PaddletotheSea - I'm with ya on "
uptight" and"
tight" - in the different songs, and I also now know the term "tight" for a "band being "tight" - in synch; good. Thanks !
Regarding hexic ring: [sic]
If you want to skip the "yada yada' as was said above, go right to yellow.
Regarding
hexagram versus hexic ring - if you really want to know the difference, I think I pretty well played out the web in info on wikipedia et al anyway on
hexagram - from "Gotta Get Away, but you mentioned as well hexic ring. I'm not sure what song it is from , but the only definition I know on a hexic ring - which you expressed frustration as did a few others on
what is the hexic ring - not much on the web, etc... here it is... and I am real sure lol that Gord did not mean this...
whatever song the hexic ring is from -I'd love to know..... OK here goes....- trying to be helpful in return -
Hexic Ring:
The hexic part:
Names of polynomials by degree
Polynomials with small degrees may be named according to their degree as follows:
★ Degree 1 - linear
★ Degree 2 - quadratic
★ Degree 3 - cubic
★ Degree 4 - quartic
★ Degree 5 - quintic
★ Degree 6 - sextic ''or'' hexic
And... in keeping, mathematically
the ring part of hexic ring:
Formal definition [of ring]
A 'ring' is a set ,R equipped with two binary operations +colon R imes R
ightarrow R and cdotcolon R imes R
ightarrow R (where imes denotes the Cartesian product), called ''addition'' and ''multiplication'', such that:
★ ,(R, +) is an abelian group with identity element ,0, so that , orall a, b, c in R, the following axioms hold:
★
★ ,a + b in R
★
★ ,(a + b) + c = a + (b + c)
etc. but where:
Given a ring R, the polynomial ring R[''x''] is the set of all polynomials in ''x'' that have coefficients chosen from R. In the special case that R is also a field, then the polynomial ring R[''x''] is a principal ideal domain and, more importantly to our discussion here, a euclidean domain.
It can be shown that the degree of a polynomial over a field satisfies all of the requirements of the ''norm'' function in the euclidean domain. That is, given two polynomials ''f''(''x'') and ''g''(''x''), the degree of the product ''f''(''x'')•''g''(''x'') must be larger than both the degrees of ''f'' and ''g'' individually. In fact, something stronger holds:
: deg( ''f''(''x'') • ''g''(''x'') ) = deg(''f''(''x'')) + deg(''g''(''x''))
So, in short, a hexic ring - and I mean the ONLY hexic ring I can find, is
A sixth (or hexic) order polynomial ring( is a set ,R equipped with two binary operations ) that also that defines a Euclidean domain etc.
and I'm REAL sure Gord did not mean this, as well read as he is LOL !!
BTW - The only other refence to hexic ring, that also seperates the two terms but contains them, and are within the context of the combinatorial search engine info.com - that accesses 6 different popular search engines and collates the results, is apparently a popular XBOX game (Hexic..?)[sic], and..Tetris.
And, together, an overheating problem gamers must just have tizzies over is called the Red Ring of Death, for which their is a special cooling fan. A fan made just for stopping the red ring of death overheating. Fascinating, captain. Not.
~holy polynomials batman !
~geo steve ....lol