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5-1 Based on the first of the two mathematical knots with five crossings. The new colour added is mauve. The 5-1 knot is also known as the cinquefoil knot. See https://en.wikipedia.org/wiki/Cinquefoil_knot for more details. Remember I am changing cord colour at each under-crossing, using reef knots to join the cords, and feeding the over-crossing cord through the reef knots.

5-1 Based on the first of the two mathematical knots with five crossings. The new colour added is mauve. The 5-1 knot is also known as the cinquefoil knot. See https://en.wikipedia.org/wiki/Cinquefoil_knot for more details. Remember I am changing cord colour at each under-crossing, using reef knots to join the cords, and feeding the over-crossing cord through the reef knots.

My first piece based on a mathematical knot with seven crossings. New colour of cord added is white.

My first piece based on a mathematical knot with seven crossings. New colour of cord added is white.

Here is the 6-2 knot as created using my knotted-cord technique. Anyone wondering yet how I get each colour to be a continuous loop? See http://katlas.math.toronto.edu/wiki/6_2 from which I have swapped over-crossings and under-crossings.

Here is the 6-2 knot as created using my knotted-cord technique. Anyone wondering yet how I get each colour to be a continuous loop? See http://katlas.math.toronto.edu/wiki/6_2 from which I have swapped over-crossings and under-crossings.

6-3 new version designed to look more like my more recent knots and the standard representations of mathematical knots. This is derived from the 3D depiction of 6-3 at http://katlas.math.toronto.edu/wiki/6_3

6-3 new version designed to look more like my more recent knots and the standard representations of mathematical knots. This is derived from the 3D depiction of 6-3 at http://katlas.math.toronto.edu/wiki/6_3

This piece is my first to have eight crossings and so eight colours, the new one added being purple. It is derived from knot 8-19 in the standard mathematical knot tables - the first to be non-alternating between under and over crossings.

This piece is my first to have eight crossings and so eight colours, the new one added being purple. It is derived from knot in the standard mathematical knot tables - the first to be non-alternating between under and over crossings.

5-2 The second of two different mathematical knots with five crossings. Compared to 5-1, some of the crossings involve different colours even though the colours are used in the same order.

The second of two different mathematical knots with five crossings. Compared to some of the crossings involve different colours even though the colours are used in the same order.

6-3 Based on what is usually numbered the third of three different mathematical knots with six crossings. The sixth colour added is brown, so the sequence so far is red, yellow, blue, green, mauve, brown, and back to red.

6-3 Based on what is usually numbered the third of three different mathematical knots with six crossings. The sixth colour added is brown, so the sequence so far is red, yellow, blue, green, mauve, brown, and back to red.

This piece is based on knot 10-146 and was inspired by the Twitter icon of @MadeleineS Knot Unknot. It is rotated 180° to correspond more with previous pieces in this series with the red to yellow cord transition.

This piece is based on knot 10-146 and was inspired by the Twitter icon of @MadeleineS Knot Unknot. It is rotated 180° to correspond more with previous pieces in this series with the red to yellow cord transition.

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