Images of Borromean Rings and Tight Clasp

A main focus of my research work has been the study of the shapes of knotted tubes when they are pulled tight. With my coauthors Joseph Fu, Rob Kusner, John Sullivan, and Nancy Wrinkle, I found a tight configuration of a link known as the Borromean rings. These Electric Image pictures show the configuration:

ThickBorromeanRings ThinBorromeanRings


These Borromean rings were built from a simpler configuration– a simple clasp formed by two ropes pulled across each other. That configuration turns out to have the surprising feature that there is a small space between the tubes. These pictures show the tubes and the space between them.

TightclaspExploded TightclaspTransparent TightclaspCloseup

All of these pictures ended up in the paper Criticality for the Gehring Link Problem.

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