GPSGuided wrote:I couldn't mentally work out how they can maintain the proportions in a full rectangular map when they use latitude 45 N and S as the reference.
The general idea is that as the west-east dimension is stretched (towards the poles), the north-south dimension is shrunk by a similar amount. So the projection preserves land area, but not shape.
The Peter projection is no more "correct" than the Mercator projection. When you project a sphere onto a flat surface, you cannot accurately model shape, area, distances and bearings. You have to choose what is important. If the Boston schools want to teach geography accurately, they need to use globes instead of flat projections.
For the purposes of bushwalking, the choice of projection doesn't matter that much. The difference between grid north and true north is likely to be small compared to the difference between grid north and magnetic north.
Here's the Peirce Quincuncial projection. I think it's the most beautiful presentation of the continents. You just have to not mind that Antarctica is split into four!

- peirce-quincuncial.jpg (151.1 KiB) Viewed 10761 times
And here are some thoughts from XKCD: