File:Line Circle Trajectory.gif
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Line_Circle_Trajectory.gif (484 × 196 pixels, file size: 615 KB, MIME type: image/gif, looped, 120 frames, 12 s)
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Summary
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SAGE Source Code:
sage: npi = RDF(pi)
sage: xtreme = 3
sage: var('x,y')
(x, y)
sage: myaxe = line([[-xtreme,1],[xtreme,1]], color = 'black', zorder = 0)
sage: iplot = implicit_plot(9*y^4+10*x^2*y^2+x^4-12*y^3-12*x^2*y+4*y^2, (x,-2.5,2.5), (y,-0.1,1.1), plot_points=600, frame=False, zorder = 1)
sage: def traj(theta):
maC = circle((0,0), 1, color = 'black', zorder = 0)
p1 = [sin(theta), cos(theta)]
p2 = [1/2*(2*sin(theta) + sign(cos(theta/2))*sqrt(4*sin(theta)^2 + 8*cos(theta) + 8)), 1]
p3 = [p1[0]+1/2*(p2[0]-p1[0]), p1[1]+1/2*(p2[1]-p1[1])]
maL = line([p1,p2], color = 'magenta', zorder = 2)
map1 = point(p1, zorder = 3)
map2 = point(p2, zorder = 3)
map3 = point(p3, zorder = 3)
ma = myaxe + maC + iplot + maL + map1 + map2 + map3
return ma
sage: a = animate([traj(i) for i in srange(0, 4*npi, npi/30)], xmin = -xtreme, xmax = xtreme, ymin = -1.1, ymax = 1.1, figsize = [6, 2.2], axes = False)
sage: a.gif(savefile = "Line_Circle_Trajectory.gif", delay=10)
| Description |
English: The trajectory of a linkage of length 2 between the unit circle and one of its tangent lines. Created using SAGE.
Deutsch: Die Trajektorie des Mittelpunkts einer Stange der Länge 2, deren Endpunkte auf dem Einheitskreis und auf einer Tangente dazu liegen. Erstellt mit SAGE. |
| Date | |
| Source | Own work |
| Author | Mwageringel |
| Other versions |
 |
Licensing
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I, the copyright holder of this work, hereby publish it under the following license:
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 19:17, 22 May 2012 | | 484 × 196 (615 KB) | Mwageringel (talk | contribs) |
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