Final answer:
Presenting the curved surface of the Earth on a flat map is difficult due to the geometric distortions that inevitably occur when rendering a three-dimensional shape (like the Earth) onto a two-dimensional space (like a map). Just as astronomical maps need unique identifiers for celestial objects, geographical maps use a grid system of latitude and longitude, but distortion still happens especially near the poles. Different map projections are designed to minimize different types of distortion, but no map projection can perfectly represent all aspects of the Earth's curved surface.
Step-by-step explanation:
The difficulty in showing the curved surface of the Earth on a flat map correctly arises from the geometric impossibility of representing a three-dimensional object on a two-dimensional surface without distortion. This process is similar to the distortions seen when light curves around a massive body like the sun, as seen in Einstein's theory of relativity. On a flat map, locations and distances can become skewed, just as light that reaches the Earth can seem to come from different locations than the known positions of the originating stars.
Just like in astronomical mapmaking, where a simple and unique identification method is needed to map out stars, galaxies, and other celestial objects, geographical mapmakers use a grid to identify each location using latitude and longitude coordinates. However, because of the Earth's spherical shape, a global map will always have some form of distortion, especially near the poles.
In the same way that radar technology can probe through obscuring layers to study the surface of Venus, or other celestial bodies, representing the Earth's surface on a flat map requires special projections. This is demonstrated by the seventeenth-century projection map 'The Whole World'. Different map projections are used to minimise distortion in different aspects such as area, shape, distance, or direction, but no flat map can be perfect in all respects because of the Earth's spherical nature.
Learn more about Map Distortion