Little explorations with HP calculators (no Prime)

[RMollov]

(05-22-2018 03:03 AM)Gerson W. Barbosa Wrote:  

(05-06-2018 06:13 AM)RMollov Wrote:  Would you show those steps here? I stopped before them thinking that's enough...

Sorry for the late reply! I stopped following this thread since page 8 or 9, so I’ve completely missed your request.
The next steps are simply the manual solution of the second-degree equation using Baskhara’s formula:

r = (-4 + sqrt(4^2 - 4*8*(-1)))/(2*8)
...
r = (-4 + sqrt(48))/16
...
r = (sqrt(3) - 1)/4

Pier has provided a drawing that illustrates the solution.

Gerson.

Thanks, Gerson
As I already mentioned, I'd be interested if that could be derived directly from geometry. Now I'm happy that's not the case.