Lessons taught; Lessons learnt

I opened my computer this morning intending to post something new, but soon got caught up in a further exploration of these square-to-square linkages. You soon notice, when creating these, that you are quite constrained in the points you can use to link the squares together. You are also limited in how ‘fast’ you can get the squares to rotate. Trying to use the least different speeds of rotation, I created this:

Geogebra applet will be here if you enable Java.

(Source: rotating_tesselation.ggb — apologies for the spelling mistake :) )

Moving the slider, you get images like this:

This can easily be extended to a tessellation of the plane by squares and rhombuses.

Question: What does it look like if we do something similar with hexagons? You can see my attempt below. Also, are there any other regular polygons we can do something similar with?

No matter how tempting, I promise I’ll move on to something else tomorrow!

Geogebra applet will be here if you enable Java.

(Source: rotating_hexagons.ggb)

Related Posts (automatically generated)

1. Visualisation: More rotating squares
2. Visualisation: Rotating polygons
3. Visualisation: Six moving lines