The Last Recreations

pp 67-84

The Topology of Knots

  • Martin Gardner

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To a topologist knots are closed curves embedded in three-dimensional space. It is useful to model them with rope or cord and to diagram them as projections on a plane. If it is possible to manipulate a closed curve—of course, it must not be allowed to pass through itself— so that it can be projected on a plane as a curve with no crossing points, then the knot is called trivial. In ordinary discourse one would say the curve is not knotted. “Links” are two or more closed curves that cannot be separated without passing one through another.