Projecting a world map on a flat surface in a fully representative way worldwide is an impossible task. In this matter, the choice of projection is important and needs to fit the purpose of the map. One of the most well-known and used map projections is the Mercator projection, a cylindrical and conformal projection. This projection preserves angles and shapes, which is essential in navigation. However, area is distorted and the distortion increases towards the poles. This makes, for instance, Europe look larger than it actually is on earth, while the size of Africa is relatively accurate.
Peters map projection, on the other hand, was created in 1974 by the german Anders Peters in response to the Mercator projection. Peters map projection is an equal-area projection, and was created in order to preserve area and present size differences between land masses. However, shapes and angles are not preserved in this projection.
Trade-off is an inevidable factor when projecting a map onto a flat surface. Flat maps can not be accurate in every aspect, and therefore map projections must be selected according to its purpose. Most people are probably more familiar with the Mercator projection, and the shapes are likely to be more similar to what we would see in e.g. national maps. When comparing Mercators and Peters map projections, the visual difference is quite striking and the projections can be percieved differently by different people. This is a topic that has been up for discussion, since the Mercator projection can be interpreted as a Eurocentristic.
Peters Projection
By Strebe - Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=16115242
Mercator Projection
By Strebe - Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=17700069