Tonight's class, we were asked to draw as many squares as we can within the dots. Coming up with 6 was not difficult... The next task was to draw any shape but only using 4 dots to connect. And coming up with that was exciting because we had to visualize in different ways from the previous activity.
We made another discovery that night that has actually already been discovered way before us. And that theorem was made by George Pick.
To cut a long story short, George Pick discovered a relationship between the area of a simple
polygon, the number of dots on the boundary of the polygon and the count points inside the polygon. We were trying to figure what exactly that relationship was in class tonight. While George Pick came up with a theory and I would assume a formula for this relationship as well, I think I'd like to classify the relationship as "it's complicated!" because what if the polygon is not a simple polygon and there are no dots in the middle of it as well? Nevertheless, I googled Pick up and found that...
Hmm, I have not tried his formula out but this calls for more Mathematical Investigation at another time!
