"Jerry W. Lewis" wrote in message ...
Charles Douglas Wehner wrote:

Such "tricks" as my "FOUR-BOX ALGORITHM" and a visualisation of the
"EULER SPIRAL" make things clear. However, to those who have not seen
the page, references to a "spiral in complex space" may seem like
mysticism.


I fail to see any fundamental difference between the "Euler Spiral" and
the "Riemann Surface" which was used to explain the mulitplicity of trig
function roots when I took Complex Analysis 30 years ago.

Jerry

I have investigated as promised. I could not give it too much time,
but I think the following is true:

In a Riemann Surface, you might have something like "logarithmic graph
paper". Consider an exponential drawn on such paper - it comes out
STRAIGHT.

So the "warp" is a warp of the WRITING SURFACE - to make what is
written seem to be more simple.

My Euler Spiral is drawn in VERY SIMPLE three-dimensional RECTILINEAR
space.

The axis into the page is made to represent the imaginary, but the
picture could be one of a spring from the suspension system of a car,
for example.

A car suspension spring will shadow a cosine onto the wall and a sine
onto the floor.

So it really is MUCH, MUCH LESS elaborate than the Riemann concept.

Charles Douglas Wehner.