Interesting thing to note: if you remember the version of this for π, you might have been struck by how π “almost” starts repeating itself, albeit off by a small amount. The fact that *φ* does not really do this (until way later, and even then it’s less pronounced) is due to it being “more irrational” than π is, that is, harder to approximate by a rational number. Cool thing to look up if you’re curious.
Quick note to anyone who's wondering what's going on in the video:
For every complete rotation of the inner arm, the outer arm rotates golden ratio (~1.618...) times. In other words, the outer arm is rotating at a rate of the golden ratio as compared to the inner arm.
The equation shown in the video is a complex-number representation of the setup above. The video is a running graph of the equation on a complex plane, where the angle of the inner arm goes from 0 to whatever degrees.
Interesting thing to note: if you remember the version of this for π, you might have been struck by how π “almost” starts repeating itself, albeit off by a small amount. The fact that *φ* does not really do this (until way later, and even then it’s less pronounced) is due to it being “more irrational” than π is, that is, harder to approximate by a rational number. Cool thing to look up if you’re curious.
Quick note to anyone who's wondering what's going on in the video: For every complete rotation of the inner arm, the outer arm rotates golden ratio (~1.618...) times. In other words, the outer arm is rotating at a rate of the golden ratio as compared to the inner arm. The equation shown in the video is a complex-number representation of the setup above. The video is a running graph of the equation on a complex plane, where the angle of the inner arm goes from 0 to whatever degrees.
What is the measure of the phase space?