Cartography is the practice of constructing maps. When you look at a map (such as that on a globe, a paper atlas, even Google maps), have you ever thought about the idea that our 3D world is being represented as flat? How do various maps help to show (or hide) our three-dimensional space?
Check out this Wikipedia entry on Cartography to see some great images of maps through history. You can also view the videos from the Dimension project (chapter 1 – projections). This video in particular explains why mathematicians refer to the surface of the earth as two-dimensional.
The Dimensions site also talks about something called stereographic projection. Look at the image below and the following video. How does this 2D stereographic projection mediate your perception of space? Are you able to see more/less than with the globe? How is this similar/different than maps you are used to seeing? Does it seem distorted to you? What would be the advantage/disadvantage of this type of map?
If you’re still wondering about this type of projection, you can read more about it on Wolfram MathWorld.
Check out this Tabula Rogeriana, 1154 map that is “upside-down”. This was considered the most accurate map of the world for nearly three centuries (and only part of Africa is shown!) This map has a unique history and is worth learning more about. What makes a map upside down anyways?