Summary

This ring has 100 holes in it, which we imagine are numbered 1 to 100. Hole 101 (or hole 0) is missing. Along the edge of the ring are large and small protrusions. These tabs are spaced five units apart and are used to mark multiples of 10 and 5.

Here are the instructions for making the cardioid.

1. Cut a piece of fine string or thread 250 inches long. The total length required is about 243 inches, so this will leave some at the end of the stringing.
2. Make sure you understand the numbering of the ring. The empty spot corresponds to hole 0. The big tab next to it is hole 100, and the small tab 5 units away is hole 5.
3. Put the string through hole 1 and tie it to the ring.
4. Put the string through hole 2 from the front. Pull it all the way through.
5. Put the string through hole 4 from the back. Pull it all the way through.
6. Continue this process going from hole k to hole 2k modulo 101 alternating front-back-front-back. The full sequence of holes is 1, 2, 4, 8, 16, 32, 64, 27, 54, 7, 14, 28, 56, 11, 22, 44, 88, 75, 49, 98, 95, 89, 77, 53, 5, 10, 20, 40, 80, 59, 17, 34, 68, 35, 70, 39, 78, 55, 9, 18, 36, 72, 43, 86, 71, 41, 82, 63, 25, 50, 100, 99, 97, 93, 85, 69, 37, 74, 47, 94, 87, 73, 45, 90, 79, 57, 13, 26, 52, 3, 6, 12, 24, 48, 96, 91, 81, 61, 21, 42, 84, 67, 33, 66, 31, 62, 23, 46, 92, 83, 65, 29, 58, 15, 30, 60, 19, 38, 76, 51, 1.
7. Tie off the string at the end.