For some reason flat-earthers have become enamored with the so-called Gleason's world map, which is an azimuthal equidistant projection of the surface of the Earth, centered on the North pole, and looks like this:
(By the way, there's no mathematical reason why the projection needs to be centered at the North pole. It can literally be centered anywhere on the surface of the sphere, and in fact the Wikipedia page linked above also shows a version centered at the South pole. It's just that centering it at the North pole gives the most useful projection because it just so happens that the vast majority of Earth's land mass is located in the northern hemisphere at this point in its geological history. For this reason the version centered at the South pole shows extreme distortion, as most of the land mass is on the outer rim from that perspective.)
Most flat-earthers claim that this is the correct map of the world, representing what it actually physically is like.
However, like with all map projections, also this one causes distorted proportions. (This is because it's mathematically impossible to map the surface of a sphere onto a flat plane without causing some sort of distortion. Either scales and sizes get distorted, or angles get distorted, or both. And in no projection can all relative distances along the surface be preserved.)
One major problem with the azimuthal equidistant projection is that it distorts aspect ratios. This is because the distance between latitude lines is equal, but the distance between longitude lines becomes larger and larger towards the edge, which makes everything look stretched along the perimeter of the circle. The farther from the center, the more distorted.
Consider, for example, Australia. In real life, physical Australia, when looked from high above, looks like this:
And this is something we can actually physically measure in real life. The North-South and East-West measurements of the country can be literally physically measured, while on land, without even having to photograph it from orbit.
In the Gleason's map, however, Australia looks like this:
It's extremely obvious that it cannot be correct. In the map it has been squeezed vertically to less than half the size. If this corresponded to real life, we could literally measure it, even on the ground.
How do flat-earthers explain this clear discrepancy?
They just don't. Like with so many things, they just ignore it. They don't pay attention to it, they don't think about it, they just shove it aside in their minds even if they happen to notice it. If they are specifically asked about it, they either dodge the question or they make some vague allusions about the map being just an approximation (even though it's still the correct accurate map of the Earth!) and quickly move to something else, shoving it off their minds.
That's how the flat-earther mind works. They are utterly convinced and indoctrinated, and they cannot accept being wrong about anything, and anything that clearly contradicts their notions is just ignored and shoved aside. They don't want to even think about it, and they just pretend like it doesn't exist.
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