Little explorations with HP calculators (no Prime)

[pier4r]

(03-27-2017 06:01 PM)Dieter Wrote:  Right, in the end you realize that both formulas are the same. ;-)

How? One should be from the Pythagoras' theorem, a^2+b^2=c^2 (where I use the two sides of the triangle to get the hypotenuse) the other is the composition of the area of the square, made up from 4 triangles and one inner square. To me they sound as different models for different measurements. Could you explain me why are those the same?

Anyway to me it is great even the numerical solution (actually the one that I search with the hp50g) but I cannot tell you if it is right or not because I did not solve it by myself, other reviewers are needed.

Edit, anyway I remember that a discussed solution mentioned the relationship of a circle inscribed in a triangle, so I guess your direction is right.