unit^unit

Hi Valery.

Valery Ochkov wrote: Yes. My graph is a^b=constant. In Mathcad without units (m=1). Why? Mathcad cannot work with unit^unit.

Finally I can see that a^b = constant in the curve! But still non understanding why 😞 . You take L2 = ln(a)/ln(L1) with L1 in meters, so maybe have more complicated expressions for the units, even at the end must to be constant = m^m.

I never see something like your curve, but I'm not a curve expert. I guess that for the curve name Valery's curve isn't the best, just because you between hands have others like logarithmic or roth, in your math toolbar picture. Maybe the "potential - exponential Valery's curve" for this, and log-Valery's, root-Valery's for the "others". There are some math or geometrical institution where can ask about some antecedent of this?

Please, give us parametric expressions of the curve, and then eqs for arc length and area. Also, someone with a lot of ability and some time can construct the mechanical system showing in the plot. Your curve represent a geometrical system, with an amazing property, which can be translated to a mechanical system, and some other electrical via mec-elec equivalents (this is a circuit showing in an oscilloscope this curve).

Raise powers are curious. They are just a resumed products, that's easy, and seems to be the same than product is for the sum. But because is not a commutative binary operation (3^5 != 5^3) have to inverses: one by the right (roots) and other by the left (logs). And that's not that easy.

Best regards.

Alvaro.