Advanced Mathematics on Dotty Grids

If you haven't already done so, take a look at An Appearing Act, Areas from Vectors, and Find the Metagiff.
These problems are designed to encourage you to think about advanced mathematical questions that can emerge from the simple context that is a dotty grid. We invite you to explore the problems, then use the submit a solution link to send us the results of your exploration. This could be a solution to one of the above problems, or your own problem that you came up with as a result of exploring dotty grids.

You can download and print off dotty paper here.
You may also wish to explore using GeoGebra.

We look forward to seeing what mathematical ideas you come up with!