Home

Soapfilms on Borromean Rings - WebGL 3D

This page shows soap films on Borromean Rings in 3D using the WebGL 3D Graphics technology, now available in the Firefox and Chrome browsers.

Firefox browser: Panels not in the viewing area at load time all start with the same image, so when you scroll down you see a lot of the same thing. But if you twirl an image with the mouse, the correct image will display.

Chrome browser: All the panels show the same image, for some reason I haven't figured out yet. But clicking in the various panels will show the various possible films.

Internet Explorer browser: Doesn't do WebGL. But get the IEWebGL plugin. But Symantec claims this file is too risky to download. Hmmm.

For old-fashioned 2D images and general commentary, see here, and for 3D using javascript see here.

Please be patient while this pages loads all the graphics data.

1. Bare Borromean rings. 2. Stable orientable manifold (no triple lines) spanning the rings. This is known as the "Seifert surface" in knot theory. 3. Stable unorientable manifold. 4. Unstable manifold resulting from poking out all six small triangular areas in the hexagon-center film. This film is unorientable.
5. Soap film spanning the rings with a hexagonal center. 6. Soap film spanning the rings with a pentagonal center. 7. Soap film spanning the rings with a square center. 8. Soap film spanning the rings with a tetrahedral point center. This film has the least area among the four fully spanning films.
9. Film resulting from poking out one of the inner triangles from the tetrahedral-point-center full film. 10. Film resulting from poking out the central hexagon in the hexagon-center film. 11. Film resulting from poking out two opposite triangular areas in the hexagon-center film. This film can be viewed as the union of an elliptical film on one ring with a twisted strip film on the other two rings, with the intersection between them resolved by splitting the quadruple lines into two triple lines. 12. Film resulting from poking out two adjacent small triangular areas in the hexagon-center film.
13. Film resulting from poking out one outer lobe in the hexagon-center film. This film exists even with zero thickness rings. 14. Film resulting from poking out one outer lobe and opposite small triangular face in the hexagon-center film. 15. Film resulting from poking out one outer lobe and one of the large triangular faces in the hexagon-center film. 16. Film resulting from poking out one outer lobe of the tetrahedral-point-center film.


Home
Susquehanna University assumes no responsibility for the content of this personal Web page. Please read the disclaimer.