Embroidery-Hooping toward the Hyperbolic Trochoid

Year: 2023 Authors: Andrew J. Simoson

Core claim

Families of hyperbolic lines generated by constant-speed motion in the unit disk produce trochoidal envelopes that can be modeled mathematically and built physically.

Topics

hyperbolic geometry, trochoid curves, curve envelopes, isometries, tactile mathematics

Domains

hyperbolic geometry, Möbius transformations, curve envelopes, trochoids, embroidery, craft visualization, kinetic sculpture, mathematical art

Methods

analytic derivation, Möbius transformation formulas, computer algebra, physical model construction

Media

embroidery hoops, yarn, weed-whacking string, zip-ties, wooden toothpicks

Source status

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