikipedia:Penrose_tiling|Penrose Tiling]] | |||
==== Knitflatables ==== | |||
* [https://issuu.com/yuliya_baranovskaya/docs/knitflatables_ybaranovskaya_2310201 Knitflatable Architecture] | |||
==== Random Networks ==== | |||
* [[wikipedia:Random_graph|Random Graph]] | |||
* [[wikipedia:Scale-free_network|Scale-free network]] | |||
* [[wikipedia:Small-world_network|Small-world network]] | |||
* [[wikipedia:Boolean_network|Boolean Network]] |