Area preserving projections of the surface of a sphere onto a plane will also tend to be population preserving projections. 

 It is not surprising at the Peters projection better represents population density.

https://en.m.wikipedia.org/wiki/Gall–Peters_projection

Incidentally, the mathematics of the Peter's projection is the same mathematics that makes it possible to ride a tricycle with square wheels on a bumpy road. 

YouTube

Square-Wheeled Tricycle

The Texas A&M Physics Department's square -wheeled trike, built by the machine shop. The trike rides on a road of repeated pieces of an inverted catenary.

It is also related to the inverted pendulem problem, wihich finds application in the segway.

https://en.m.wikipedia.org/wiki/Inverted_pendulum

https://www.researchgate.net/figure/3-Segway-is-one-of-inverted-pendulum-applications_fig3_330825329

I'd love to see a world map inverted, or at least with the southern hemisphere accentuated and highlighted, so we could see the regions not usually depicted. I mean, the early navigators managed to get around both South America and Africa, but world maps don't even give Antarctica hardly a blip.

Unfortunately it is still wrong, and completely out of proportion.  Greenland is still way too large.

This one is better.

Wow! Thanks, it saved me from retrieving and lifting two pound books, and dusting them off.

I always thought that information is too North Hemisphere influenced. Glad you can give a scope from your side of the world.

Really cool!