The transition from degrees to radians is often the most traumatic mathematical change that the student has to endure when moving from elementary to intermediate mathematics. The simplicity of 360° seems so much more welcoming than the equivalent of
\(2\pi\) radians for the angle of a full circle.
\(\pi\) is forbidding, because it is not
the convenient fractional fiction \(\frac{22}{7}\), but rather a number which is both
transcendental and
irrational and therefore, somewhat “untidy”. Surely this tradeoff between simplicity and complexity must have been worth it, or it would not have been so ordained. Here we attempt to fathom
the method in the madness.