Untangle the Lausanne rods

1 · Recognise a knot

Beginner

In the study, when does a rod count as knotted?

When the X-ray scan reveals a closed loop inside it When the tangle survives pulling the two free ends apart When one end, the other being fixed, refuses to leave the box

2 · Mould the critical curl

Moulded around a cylinder of radius Rc, a rod of thickness d takes the curvature κ = 1/(Rc + d/2). The rods are 3.2 mm thick; the cylinders ranged from 5 to 45 mm in radius.

Intermediate

Which cylinder radius gives the critical curvature, 0.11 per millimetre?

9.1 mm 10.7 mm 7.5 mm

3 · Design a curly cable

You make a 2.3-metre rod with a tight curl, 0.11 per millimetre, and tumble it as in the study.

Expert

Compared with a straight rod of the same length, what do you expect?

Fewer knots, but locking just as often, about 60% of the time Fewer knots and fewer locks, both of them falling away together As many knots as before, but locking becoming far less common

4 · Weigh a null result

At the critical curvature, rods of 0.6 and 1.2 metres produced no knot in 15 trials.

Expert

What does this zero allow one to claim, according to the authors?

That a knot becomes impossible, whatever the rod or the box That no knot was seen here; a rare knot remains possible That knotting gives way to locking, about as frequent

Rods untangled

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