Can you explain the strategy for winning this game with any target?
Draw a square. A second square of the same size slides around the
first always maintaining contact and keeping the same orientation.
How far does the dot travel?
Can you explain how this card trick works?
* What do you notice about $(4,0)$ figures?
* Choose another particular value for $(p,i)$ and explore
* Have you tried drawing shapes with the same area?
* What do you notice about those figures whose areas are the
* What ways are there of increasing the area by $1$ unit?
* Draw more figures; tabulate the information about their
perimeter points ($p$), interior points ($i$) and their areas