Construction of Angle Measure

This construction has the following structure: we begin by establishing a relationship between real numbers and their expressions in binary notation (Section 2). After introducing a few definitions and theorems to allow us to operate geometrically on a semicircle (Section 3), we construct the real number that corresponds to a given angle (Section 4). Using this construction, we then construct the angle that corresponds to a given real number in (0, 1), and show that the relationship is one-to-one (Section 5). Finally, we present and prove a theorem stating that angle measure exists and is unique, and provides some useful properties (Section 6).