MoebiusInvolutiveBasic

Basic involutive Moebius function

Function  y = x/(x-1) is self-inverse: x = y/(y-1) (symmetric on first diagonal y=x).
It is the function giving the ratio  y = XA/XB for a point on line AB described parametrically through.
                                                            X = (1-x)A + xB.
Then the ratio.
                                                            y = XA/XB = x/(x-1).
The graph of the function describes a rectangular hyperbola. The red points are the foci of the hyperbola.
Point (1,1) is its center and x = 1, y = 1 are its asymptotic lines.

Basic involutive Moebius function

See Also