Eulers Spiral and the Zylinder - page 1

I am using material and images with kind permission from:

http://wehner.org/euler/index.htm

It is worthwhile following the link as Wehenr shows how these functions map onto a cyclinder (and I would say a zylinder or complex cylinder too)

Euler noticed the inreconnected nature of the real and imaginary exponential and trigonometric (sine) functions.
I have extended Euler's ideas to fit on and within my zylinder or complex cylinder.
This allows for two complex waves to form a REAL wave! It may also work in reverse fashion to resolve a real wave into its imaginary component wave parts.
We start by looking at 4 boxes that give pwer series that were manipulated by Euler.
For a quick overview on page 5 click here

Continued on Page 2