32. Using TAU

What is TAU?

Short answer: It is the Greek letter .

Long answer: It is a Greek letter used to define the proportion of the circumference of a circle to its radius. Put simply, TAU is one turn of an entire circle, so 2*PI.

TAU allows us to express sinuses, cosines, and angles in a more intuitive and simple way. For instance, the well-known angles of 30⁰, 45⁰, 90⁰, and so on can be easily expressed in radians via TAU as a fraction of a circle, as in the following figure:

Figure 1.25: Angles represented using TAU

This is more intuitive than PI. It is like slicing a pie into equal parts. For instance, if we slice at TAU/8 (45⁰), it means that we sliced the pie into eight equal parts. If we slice at TAU/4 (90⁰), it means that we sliced the pie into four equal parts.

The value of TAU is 6.283185307179586 = 2 * 3.141592653589793. So the relationship between TAU and PI is TAU=2*PI. In Java, the well-known PI is represented via the Math.PI constant...