Math & Geography

Geography is about understanding phenomena on the surface of the earth like winds, tides, pressure & heat waves, seasons, vegetation etc. Scientific study of these necessitated the graphing of the surface of the earth using latitudes & longitudes. These were enabled by using principles of both plane and spherical geometry.

The measuring of the contours of the Earth needed Trigonometry. The Everest was designated as the highest mountain peak without going anywhere near it!

Drawing Maps

The outlines of any region on the earth, whether political or economic is represented by maps which use ideas of scaling.

The Earth is a sphere, which is a 3-D object. Drawing a map on paper is a process of converting the curved surface of the Earth into a plane 2-D figure.

This is theoretically not possible. The 3-D surface of the Earth has many properties - the shape of the boundary, the size of the area, the directions between different points etc.

Hence to convert 3-D data into a 2-D map, many mathematical ideas, called projections, are used. Most of our school maps are made with what is called Mercator's Projection. This preserves the angle between different places and hence good for navigation. But it distorts the area. In school maps you will find the area of Greenland almost the same as that of Africa.

So various projections have been developed, keeping in mind the use to which the 2-D map is going to be used.

The daily weather patterns around the earth are tracked continuously and displayed visually using specialized computer software.

The prediction of eclipses and comets is made possible by using complex math.

The ubiquitous GPS which is used in most cars uses ideas of spherical trigonometry to locate the car within an accuracy of one metre.

The Earth is spherical. But maps that students study are drawn on plane surfaces. Students need to keep in mind the distortion of sizes of countries done in this process. Countries above & below the tropics of Cancer and Capricorn appear much bigger than actual. That is the reason there are different kinds of map projections.

Other points – latitudes, longitudes, the important latitudes – equator, tropic of cancer etc Important longitudes Mapping the Earth with triangulation. Possible because triangles are rigid. Once we know the length of a base of the triangle and the angles subtended by a point at the two ends of the base, the lengths of the lines joining the point to the 2 extremities of the base can be determined. The mapping of India through triangulation and the revelation that Mt Everest was the highest mountain are very interesting pieces of history which have been documented.