A tweet from Patrick Honner inspired one of our projects and a slew of programs illustrating the pattern in different ways:
We used two from Dan Anderson in our project:
That project is here:
In the project the boys struggled a little with understanding how many degrees each shape needed to be rotated to end up in the same position. I was a little caught off guard by the difficulty they were having, but afterwards thought that these Moiré Pattern computer projects (and the Numberphile video, too) were a great way to introduce rotations to kids.
So, tonight we revisited the idea of rotation to try to make things a little clearer. First up was an equilateral triangle. In the less abstract setting of the dining room table, the kids were able to talk through the rotational ideas a little more easily:
Next we looked at a square. After the discussion my older son gave about the equilateral triangle, my younger son was able to give a nice description of what was going on with the square:
The last shape we looked at was a regular pentagon. My older son thought that the rotation angle + the interior angle of each shape (or at least a regular polygon) would add up to 180 degrees. I asked the kids to figure out why that was true for the pentagon:
Finally, as a special little treat / challenge, I showed the boys a strange situation where you have to rotate something 720 degrees around the center to get back where you started. This surprising rotational trick is something that I learned back in my abstract algebra class in college from Mike Artin.
So, a fun project and a nice little surprise – the Moiré Patterns idea is a great way to introduce kids to rotations!