The Optimal Twisted Paper Cylinder

2023/09/25 by Montgomery, Noah, Schwartz, Richard Evan · 3 citations
#FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2309.14033

Abstract

An embedded twisted paper cylinder of aspect ratio λ is a smooth isometric embedding of a flat λ× 1 cylinder into \R³ such that the images of the boundary components are linked. We prove that for such an object to exist we must have λ>2 and that this bound is sharp. We also show that any sequence of examples having aspect ratio converging to 2 must converge to a (non-smooth) 4-fold wrapping of a right-angled isosceles triangle.

Cited by

• Ribbonlength bounds for pretzel links and knots with ≤ 9 crossings
• Ribbonlength upper bounds for small crossing knots and links
• Bounded ribbonlength for knot families and multi-twist Möbius bands

Related

• The Crisscross and the Cup: Two Short 3-Twist Paper Moebius Bands
• Constructing many-twist Möbius bands with small aspect ratios
• Weaving paper strips for designing of general curved surface with geometrical elasticity
• Geometry of Călugăreanu's theorem
• The Optimal Paper Moebius Band