### A Rotation by One Turn is 1

#### by fortmarinus

In Michael Hartl’s^{i} Tau Manifesto^{ii}^{iii}, he addresses a criticism of the Tau formulation which points out that the -form of Euler’s equation only relates 4 fundamental constants (e, i, circle constant, and 1), while the -form relates 5 (despite needing to be re-arranged to do so). In response, he jokingly tacks on a trivial ‘+0’ to the -form to put it on par with the -form.

Re-arranged Pi form |
Trivially Modified Tau form |

Full Pi form |
Full Tau form |

However, all joking aside, is a complex number which evaluates to the complex number (1 + 0i). Thus, it is not trivial to represent the zero, in fact, it is thoroughly correct to do so. Conversely, the cleverly re-arranged -form is even uglier than previously thought, as it breaks up its own complex number evaluation (-1 + 0i) and places half of it on either side of the equation.

Both forms properly include a zero, but the modified -form breaks the symmetry of the solution, while the -form maintains its symmetry without modification.

Now, as a disclaimer on the debate, I believe that the debate is not about choosing a constant or a symbol that makes equations look prettier; this is utterly secondary and wholly counterproductive. The debate is about the proper definition of the fundamental circle constant. Which, is , obviously^{iv}.