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=== Links === | === Links === | ||
==== Ellipses ==== | |||
* [https://en.wikipedia.org/wiki/Ellipse Ellipse] on Wikipedia | * [https://en.wikipedia.org/wiki/Ellipse Ellipse] on Wikipedia | ||
* [[wikipedia:Generalized_conic#Multifocal_oval_curves|Multifocal oval curves]] on Wikipedia | * [[wikipedia:Generalized_conic#Multifocal_oval_curves|Multifocal oval curves]] on Wikipedia | ||
* [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 ==== | |||
* [[wikipedia:de:Anker-Steinbaukasten|Anker-Steinbaukasten]] | |||
== Knots and Splices == | |||
=== Links === | |||
==== How are threads made? ==== | |||
==== Self-Assembly ==== | |||
* [http://news.rice.edu/2016/04/14/nanotubes-assemble-rice-introduces-teslaphoresis-2/ Teslaphoresis] = self-assembly of threads | |||
* Spontaneous Patterns in vibrated Ball Chains: [http://www.maths.bris.ac.uk/~majge/hjce.06.pdf Knots] and [http://cnls.lanl.gov/~ebn/pubs/spiral/spiral.pdf Spirals] | |||
==== Knotting ==== | |||
... | |||
==== Splicing ==== | |||
... | |||
==== Knot Theory ==== | |||
... | |||
== Braids == | == Braids == | ||
== Networks == | == Networks == | ||
Revision as of 09:35, 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
Kits
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
...