Mathematics In Geography

 

After stumbling across the Mathematicians Seamounts, I wondered if there were other geographical features with math names.  Instead, I came across the term mathematical geography which is defined as a "branch of geography that deals with the figures and motions of the earth, its seasons and tides, its measurement, and its representations on maps and charts by various methods of projection." according to Merriam-Webster online dictionary. 

So geography looks at the science of the planet itself, relationships such as nature to nature or nature to man or the phenomena in either cultural or natural happenings or occurances.  This means that mathematics is used in regard to the form and shape of the earth, movements within the earth, variables of time and elements of longitude, cartography and map making, climatology, and physiography or physical geography.

Thus I looked into the topic a bit deeper and I found a short abstract listed more ways than I realized.  For instance, Euclidian Geometry is used in surveying small areas such as a field or a house lot while spherical geometry combined with trigonometry to construct map projections.  Furthermore, people have been able to figure out new applications such as using Topology in spacial analysis of networks. As far as networks go,  graph theory has the indices used to describe the different types of networks such as drainage patterns.

Then differential equations are used to study and explain the dynamic processes such as the rock cycle in geomorphology or the study of of the physical features of the earth and their relation to geological structures.  In addition, statistical methods are used to analyze data for regional geography.  Some of these methods are trend surface analysis which uses least squares regression, or factor analysis.  

Of course geography uses a variety of different mathematical models to simplify various problems in geography.  Some examples include the gravity model, simulation models and the Markov chain stochastic model.  Mathematical models can help simulate earthquakes, volcanic eruptions, tsunamis, etc because these all cause disasters and they want to predict where these happen so they can prevent deaths.  

So math is used to find distances between places, the gradient or slope of hills, heights of places, locations given in degrees, minutes, and seconds, perhaps with longitude and latitude depending. 

Now for a small interesting historical fact - This particular secant formula came out of navigation and cartography in the 17th century. The formula - 

is one that many many students struggle with.  It came out of a time when mathematicians and cartographers struggled to understand the Mercator map projection. Originally maps were done on a rectangular grid but Mercator wanted to create a project that preserved both angles and distances.  He figured out a way but was not able to explain it so after a few years, a mathematician explained it using the basic equation which ended up as the above equation.  So here we see how one of the differential equations is used.

This is fascinating how math is used in geography.  Let me know what you think, I'd love to hear.  Have a great day.