Revision as of 17:09, 14 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 multi-focal 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 multi-focal 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

@@ Line 1: / Line 1: @@
 = 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 multi-focal 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 [https://twitter.com/astonishedstag/status/720114478768070658 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 multi-focal 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 ===
+* [https://en.wikipedia.org/wiki/Ellipse Ellipse] on Wikipedia
+* [[wikipedia: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
+* [http://arxiv.org/pdf/math/0702005v1.pdf Semidefinite Representation of the k-Ellipse]
 == Knots ==
 == Braids ==
 == Networks ==