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* how to draw a circle ( d = const.) | * how to draw a circle ( d = const.) | ||
* how to draw an ellipse ( a + b = const.) | * how to draw an ellipse ( a + b = const.) | ||
* how to draw | * how to draw multifocal ellipses (a + b + c = const.) | ||
* how to draw egg-shaped curves (3 * a + b = const.) | * how to draw egg-shaped curves (3 * a + b = const.) | ||
* how to measure the circumference of a circle | * how to measure the circumference of a circle | ||
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* We discovered the 3d ellipsoid (a + b = const.) | * We discovered the 3d ellipsoid (a + b = const.) | ||
* We found that | * We found that multifocal 3d ellipsoids have a doughnut-topology. | ||
* We found two different ways to create ellipsoid shapes: | * 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 polygon method, where the thread forms a polygon going through the focal points and the drawing point | ||
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* [https://en.wikipedia.org/wiki/Ellipse Ellipse] on Wikipedia | * [https://en.wikipedia.org/wiki/Ellipse Ellipse] on Wikipedia | ||
* [[wikipedia:Multifocal_oval_curves| | * [[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] | ||
Revision as of 17:19, 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 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