| 2)
We can also look for some specific shapes to explore: circles and spirals
are probably the best examples. Geometry of the circle, for
instance, can be explored by looking at the relations between rotation
and iteration. A circular braid will be generated any time you have a
braid with rotation and sufficient numbers of plaits (that is, sufficiently
high number of iterations). So you can ask students to do an inquiry exercise:
How many plaits are required to create a complete circle? It depends on
the rotation--the higher the rotation, the fewer plaits you need. If you
are only rotating by 1 degree in each plait, then you will need 360 plaits
to go full circle (that’s only 359 iterations, because you get one plait
to start with; in other words there is a “zeroth” iteration at start).
A 10 degree rotation will require only 36 plaits to make a full circle.
And so on. Having them discover this relationship on their own would be
an empowering exercise. Do these results change if you don’t use the default
translation of 100%? If you don’t use the default of 100% dilation? [TIP:use a
small starting dilation, like 20%, so that they can fit all of the braid
on the screen at once] |
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