Cool tools: Fun with legislative maps
An online database, redistrictingnation.com uses map-based geometry to rank Congressional and state legislative districts. Here is a screen shot for the 13th District of Pennsylvania:
The map itself shows the highlighted district, and the bar charts on the right rank the shape of the district using several geometry-based formulas (which are explained). Districts that rank 'low' on these charts MIGHT be gerrymandered - other factors play into districting, of course (for example, Cape Cod ranks pretty low, but the ocean probably has something to do with that).
This is a good basis for questioning and research.