The simplest helix graph is generated by Euler’s equation in 3Di coordinates:
A simple coefficient in the exponent determines the frequency:
As we go through the sections of the book, it becomes clear why Euler’s Formula is regarded as the most remarkable equation in mathematics. It is innate almost everywhere.
See section 6.0 Euler’s Formula Upgraded, Helix and Spiral Functions for more discussion.
By adding a second term with a frequency close to the first one, a ‘Beat Helix’ results:
Three plane projection with
3Di object with
Animation 5 ’Beat Helix’