The topologist’s map of the world

This map, at first glance, similar to a medieval map of the world ‘mappa mundi’, is the topologist’s map of the world, showing international borders, and nothing else.

Topology in math is the study of properties that are preserved when a shape is curved or elongated. So a circle and a square are topologically equal because they are both a simple loop. A figure eight isn’t comparable to them since it has the intersection point and two loops.
This map is showing the basic adjacency within regions, without consideration for the complicated shapes the areas take. In topology, the borders can be smoothed out, but the adjacency is a fixed property that remains no matter how much the edge is reshaped.

Click to continue reading >>

Maps that explain the world