I would like to tell people to refer to election cycles as X mod 4. Alternatively, using the terms "on", "off", and "odd".
Virginia and New Jersey holds their statewide elections on 1 mod 4 years. Kentucky holds its statewide elections on 3 mod 4 years. Both of these can also be described as being held on odd years.
A wide variety of federal, state, and local elections are held on 2 mod 4 years, also known as "off" years.
And years with presidential elections are held on 0 mod 4 years, commonly referred to as "presidential" years, but why don't we just continue the analogy and use a back-formation to make it consistent and call them "on" years.
Coincidentially, the summer Olympic Games are also held on 0 mod 4 years, while the winter Olympic Games and the World Cup in soccer are held on 2 mod 4 years.
If you need extra specificity, just append the term "Gregorian" to these. e.g. "Virginia holds its statewide elections in Gregorian 1 mod 4 years."
Maybe I should use a constant other than i in my ring, as my ring is a subset of the complex numbers, but my i maps to a value other than i in that field.
Okay, I think I've decided on upsilon instead of i, phi instead of j, and maybe tau instead of k. (Maybe not because tau is already a constant in complex numbers...)
I can't be completely sure without tedious manual verification but I think that ring is just Z[ζ] where ζ is a fifth root of unity. IIRC that ring actually gets use in one description ("cut-and-project") of the possible Penrose tilings
I can't be completely sure without tedious manual verification but I think that ring is just Z[ζ] where ζ is a fifth root of unity. IIRC that ring actually gets use in one description ("cut-and-project") of the possible Penrose tilings
Macaulay2 is telling me it's the zero ring. Possibly @vtk made a mistake in one of the identities.
Perhaps I should have said I re-invented it. I'm not surprised it's already been studied by someone, but this specific ring really isn't covered in-depth on Wikipedia, and the only math class I ever took that even came close to this stuff I had to drop because the homework was a nightmare.
Comments
Virginia and New Jersey holds their statewide elections on 1 mod 4 years. Kentucky holds its statewide elections on 3 mod 4 years. Both of these can also be described as being held on odd years.
A wide variety of federal, state, and local elections are held on 2 mod 4 years, also known as "off" years.
And years with presidential elections are held on 0 mod 4 years, commonly referred to as "presidential" years, but why don't we just continue the analogy and use a back-formation to make it consistent and call them "on" years.
Coincidentially, the summer Olympic Games are also held on 0 mod 4 years, while the winter Olympic Games and the World Cup in soccer are held on 2 mod 4 years.
If you need extra specificity, just append the term "Gregorian" to these. e.g. "Virginia holds its statewide elections in Gregorian 1 mod 4 years."
[/things no one but gmh cares about]
of course in real math π isn't a constant either