Perko pair knots

These are the famous Perko pair knots, listed as distinct knots in many knot tables since the 19th century, until Kenneth Perko showed in 1974 that they were in fact the same knot. He proved the equivalence by showing a sequence of diagrams leading from one to the other. The following sequence is a different demonstration of the same fact, obtained by relaxing the two knots using KnotPlot.

A movie of the deformation is included as one of the standard KnotPlot demos. View it by first installing KnotPlot, then click on the "DemoA" panel and then "Perko pair".

Perko A (10₁₆₁)

Perko B (formerly 10₁₆₂)

Perko knot A step 1

Perko knot B step 1

Perko knot A step 2

Perko knot B step 2

Perko knot A step 3

Perko knot B step 3

Perko knot A step 4

Perko knot B step 4

Perko knot A step 5

Perko knot B step 5

Perko knot A step 6

Perko knot B step 6

Perko knot A step 7

Perko knot B step 7

Perko knot A step 8

Perko knot B step 8

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