31 May
2015
31 May
'15
3:55 a.m.
Neat solution, Gene! [And thanks for explaining what the problem was ...] On 5/30/15, Dan Asimov <dasimov@earthlink.net> wrote:
... The formula where r = s = t is g(s), where
g(s) := f(s,s,s) = (1 - 2s)^2 / (s^2 - s + 1)
And ask some questions whose answer I have no idea about so far:
* Why is g(s) the ratio of two quadratic polynomials?
* Why is f(r,s,t) the ratio of two sextic polynomials?
* Is it even obvious a priori that the formulas should be rational functions? ...
In case r = s = t and equilateral, (s^2 - s + 1) happens to equal the squared length of the s-median. WFL