should be THE circle constant? What a silly question! Who says there must be only one
circle constant? Why not have an entire family
of circle constants, including both
? The real question is, which circle constant should be the fundamental
one, from which the rest of the family is derived? Well,
is the upper limit of the set
which we can define as the set of all "proper angles", i.e., the minimal set which represents every possible direction or orientation. Every other real value is congruent with some value in this set, via the operation
. So there can't be any interesting circle constant greater than
, because it would just be congruent with some other interesting constant between
. So if
is a candidate for "fundamental circle constant", it must be the largest possible one. That would make any other interesting circle constants some sort of fraction of
. It pretty much follows that
must be the more fundamental.
I propose the following convention:
. Some of the more interesting examples:
- the full-circle constant
- the semicircle constant = straight angle = "semitau"
- the tertiant-circle constant = triangle exterior angle = "tertiantau"
- the quadrant-circle constant = right angle = square exterior angle = "quadrantau"
- the sextant-circle constant = hexagon exterior angle = "sextantau"
- the octant-circle constant = diagonal angle = octagon exterior angle = "octantau"
- the unciacircle constant = dodecagon exterior angle = "unciatau"
-ists should have no complaint about not being able to use
as a single constant wherever they think it makes an equation more "elegant" or "efficient". However
would appear in the guise of
-ists can read as
, and proceed to refactor the equation into a more "elegant" and "efficient"
In other words, you can all have your have your