Loops, Knots, and Unknots

The carved stone decorations on the Bulfinch Gatehouse, located near the White House in Washington, D.C., look like mathematical knots.

Mathematically, a knot is a one-dimensional curve that winds through itself in three-dimensional space and catches its own tail to form a loop. If the loop has no knot in it and can be manipulated and made tangle-free to look like a circle, mathematicians call the loop an unknot.

Are the Gatehouse designs true knots or merely disguised unknots?

Looped decorations adorn a Bulfinch gatepost near the National Gallery of Art.

Depending on the tangle, it can be enormously difficult to distinguish a knot from an unknot by eye. Mathematicians have tools to help them identify and distinguish knots, but they have no general algorithm to determine if a tangled curve is a knot or if two given knots are interlocked.

Photos by I. Peterson