Density Equalizing Maps (Worldmapper)
Here is a standard Land Area Map of the world:
John Pritchard, from the Geography Department at the University of Sheffield, was kind enough to give an overview of the process involved in the creation of these maps for this blog post:
A cartogram can be thought of as part map, part pie-chart. It attempts to keep areas (such as countries) in roughly the same place, whilst changing their size to reflect the value of a variable, for example, population. A world cartogram of population would show, for example, China and India as larger than their land area size, and Australia as smaller.
An algorithm that creates a cartogram from a map, preserving recognisable shapes whilst resizing countries, has been something of a‘holy grail’ of the cartogram world. The solution we use forWorldmapper, from Mark Newman and Michael Gastner at the University ofMichigan, is inspired by the diffusion of gas molecules. If you imagine the example of human population, the algorithm would have the effect of allowing the population of a densely populated country to ‘diffuse’, pushing back the boundaries of neighbouring, less densely-populated countries, until population density was evenly spread.
Interesting that this application to geography was inspired by chemistry!
Here are a few more maps that I found interesting. A map of War Deaths:
Finally, a great comparison of wealth in the years 1500 and 1990:
To learn more about how the maps were created, see the Worldmapper “About” page.
These maps would make a great exclamation point on a problem about percentages. For example, first you calculate the the percentage of deaths caused by war from several continents (North America, Africa, etc.). Then after the calculations, you can emphasize the findings with the appropriate map.
Most of the maps (at least, all the ones that I looked at) are accompanied with data or descriptive numerical information that you could easily build a word problem from.