You Can't Keep Both Size and Shape

Picture stretching a photo of a circle sideways until it's an oval — the area inside might stay exactly the same, but it's definitely not a circle anymore. Or picture squishing that oval back into a circle — now the area probably changed. Map projections face this exact problem with every single country, all at once, everywhere on Earth.

Equal-area maps, like Equal Earth or Gall-Peters, protect size: a country's true size on the globe shows up as its true size on the map. The price is that shapes get bent — a circle on the globe might turn into a squashed oval on the map.

Conformal maps, like Mercator, protect shape and direction: a small circle on the globe stays a circle on the map, and compass directions stay true. The price is that size gets warped, sometimes a lot — a small circle near the pole gets projected as a much bigger circle than a small circle near the equator, even though both were the same size on the globe.

And compromise maps like Robinson or Winkel Tripel don't fully protect either one — they just make sure nothing gets outrageously wrong anywhere, which is why they're popular for general 'here's the world' posters.