2.7 Helixes in 3Di
The simplest helix graph is generated by Euler’s equation in 3Di coordinates:
![]()
Interval
:

A simple coefficient
in the exponent determines the frequency:
![]()
with ![]()

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.
2.71 Beat Helix
By adding a second term with a frequency close to the first one, a ‘Beat Helix’ results:
![]()
with ![]()
FRP

TIP

RSIP,
:

Three plane projection with ![]()

3Di object with ![]()


Animation 5 ’Beat Helix’