exp: parabolic -> elliptic pencil
 | this activity is a page of geogebra-book elliptic functions & bicircular quartics & . . .(30.04.2023) |
this activity is also a page of geogebra-book geometry of some complex functions october 2021
-- -- -- z - plane : -- exp --> --> --> --> w = exp(z) -- w - plane
move a, b, c; change , ,
The complex exponential function forms
the parabolic pencil of circles, which consists of the axis-parallel straight lines,
to the elliptic-hyperbolic pencils of circles consisting of the straight rays emanating from the origin
and the concentric circles.
The exponential function is simply periodic: the parallels to the -axis are mapped onto the concentric circles:
change the parameter interval using .
The pencil of parallels which intersect the axis parallels at a constant angle give
parallel loxodromes under the exponential function: these are the curves which intersect the origin rays
at a constant angle: logarithmic spirals.