There are basically two approaches to classical Euclidean plane geometry—the synthetic approach and the metric approach. The older of the two is the synthetic approach followed by Eucliding later by Hilbert. In the Eucliding treatment, one begin by assuming as undefined the relations of betweenness, congruence of segments, and congruence of angles. The metric treatments, initiated by G. D. Birkhoff in the 1930s, assumes the existence of the real numbers (or a set of postulates that guarantees the existence of the real numbers) and the existence of a distance function d and an angle-measure function m.