Cartography and Math

  Cartographers or map makers use quite a bit of math in the creation of maps.  I suspect if you asked most students "What math is used in map making?" they'd respond with a shrug, or its only used in the key in the corner.

In truth, cartographers use quite a bit of math.  They use math in map scales, coordinate systems, and map projection to begin with.  The math scales shows the relationship between distance on a map and distance in real life as a fraction or ratio.

The coordinate systems refers to the numerical representation of locations of places on the planet while map projection is a mathematical transformation of points from a curved surface to a flat surface.  Did you know there are at least 18 different map projections including the Mercator which is the one most people are familiar with.  They type of map projection chosen depends on what needs to be shown.  This site has a great explanation of all the different types of map projections. 

Back to the coordinate systems used in cartography.  One is the geographic coordinate system which is based on longitude and latitude to pinpoint the exact location of any place on earth.    The other type is a projected coordinate plane which takes the earths curved surface and projects it onto a coordinate system.

New Zealand Maths has a nice unit created which has students creating their own maps of the classroom complete with scale and coordinate planes to mark the location of an object on the map. The nice thing about this activity relates magnetic north to true north. 

I can hear my students telling me that paper maps are out of fashion.  Maps are on their phones, so that information is not up to date but contrary to that opinion, they are wrong.  Math is even more important because mathematical equations referred to as mathematical exact visualization are what allow you to move your view of the map around, check out streets as if you are driving down them or keep track of the various labels of building, hotels, etc.

These mathematical equations are needed so the viewer can move digital maps around and still return back to your location.  Tomorrow, I'm going to look into the use of maps and math to find patterns in crime. 

Let me know what you think.