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
- Ellipse on Wikipedia
- Multifocal oval curves on Wikipedia
- On the description of oval curves by James Clerk Maxwell
- Semidefinite Representation of the k-Ellipse