Knitting Hyperbolic Pants

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In the book Making Mathematics with Needlework, patterns are given for knitting several different sizes of hyperbolic baby pants using particular gauges of yarn. Those patterns were created using Mathematica, and this Demonstration allows anyone to generate knitting patterns for hyperbolic pants. It is necessary to knit and measure a gauge swatch before generating a custom pattern, because both stitch and row gauge are needed for the pattern creation. (As well as, of course, some dimensions of the finished pants.)

Contributed by: Sarah-Marie Belcastro (June 2009)
Open content licensed under CC BY-NC-SA



A hyperbolic octagon can be folded up into a pair of pants. The knitting pattern given here creates a close approximation of a non-regular hyperbolic octagon. In turn, the resulting octagon folds into pants that have proportions matching a baby or toddler (but not so much an adult human). For more information on the mathematics underlying these knitting patterns, please see Making Mathematics with Needlework.

S-M. Belcastro and C. Yackel, "Stop Those Pants!" in Making Mathematics with Needlework, S-M. Belcastro and C. Yackel, eds., Wellesley: A K Peters Ltd, 2007.

Snapshot 1: a pattern for a large pair of pants made of sock yarn

Snapshot 2: a pattern for a tiny pair of pants made of superbulky yarn

Snapshot 3: a pattern for impossible pants, where the stitch gauge is much larger than the row gauge

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