Monday, October 29, 2012

Cut and Paste Transformations

Inspired by Mr. Lanier's challenge sheet (particularly challenge #2--which involved transforming an irregular pentagon into a rectangle), I decided to try to create some of my own versions of cut and paste transformations. I wasn't sure how to go about this at first, so I tried a couple of different methods.
First, I tried this by drawing a rectangle on a sheet of graph paper that was say, 40 units in area. Then, I would try to draw a different shape that was 40 units in area. This was too difficult though, because with basically all other shapes besides squares/rectangles, not all of the individual units would be completely filled, so it was hard to calculate exactly how many units the new shape took up.
I found that it was easiest to take a square, for example, and then cut it up into smaller triangles, squares, etc., and then use those smaller shapes to construct a new shape with the same area as the previous one.

I started with a rectangle (50 units in area):
Then, I cut it up into lots of smaller triangles, and one one by ten unit long rectangle. I put them back together, and ended up with something like this:
I did the same for an octagon, but this time, I am posing it as a challenge for you guys. Here is the shape I got upon dividing an octagon, and then re-constructing it (using the method above). How could you use this to make an octagon? what would the area be? Let me know how you approached this problem.


  1. Great post, Lucy!
    I'm trying out your octagon puzzle now.

    1. I'm worried that I'm not exactly clear on what's going on with your shape in its lower-right part. Where exactly to those corners lie?