The Japanese architect Hajime Narukawa claims to have resolved the centuries-old problem of how to draw an oblate spheroid Earth on a flat plane. This is the map of the world that Narukawa produced. It looks very different from the version produced by Gerardus Mercator in the 16th century. Mercator devised a map with straight lines of longitude and latitude which helped in sea navigation.
AuthaGraph World Map
Go here to read how Narukawa achieved this more realistic map of the world.