File:Steiner chain animation-50dpi.gif
Page contents not supported in other languages.
Tools
Actions
General
In other projects
Appearance
Steiner_chain_animation-50dpi.gif (250 × 251 pixels, file size: 1.35 MB, MIME type: image/gif, looped, 126 frames)
![]() | This is a file from the Wikimedia Commons. Information from its description page there is shown below. Commons is a freely licensed media file repository. You can help. |
Summary
DescriptionSteiner chain animation-50dpi.gif |
English: Animation of a Steiner chain of 9 circles, showing that the locus of the position of the circles' centres is an ellipse (in red), and that the locus of the contact points between the circles is a circle itself (in orange) |
Date | |
Source | https://twitter.com/j_bertolotti/status/1039543306433249280 |
Author | Jacopo Bertolotti |
Permission (Reusing this file) |
https://twitter.com/j_bertolotti/status/1030470604418428929 |
Mathematica 11.0 code
n = 9; \[Theta] = \[Pi]/n; \[CapitalDelta]\[Theta] = (2 \[Pi])/n; R = 0.2; \[Rho] = R/(1 + 1/Sin[\[Theta]]); r = \[Rho] (1/Sin[\[Theta]] - 1); center = {.3, 0}; plots = Reap[For[start = 0, start <= 2 \[Pi], start = start + 0.05, CandR = Table[{center[[1]] + (\[Rho] + r) Cos[i], center[[2]] + (\[Rho] + r) Sin[i], \[Rho]}, {i, start, start + (n - 1)*\[CapitalDelta]\[Theta], \[CapitalDelta]\[Theta]}]; createcoord[{x_, y_, z_}] := {(x )/(x^2 + y^2 - z^2), (y)/(x^2 + y^2 - z^2), z/(x^2 + y^2 - z^2)}; innerc = createcoord[Flatten[{center, r}]]; outherc = createcoord[Flatten[{center, R}]]; ellipseCenter = {(outherc[[1]] + innerc[[1]])/2, 0}; ellipseA = Abs[createcoord[{center[[1]] + \[Rho] + r, 0, \[Rho]}][[1]] - ellipseCenter[[1]]]; ellipseC = (outherc[[1]] - innerc[[1]])/2; ellipseB = Sqrt[ellipseA^2 - ellipseC^2]; tmp = Map[createcoord, CandR]; p1 = {x, y} /. Solve[{(x - tmp[[1, 1]])^2 + (y - tmp[[1, 2]])^2 == tmp[[1, 3]]^2 && (x - tmp[[2, 1]])^2 + (y - tmp[[2, 2]])^2 == tmp[[2, 3]]^2}, {x, y}][[1]]; p2 = {x, y} /. Solve[{(x - tmp[[3, 1]])^2 + (y - tmp[[3, 2]])^2 == tmp[[3, 3]]^2 && (x - tmp[[2, 1]])^2 + (y - tmp[[2, 2]])^2 == tmp[[2, 3]]^2}, {x, y}][[1]]; p3 = {x, y} /. Solve[{(x - tmp[[3, 1]])^2 + (y - tmp[[3, 2]])^2 == tmp[[3, 3]]^2 && (x - tmp[[4, 1]])^2 + (y - tmp[[4, 2]])^2 == tmp[[4, 3]]^2}, {x, y}][[1]]; c = Abs[{xc, yc, rc} /. Solve[((#1 - xc)^2 + (#2 - yc)^2 == rc^2) & @@@ {p1, p2, p3}, {xc, yc, rc}][[1]] ]; Sow@Show[ Graphics[{Orange, Thick, Evaluate[Circle[{c[[1]], c[[2]]}, c[[3]]] ]}], Graphics[{Black, Thick, Circle[{#1, #2}, #3] & @@@ Map[createcoord, CandR] }], Graphics[{Blue, Thick, Circle[{#1, #2}, #3] & @@@ {innerc, outherc} }], Graphics[{Red, Thick, Circle[ellipseCenter, {ellipseA, ellipseB}]}], Graphics[{PointSize[0.02], Point[Map[createcoord, CandR][[All, 1 ;; 2]]] }] ]; ];][[2, 1]]; ListAnimate[plots]
Licensing
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.
http://creativecommons.org/publicdomain/zero/1.0/deed.enCC0Creative Commons Zero, Public Domain Dedicationfalsefalse |
![]() |
This file, which was originally posted to
https://twitter.com/j_bertolotti/status/1039543306433249280, was reviewed on 19 October 2018 by reviewer Ronhjones, who confirmed that it was available there under the stated license on that date.
|
Captions
Add a one-line explanation of what this file represents
Items portrayed in this file
depicts
some value
11 September 2018
image/gif
File history
Click on a date/time to view the file as it appeared at that time.
Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 08:29, 12 September 2018 | ![]() | 250 × 251 (1.35 MB) | Berto | User created page with UploadWizard |
File usage
The following pages on the English Wikipedia use this file (pages on other projects are not listed):
Global file usage
The following other wikis use this file:
- Usage on es.wikipedia.org
- Usage on ja.wikipedia.org
Metadata
This file contains additional information, probably added from the digital camera or scanner used to create or digitize it.
If the file has been modified from its original state, some details may not fully reflect the modified file.
GIF file comment | Created with the Wolfram Language : www.wolfram.com |
---|
Retrieved from "https://wiki.riteme.site/wiki/File:Steiner_chain_animation-50dpi.gif"