This necklace is one example of hyperbolic crochet. This necklace was made of cashmere yarn with a trailing thread of lurex. The hyperbolic balls are threaded on a crocheted chain and tied to form a necklace. Hyperbolic crochet blends crochet stitches with mathematical formulas to turn a 2D object (length by width)  into a 3d object (length by width by depth). In doing hyperbolic crochet, several chained stitches are formed into a circle, then each chain receives one or more single crochet stitches, continuing around and around following the same pattern of increases until a ball is formed due to mathematical principles of space. For the necklace, there were 3 increases in every stitch. It will also work with increases in 1 or two stitches and regular stitches in all others. The pattern must continue throughout the work. Depending on the yarn or thread, the stitch style (single, double, half double, etc.), the hook, and personal thread tension a vast array of balls, in many sizes, can be made. Various wavy shapes can also be made, simulating ocean coral.
carol.haas.546 months ago

Absolutely love this!! Am just discovering hyperbolic crochet and this will be my first piece of jewelry to apply the technique. Thank you and please keep the ideas coming.

fiola4 years ago
Non-euclidean crochet. This is really something...
jeffreyd005 years ago
Katzsta: How long does it take you to make one of these necklaces?
Katzsta (author)  jeffreyd005 years ago
It all depends on how big you want it and how frequently you do an increase. Considering that for the necklace, for one ball, the first round may have 6 stitches, the second round will have 18, the third will have 54, the fourth will have 162, etc. It really begins to add up. I would say each ball in the necklace was 1-2 hours.
scoochmaroo5 years ago
Very lovely, and well explained.
kelseymh5 years ago
The Institute For Figuring has a good resource for crocheted hyperbolic surfaces. Daina Taimina, a professional mathematician, originated the technique, and coauthored a text on non-Euclidean geometry with her husband, also a mathematician, using some of her work as examples.
Kozz5 years ago
random: if I recall correctly, a rope or chain (say, one strung loosely between two posts) will hang according to a hyperbolic curve.
CameronSS Kozz5 years ago