From https://www.cs.sfu.ca/~ggbaker/zju/math/planar.html https://www.cs.sfu.ca/~ggbaker/zju/math/planar.html connecting utilities (electricity, water, natural

From https://www.cs.sfu.ca/~ggbaker/zju/math/planar.html https://www.cs.sfu.ca/~ggbaker/zju/math/planar.html connecting utilities (electricity, water, natural gas) to houses. If we can keep from crossing those lines, it will be safer and easier to install. Connecting components on a circuit board: the connections on a circuit board cannot cross. If we can connect them without resorting to another layer of traces, it will be cheaper to produce. Subway system: if subway lines need to cross, we've got some serious engineering to do. Also: The study of two-dimensional images often results in problems related to planar graphs, as does the solution of many problems on the two-dimensional surface of our earth. Many natural three-dimensional graphs arise in scientific and engineering problems. These often come from well-shaped meshes, which share many properties with planar graphs.