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* [https://archive.org/stream/scientificpapers01maxwuoft#page/n39/mode/2up On the description of oval curves] by James Clerk Maxwell | * [https://archive.org/stream/scientificpapers01maxwuoft#page/n39/mode/2up On the description of oval curves] by James Clerk Maxwell | ||
* [http://arxiv.org/pdf/math/0702005v1.pdf Semidefinite Representation of the k-Ellipse] | * [http://arxiv.org/pdf/math/0702005v1.pdf Semidefinite Representation of the k-Ellipse] | ||
==== Kits ==== | ==== Educational Kits ==== | ||
* [[wikipedia:de:Anker-Steinbaukasten|Anker-Steinbaukasten]] | * [[wikipedia:de:Anker-Steinbaukasten|Anker-Steinbaukasten]] | ||
* [http://www.lectron.de/|Lectron Elektro-Baukasten] | |||
* LEGO, KNEX, LEGO-Mindstorms ... | |||
==== Sewing Boxes ==== | |||
* [http://collections.lacma.org/node/178749 Sewing Box with Implements] | |||
* [https://www.youtube.com/watch?v=4FQoeVWsHsY Sewing Box Cabinet] by Kiki van Eijk | |||
==== Tool Boxes ==== | |||
* [[wikipedia:Survival_kit|Survival Kit]] | |||
* [http://juan.choriticos.net/fotos/delft/36/zurich/20030713/p1010009-11-0-2.shtml Dentist Toolkit] | |||
* Pictures of [https://www.google.de/search?q=surgical+set&tbm=isch surgical sets] and [https://www.google.com/search?q=werkzeugkoffer&tbm=isch tool boxes] | |||
== Knots and Splices == | == Knots and Splices == | ||
Revision as of 10:20, 19 April 2016
Computing with Thread: Part I
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
Observations
- 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
Homework
- 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
Links
Ellipses
- Ellipse on Wikipedia
- Multifocal oval curves on Wikipedia
- On the description of oval curves by James Clerk Maxwell
- Semidefinite Representation of the k-Ellipse
Educational Kits
- Anker-Steinbaukasten
- Elektro-Baukasten
- LEGO, KNEX, LEGO-Mindstorms ...
Sewing Boxes
- Sewing Box with Implements
- Sewing Box Cabinet by Kiki van Eijk
Tool Boxes
- Survival Kit
- Dentist Toolkit
- Pictures of surgical sets and tool boxes
Knots and Splices
Links
How are threads made?
Self-Assembly
- Teslaphoresis = self-assembly of threads
- Spontaneous Patterns in vibrated Ball Chains: Knots and Spirals
Knotting
...
Splicing
...
Knot Theory
...