String Figures and Knot Theory
- mathematics of the unknot under tension

by Martin Probert

Part II - Examples (illustrating Part I)

Examples of motifs

Four motifs met frequently are illustrated in fig. 3. From left to right the motifs are a single-crossing, a double-crossing, a spiral triple-crossing and a triangular triple-crossing.

string figure
Fig. 3

Infinitely many different motifs exist. For example, two segments of string might twist around one another in spiral fashion through any multiple of 180 degrees to create a motif.

Each motif of fig. 3 above together with the corresponding motif of fig. 4 below make up a pair of motifs of opposite parity.

string figure
Fig. 4

An example of motifs in a three-dimensional string figure

String figure glossary

string figure
Fig. 5 - The Worm
North America 1904 (Jayne)

Construction: Insert the thumbs into the loop and separate the hands. Pass the index fingers into the thumb loop from above and pick up the near thumb string. Pass the right thumb to the left and, from below, pick up the string running from the left thumb to left index. Extend. With the teeth pick up, from the back of the right thumb, the lower loop, pulling the loop up over the upper loop and off the right thumb, but maintaining hold of the loop with the teeth. Adjust the figure so that the mouth loop lies symmetrically between the left and right hands. Pass the little fingers under the strings and up into the thumb loop from below, then push the far thumb string and near index string away from you and under the far index string, then with the little fingers hook the far index string to the palm. Release the mouth loop and extend.

The 3D framework of the Worm

The 3D framework of a string figure has been defined earlier. The 3D framework in the Worm is made up of the contacts P1, P2, P3, P4, P5 and P6.

Equivalent motifs

Motifs in corresponding positions in two look-alikes are equivalent if, without involving the supporting single strands, the interiors of the motifs may be manipulated into identical configurations. The motifs in fig. 6 are equivalent.

string figure
Fig. 6

For the construction of a string figure possessing four such motifs, see Double Crow's Feet on this web site.

A further example of look-alikes

We recollect that look-alikes were defined as string figures which differ from each other only in the parity of one or more motifs. The points of support remain fixed (see the notes on the characteristics of string figures). At first glance such figures appear identical (e.g. Stone Money and Star, illustrated in figs 1 and 2). The existence of look-alikes is evident to anyone who has studied string figures collected from around the world.

The ‘bears’ in figs 7, 8a and 8b are also look-alikes of each other.

String figure glossary

string figure
Fig. 7 - Brown Bear
Arctic 1924 (Jenness)

Construction: Insert the thumbs into the loop; pass the left index up into the loop from below; pass the right index over the left thumb-index string and with the front of the fingertip hook this short string to the right, the right index turning away and up as the hands separate; extend fully. On each side pass the middle, ring and little fingers up into the index loop from below, and with them close the near index string to the palm; pass the left index into the right index loop from above, and pick up the far right index string, the left index turning away and up as the hands separate. Navaho the left index loops, the original left index loop slipping up over the latest loop; separate the hands. Pass the left thumb into the left index loop from below; navaho the left thumb loops. Release the left index loop. Release the right thumb loop and extend.

string figure
Fig. 8a

string figure
Fig. 8b

String Figure Mathematics - Part III
String Figure HOME PAGE