Here on Spatially Challenged, I post things people ask me about. The bigger topics (SAGA GIS, data sources, Word tricks, etc.) get turned into series of how-to posts, and the smaller questions inspired a series of vocab posts. Today we’re talking about the words Euclidean and Cartesian.
Euclidean means “related to Euclid.” Euclid was a Greek mathematician, and a lot of the geometry you learned in school is derived from his work. He’s also known for using deductive reasoning in his mathematical proofs. Want to know more about Euclid? Check out his page on The Store of Mathematics— an awesome site connecting history, math, and science.
A Euclidean world is a world where the rules, or axioms, that Euclid’s understanding of geometry apply to, such as a flat plane. Euclid also has geometry rules that exist in three dimensional space, but you won’t see him talking about spherical geometry.
One reason I’ve been asked about Euclidean worlds recently has to do with analyzing distance data. If you look at the Euclidean distance between two points, you measure the straight line that connects the points. Another way to think about this is the “as the crow flies” distance between two places. But, in reality sometimes it’s more useful to think about the most direct street-route between two locations, which would not be Euclidean.
Cartesian means “related to Descartes,” who was a French philosopher. A Cartesian plane is the usual coordinate plane you see in school (see example to the left). These planes have two perpendicular, numbered axes and can be used to related Euclidean geometry and algebra. For example, you can get the Euclidean distance between two points by using the X and Y coordinates of the points. If you have a map based on a State Plane Coordinate coordinate reference system, calculating these distances is fast and easy.
Just as Euclidean geometry exists in dimensions greater than two, Cartesian planes are also possible in 3+ dimensions. These higher dimensions are super cool and useful for modeling, but I won’t get into them today.
Do you have words you aren’t quite sure about? Feel free to send them my way via the contact for or Twitter (@EGmatcham). Thanks!