51M04: Elementary Euclidean geometry (2-dimensional)
Ordinary plane geometry (such as is studied in US secondary schools) holds an irresistible appeal, although many results derive what appear to be unimaginative conclusions from tortured premises. Nonetheless, from time to time something catches our eye and gets us to think about ordinary triangles and circles.
Constructibility with compass and straightedge is dealt with elsewhere.
Tilings and packings in the plane are part of Convex Geometry.
Many topics regarding polygons (e.g. decompositions into triangles and so on) are treated as part of polyhedral geometry.
Parent field: 51M - Real and Complex Geometry
A compendium of plane curves
For computational geometry see 68U05: Computer Graphics