How do maps show the shape of the Earth on a flat page?

Because Earth is roughly spherical, cartographers must mathematically project its surface onto a plane. The Mercator projection, created in 1569 by Gerardus Mercator, preserves direction well for navigation but greatly enlarges polar regions. Other projections, such as Gall-Peters or Robinson, try to balance different kinds of distortion. No flat map can perfectly preserve all properties at once because the surface of a sphere cannot be unfolded without some stretching or compression. That is why different maps are used for different purposes.