Die Borromäischen Ringe

Teaser Image Die Borromäischen Ringe - (2006) 4 min
ID: 2006-14
Director: Charles Gunn, John M. Sullivan
Country: ger
Age Rating: 0
Distributor: Springer Verlag
Genres: Short Movie, Animated Movie
Languages: German, English

This video, premiered at International Congress of Mathematicians 2006, explains the mathematics behind the new International Mathematical Union logo. The logo depicts the Borromean rings (three linked rings with the property that no pair is linked) in the form they have when tied tight. This tight configuration has pyritohedral symmetry, with the rings lying in orthogonal planes.

The video starts with an exploration of this symmetry group, featuring Fuller’s “jitterbug”. A five-coloring of the icosahedron edges shows how the pyritohedral group fits into the icosahedral group. The Borromean rings then appear as three golden rectangles, with pyritohedral symmetry.

After an interlude showing how the rings have been used in many cultures as a symbol of interconnectedness, the video depicts a tightening process. It preserves the symmetry and leads to the tight configuration, which is explored with various rendering styles.

This film is included in the compilation MathFilm 2008 DVD.