Mast Kalandar

bandar's colander of random jamun aur aam

Fri, 07 Mar 2008

< Testing testing or breaking toys | · | Proposal for IMSc web re-organisation >

Schlafly double-six movie


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A Schlafly double-six is defined as a collection of six pairs of skew lines (Pi,Qi) in space so that for each i different from j, Pi meets Qj; the Pi's do not meet each other and the Qj's do not meet each other either.

The construction of such a sextuple has been known since 1858 when Steiner discussed the 27 lines on a cubic surface with Shläfli. More history surrounding the 27 lines can be found at the History of Mathematics web site.

Last year, in response to a "coffee-table" conversation at CalTech, I provided a [two-page write-up][shlafly article] on how one can visualise the construction of such a double-six. As "proof of concept", I produced a number of different povray source files which would draw the constructed lines. I then gave a talk based on the write-up in the AIS school at IIT, Chennai in summer 2007.

In December, we had a visit from Etienne Ghys who gave a wonderful presentation regarding the Lorenz attractor and its connection to modular knots. He had produced some movies using povray which neatly illustrated his talk. During discussions, he persuaded me that it would be nice to have a movie about the double-six.

The IMSc Seminar Week seemed like a good excuse to work on my "film debut"! Unfortunately, I under-estimated the amount of time this would take and almost chickened out. With a little help from schroot on a faster machine, I was able to create the movie and also present my talk today.

Let me add that I feel more than a bit embarrassed at using non-free software (povray) to make the movie. I could have used blender to create the movie but then the source would be opaque as it would have been "drawn by hand". The language povray is free and the source for the movie is quite (I think!) expressive.


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