I am trying to get any roots of any order graphically. For rational roots (i.e., a^(1/n)) the inverse process of elevation to the nth natural power can be followed in inverse way as the images show, till you have from origin to the bottom of the line that gives the nth root a measure = 1. This can't be done but iteratively till you meet this 1 value as closely as you are able to attain.
Setting the problem parametrically in Autocad gives inmediately the solution (but in the process it will have solved the root or something akin to it so it is not truly a graphical procedure). The bases of the main rectangular triangles (the value we are searching for graphically) are
a^(2/3) for the cubic root a^(3/4) for the 4th root a^(4/5) for the 5th root etc
not surprisingly because once multiplied by the corresponding root have to give a.
So I am searching how to state these bases graphically by conventional means "without" solving the root or some akin root. (Of course it will solve it but the intent is that it not be with the analytic power of computation, but graphical device). ¿Any help?
After that we would still better think something better for numbers elevated to any real number, for who wants to elevate say 3469234689^(1/239) just to get some approximation? This to explore the niceties of graphical computation.