Given a triangle $\Delta$ with sides of length $a\le b\le c$, consider the number
$$q=\frac{a^4+b^4+c^4}{(a^2+b^2+c^2)^2}$$ and observe that $\frac13\le q\le\frac12$ and the extremal values of $q$ characterize some geometric properties of the triangle $\Delta$. Namely:


$\bullet$ $q=\frac13$ if and only if $a=b=c$ (which means that the triangle $\Delta$ is regular);


$\bullet$ $q=\frac12$ if and only if $c=a+b$ (which means that the triangle $\Delta$ is degenerated).


I am writing a paper (in applications of math to Electric Engineering) where the number $q$ is applied for evaluation of the deviation of a triangle (describing the quality of 3-phase electric energy) from being regular, and need to call the number $q$ somewhow (for example, *quadrofactror*), but wonder if $q$ already has some standard name. This motivates my



> 
> **Question.** Has the number $q$ some standard name in Plane Geometry?
> 
> 
> 



A number characterizing the deviation of a triangle from the regular triangle
Added to my comment above, this time taking care of my carelessness in not normalising: one has the formula
$$\frac{16 A^2}{(a^2+b^2+c^2)^2}=1-\frac{2(a^4+b^4+c^4)}{(a^2+b^2+c^2)^2}
$$
which shows, at least in my book, that a normalised version of the area $A$ (more precisely of its square) does the trick.


