File:MobiusSawtooth.png
Jump to navigation
Jump to search
Size of this preview: 731 × 600 pixels. Other resolutions: 293 × 240 pixels | 585 × 480 pixels | 936 × 768 pixels | 1,248 × 1,024 pixels | 2,496 × 2,048 pixels | 3,252 × 2,668 pixels.
Original file (3,252 × 2,668 pixels, file size: 1.64 MB, MIME type: image/png)
Captions
Captions
A Möbius strip, with a sawtooth wave traced along it to serve as a static demonstration of its non-orientability.
Summary
[edit]
This diagram was created with Mathematica.
| Description |
English: An static demonstration of the non-orientability of the Möbius strip. A filled sawtooth wave is traced along the Möbius strip; after completing a half-revolution, the wave returns mirrored, due to the strip's non-orientability.
The strip has a gradient color and opacity, primarily for visual effect. The sawtooth wave remains at full opacity, but its color is the complement of the strip to maintain maximum contrast. |
| Date | |
| Source | Own work |
| Author | Lemondoge |
| Source code | Mathematica codek[a_, b_, t_] := a + (b - a)*t^3
f[u_, v_] := {(1 + v/2 Cos[u/2]) Cos[u], (1 + v/2 Cos[u/2]) Sin[u],
v/2 Sin[u/2]}
SetAttributes[f, Listable] (*for convenience*)
(* generate image *)
mobius = Show[
ParametricPlot3D[f[u, v], {u, 0, 2 Pi}, {v, -1, 1},
ColorFunction ->
Function[{x, y, z, u},
RGBColor[k[0.880722, 0, u], 0.611041, k[0.142051, 1, u],
1 - (u)^3]],
Axes -> False, Boxed -> False, MeshFunctions -> {#5 &},
(* make a cutout to prevent z-fighting with sawtooth *)
RegionFunction ->
Function[{x, y, z, u, v}, v - Mod[u, Pi/4]/(Pi/4) <= 0],
PlotPoints->650
],
(* custom-bake the v mesh, and highlight u =
0. every other v mesh line terminates early to prevent overlap with sawtooth *)
Graphics3D[{GrayLevel[0.2],
Table[Line[
f[Pi/8*i, {-1, 0.5 Mod[i, 2]}]
], {i, 1, 16}], Thick, Black, Line[{{0.5, 0, 0}, {1.5, 0, 0}}]
}],
(* line *)
ParametricPlot3D[f[u, 1], {u, 0, 2 Pi}, PlotStyle -> Thick,
ColorFunction ->
Function[{x, y, z, u},
ColorNegate @
RGBColor[k[0.880722, 0, u], 0.611041, k[0.142051, 1, u]]],
PlotPoints->300
],
(* sawtooth *)
ParametricPlot3D[f[u, v], {u, 0, 2 Pi}, {v, -1, 1},
Mesh -> None,
RegionFunction ->
Function[{x, y, z, u, v}, v - Mod[u, Pi/4]/(Pi/4) > 0],
ColorFunction ->
Function[{x, y, z, u},
ColorNegate @
RGBColor[k[0.880722, 0, u], 0.611041, k[0.142051, 1, u]]
],
PlotPoints->650
]
];
Export["mobiusSawtooth.png", ImageCrop[Rasterize[mobius,Background->None,ImageResolution->1000]]]
|
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
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 19:03, 21 June 2023 | | 3,252 × 2,668 (1.64 MB) | Lemondoge (talk | contribs) | Uploaded own work with UploadWizard |
You cannot overwrite this file.
File usage on Commons
There are no pages that use this file.
