GMU:Computing with Thread/Part1: Difference between revisions

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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 multi-focal ellipses (a + b + c = const.)
* 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 multi-focal 3d ellipsoids have a doughnut-topology.
* 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|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]

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

Knots

Braids

Networks