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# The Shape of Maps

By Jessica Lort

So, do you like curves?

We hope so because the Earth is a curvy place. The Earth itself is a three-dimensional, spherical shape. That is a lot of curvature. More specifically the Earth is an ellipsoid. An ellipsoid is a mathematical model that is the shape of the Earth, approximately the shape of a flattened sphere, formed by rotating an ellipse. Yet, how are we able to accurately show locations from a multidimensional object onto a flat piece of paper?

This is known as map projection, and there are multiple methods of precisely converting these locations from the Earth onto a two-dimensional surface. The most common method is a Mercator projection which falls under cylindrical projections. The Mercator projection is the basis for the Universal Transverse Mercator (UTM) coordinate system, originally adapted by the U.S. Army.

Did you know that “all maps lie flat, and all flat maps lie”? Imagine unraveling a sphere and trying to flatten it. All projections have distortions. This is because there will always be some error when transforming geographic coordinates onto a flat surface. Specific projections may minimize distortion in shape, length, direction, or area. For example, a map that minimizes distortion in shape is called conformal.

Each map is designed to tell a story and depending on what you want your map to portray, will determine the type of error or distortion it will display. Minimizing error for one factor will inevitably increase it for other parameters.

There are two other factors, besides map projection, that play a role in transforming geographic coordinates onto a surface. These factors are known as Projected Coordinate Systems and datums. You may have heard of longitude and latitude which are geographic coordinates that refer to a physical location on the Earth. A Projected Coordinate System uses X and Y instead of longitude and latitude. It takes those geographic coordinates and places them on a map using a particular map projection. Map projections are how Projected Coordinate Systems are displayed on a flat surface. The most frequently used Projected Coordinate Systems are UTM and State Plane Coordinate System (SPCS).

A datum is a set of parameters and points that defines the coordinate system reference, which describes the size and shape of the Earth. It provides a reference for measuring locations on the Earth’s surface. It also defines the origin and orientation of geographic coordinates. The most common datum is The North American Datum of 1983 (NAD 1983).

Map projection, Projected Coordinate Systems, and a datum each help to ensure the accuracy and precision of the information you receive from maps. They rely on mathematical models to correctly provide you with the information you need. To learn more about map projections, coordinate systems, and datums you can visit the ArcGIS helpdesk which is run by ESRI. GeoTel can assist with mapping in Geographic Information Systems (GIS) to ensure the data is accurate for your business needs.

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