I propose the following convention: [tex]\forall n \in \mathbb{N}^*[/tex], let [tex]\tau_{n} = \frac{\tau}{n}[/tex]. Some of the more interesting examples:

- [tex]\tau_{1} = \tau =[/tex] the full-circle constant
- [tex]\tau_{2} = \frac{\tau}{2} = \pi =[/tex] the semicircle constant = straight angle = "semitau"
- [tex]\tau_{3} = \frac{\tau}{3} =[/tex] the tertiant-circle constant = triangle exterior angle = "tertiantau"
- [tex]\tau_{4} = \frac{\tau}{4} = \eta =[/tex] the quadrant-circle constant = right angle = square exterior angle = "quadrantau"
- [tex]\tau_{6} = \frac{\tau}{6} =[/tex] the sextant-circle constant = hexagon exterior angle = "sextantau"
- [tex]\tau_{8} = \frac{\tau}{8} =[/tex] the octant-circle constant = diagonal angle = octagon exterior angle = "octantau"
- [tex]\tau_{12} = \frac{\tau}{12} =[/tex] the unciacircle constant = dodecagon exterior angle = "unciatau"

This way, [tex]\pi[/tex]-ists should have no complaint about not being able to use [tex]\pi[/tex] as a single constant wherever they think it makes an equation more "elegant" or "efficient". However [tex]\pi[/tex] would appear in the guise of [tex]\tau_{2}[/tex], which [tex]\tau[/tex]-ists can read as [tex]\tau/2[/tex], and proceed to refactor the equation into a more "elegant" and "efficient" [tex]\tau[/tex] form.

In other words, you can all have your have your [tex]\pi[/tex] and [tex]\eta[/tex] too!