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I can't get over how wrong my idea of Brazil's shape was.
That is a distortion, I think. Look at the longitude and latitude lines in the sea.
It looks as if this map generally is designed to localize the inevitable shape distortions to areas where there isn't "interesting" detail and therefore those distortions aren't as obvious. But because of the way Brazil sticks out, it ended up getting stretched a fair bit.
That was my first reaction, until i remembered that i've seen a globe before, and my general perception of the shapes of countries is informed by a globe and not just the mercator projection.

This map might bill itself as "the most accurate", but it's still making some crazy distortions. Mercator might get some sizes wrong, but it gets the shapes mostly right.

I'm wondering how the map looks with the States or Europe in the center. Of course, the Japanese creator has Japan in the centre... :-)
Ugh, it's not more accurate, hell accurate don't even mean anything here. This is just a projection that makes different compromises making a pseudo sphere fit on to a plane. Projections are tools, different ones have different uses.
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I'd argue with the "most accurate" designation the article uses. There are lots of projections out there. Use the one that best optimizes for the things you care about.

This projection is neat, but has its own obvious tradeoffs (e.g., difficult to readily see how some landmasses relate to each other spacially. Antarctica in particular).

For example, the Japan is in the center. So it has this bias every world map has. "We are the center of the world"
I got curious and had to check the numbers, just to know what's real:

Australia: 7.7 million km²

United States: 9.8 million km²

Europe: 10.2 million km²

Russia: 17.1 million km²

Africa: 30.37 million km²

This is interesting and I understand how every map is a compromise but it really bothers me how distant this projection makes Antarctica look from New Zealand (one of the gateway countries to the continent, especially the Ross Ice Shelf area).