Little explorations with HP calculators (no Prime)

[Gerson W. Barbosa]

(04-08-2017 10:16 PM)Han Wrote:  I think that (in your first solution) if you had at least mentioned that the relative ratio of the areas remains the same regardless of the shape by considering the law of cosines and using Heron's formula (and thereby leaving the details as "an exercise for the diligent reader"), then your original solution would very well have been complete. (That was why I was repeatedly asking how you decided the shape did not matter -- because I myself and perhaps several others did not see the connection of the law of cosines and Heron's formula. I did use the law of cosines, but mainly to get the corresponding sine values, and certainly not the same way you did.)

Very likely I didn't make myself clear, although I thought I did. Anyway no problem about the questionings. They appeared somewhat disturbing to me because I failed to understand where I had gone wrong. From my point of view I haven't used any forbidden shortcut to get to the solution, but I understand there was some lack of rigor in my statements. If it weren't for these questionings, I'd probably still be pleased with my first solution. Also, the discussions have prompted you, much more than me, to work out really professional contributions for the thorough understanding of the problem. Thank you very much for your patience!

Gerson.