# Christopher Danielson’s square problem

Saw an interesting problem on twitter last night:

with this one extra clarification on the shape:

Seems like a good problem for a kid learning geometry, so I tried it out with my older son tonight. First we looked at the two twitter posts to make sure that he understood the problem and I asked him to come up with a plan for how to solve it:

Next we went to the white board to work out the solution. He did a good job following through on this plan, which was nice. One thing that I thought might give him a little difficult was that the 4th root of 3 appears in his solution. However, he did not simplify the numbers in the problem the way I expected him to, so the 4th root of 3 didn’t appear ðŸ™‚

Definitely a fun little problem. One alternate problem that I skipped because I thought it would be too difficult was finding the area of a different square hiding in Danielson’s picture. The “center” of the 4 pointed star is also a square – what area does it have if the kites have area 1?

# Fibonacci, Zome, and Patterns of the Universe

The kids wanted to do an other project using Patterns of the Universe today:

Yes!!

Flipping through the book last night I found a neat page featuring golden rectangles, so I turned that into a little half coloring / half zometool project for this morning.

We started by talking about the picture in the book. The kids were interested in the spiral pattern and my older son remembered a few of the properties of “golden” rectangles:

Next we built a golden spiral on the living room floor using our zometool set. We actually did a similar project about a year ago, so the ideas weren’t totally new:

Fibonacci Spirals and Pentagons with our Zometool Set

I liked hearing their description of how the Fibonacci sequence appear in the shape – it was a nice way to get talking and thinking about math ideas:

While I cleaned up the Zometool pieces the kids colored in Patterns of the Universe. Here are their descriptions of their colorings. Here’s the one from my younger son:

and here’s my older son:

So, a fun little project for kids connecting the Fibonacci numbers to some geometric patterns. It is neat to hear how the kids think about these connections. I really love how the coloring ideas in Patterns of the Universe lead so naturally to fun projects!