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3 votes
1 answer
394 views

Min Bend Orthogonal Knots

I am seeking literature on 3D orthogonal drawings of knots, especially minimum bend drawings. An orthogonal drawing employs segments parallel to the axes of a Cartesian coordinate system. A bend is a ...
Joseph O'Rourke's user avatar
13 votes
3 answers
1k views

Random Reidemeister moves to unknot

Suppose one has a link diagram of the unknot, and applies random Reidemeister moves until the unknot is reached. Surely it requires an exponential number of moves, exponential in, say, the crossing ...
Joseph O'Rourke's user avatar
7 votes
1 answer
938 views

Which knots' stick numbers are twice their crossing numbers?

Looking at a table of minimum stick numbers for knots (table here), it seems the known upper bound of $2 c(K)$ in terms of the knot crossing number $c(K)$ is realized by the trefoil $3_1$—it ...
Joseph O'Rourke's user avatar