### 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’