> The rational angles are only used to introduce the trigonometric functions. From then on we can deal with any real angle using arcs of circles and trigonometr

> The rational angles are only used to introduce the trigonometric functions. From then on we can deal with any real angle using arcs of circles and trigonometric functions. This whole technology is built on a foundation of calculus (limits, infinite sums). > we need angles to make sense of geometry Euclid’s version of geometry involves no angle measures whatsoever. Vector methods (of the type which should be preferred for most geometrical modeling and computation) generally need no angle measures. Angle measures get useful when dealing with uniform circular motion: astronomy and navigation, signal processing, etc., but are largely superfluous for geometry per se.