File:Hypocycloids vs radius.gif
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Hypocycloids_vs_radius.gif (600 × 394 pixels, file size: 6.08 MB, MIME type: image/gif, looped, 315 frames, 32 s)
Captions
Captions
Hypocycloids with variable ratio between the radii of the circles generating them.
Summary
[edit]
| Description |
English: If you track a point on a circle rolling without sliding inside another (bigger) circle, the family of curves you get is called "hypocycloids". If the ratio between the two radii is a rational number, the curve will be closed. |
| Date | |
| Source | https://twitter.com/j_bertolotti/status/1407987930682044417 |
| Author | Jacopo Bertolotti |
| Permission (Reusing this file) |
https://twitter.com/j_bertolotti/status/1030470604418428929 |
Mathematica 12.0 code
[edit]
R = 4;
x[t_, r_] := (R - r) Cos[t] + r Cos[(R - r)/r (t)];
y[t_, r_] := (R - r) Sin[t] - r Sin[(R - r)/r (t)];
frames = Table[
GraphicsGrid@Partition[Table[
Show[
ParametricPlot[{x[\[Tau], r], y[\[Tau], r]}, {\[Tau], 0, t}, PlotRange -> {{-6, 6}, {-6, 6}}, Axes -> False, PlotStyle -> {Red}]
,
Graphics[{Black, Thick, Circle[{0, 0}, R], Circle[{(R - r) Cos[t], (R - r) Sin[t]}, r], Red, Disk[{x[t], y[t]}, 0.2]}, PlotRange -> {{-6, 6}, {-6, 6}}] ]
, {r, 0.5, 3, 0.5}], 3]
, {t, 0.001, 10 \[Pi], 0.1}];
ListAnimate[frames]
Licensing
[edit]
I, the copyright holder of this work, hereby publish it under the following license:
 
|
This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication. |
| The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.
|
File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 09:24, 24 June 2021 | | 600 × 394 (6.08 MB) | Berto (talk | contribs) | Uploaded own work with UploadWizard |
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