The Golden Ratio rolling in Euler's constant hypocloids (visualization)

This short animation shows the beginning of the creation of the golden ratio hypocycloid (where the ratio between the radii of the two circles is the golden ratio) rolling inside of the creation of the e-hypocycloid (where the ratio between the radii of the two circles is Euler's constant, e). Because both numbers are irrational, both hypocycloids will never close, so we end after about 1.5 minutes.

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Music in this video
Attribution 4.0 International (CC BY 4.0)

[nazrulhaque]

What a beautiful piece it is! Sometimes i wonder.. Mathematics is like the movie harry potter, full of mystery, amazement and imagination.... we see unexpected things occur often in Mathematics and in the same time i also feel happy that they actually exists....Don't know why but it’s good to realise that someone has explored it through his creative thinking ❤️.

[taylorwoods]

couldn’t you take both ratios to be any positive number greater than 0 and the same thing will happen because the circle has infinite points

[maxmudita]

The ratio between the radii of which two circles is Eulers constant?

[erawanpencil]

I'm confused, which circles are which? @00:16. there's an emergent purple circle and then an emergent small blue circle in the very center. Both are different that the two hairline circles that the video began with. Then there's the disc containing all of them. Regardless of which are which, can you explain the signficance/rules that the rolling is occurring by?

[nasim]

I suppose this is how the pupil of our eye was created by God 😮😇😍