Patterns in circular motions

Dance of circular motions ___________________________________________________________________________ Script of the video: In the plane, we draw a circle. Divide this circle into equal parts by n points. Draw large circles tangent to the small circle at these points. With k dots, place these dots on the large circles one by one. This is the first large circle. We place the first dot on the first large circle. Its initial phase is phi 1 equals 0. Next, place the second dot on the second large circle. Its initial phase is phi 2. On the third large circle, the third dot will have an initial phase of phi 3. And so on. In general, on a large circle, the i-th dot will have an initial phase of phi i. Note that the phase difference delta phi between consecutive dots is constant. Let the dots move on their circles with constant speed. Here are some interesting models with some values of n, k, delta phi ---------------------------------------------------------------------------------------------- The effect was programmed by Nguyenthinh_academy using the Manim library of the Python programming language ------------------------------------------------------------------------------------------------- *Music by Vincent Rubinetti Download the music on Bandcamp: https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown Stream the music on Spotify: https://open.spotify.com/playlist/3zNK20qC96mVSww60lVi1k ------------------------------------------------------------------------------------------------- ***Sound Effect from Pixabay -------------------------------------------------------------------------------------------------- Song: Rage Sound - Leaf Flying Into The Sky Music provided by Tunetank. Free Download: https://tunetank.com/track/4204-leaf-flying-into-the-sky/