This was M's independent discovery. He noticed this one rock that was red (the rest were whitish-grey) and said that it was obviously a Martian rock.
Later on we came across a beautiful spiral path...
... and a long and mysterious-looking infinite sequence with a limit (a tree tunnel). So we ran along its entire length.
We stopped at a small pond with koi fish and frogs and watched them. M wanted to catch fish, but I had to explain that these are not for catching. So he just sat there looking for the largest and the smallest of them for a while.Another unexpected zomatical (zoologically-mathematical) find was this little lizard that we spotted. I mentioned how both sides of the lizard's body were symmetrical and we talked a bit about this lizard's line of symmetry.
Then we walked around some more just enjoying the gardens. And then it was time to go back to where we started - to another koi pond with a big waterfall. And so we found another one of the clues - the boundary between two states of matter (in this case - solid and liquid).
When the rest of the trekkers all got back, there was a short discussion of the trek and then we all made a right-angle triangle (since I guess none could be found in the arboretum).
How much of this all stuck with M? Ok, the Martian rock and the spirals did, but the rest - I'm not sure. But you know, it's ok. This was our first Math Trek outing and we both loved it. The main idea was to discover all the beautiful things around us and to not be afraid of connecting them with mathematical concepts. Who knew math could be this relaxing!