Richard Evan Schwartz

Optimal Moebius Band Suite

This webpage has links that relate to my solution of the Halpern-Weaver Conjecture about optimal paper Moebius bands. Here is the main paper.

R. E. Schwartz, The Optimal Paper Moebius Band
Annals of Mathematics Vol 201.1 (2025) pp. 291-305

Here is a friendlier and less formal version written for undergraduate math majors and/or advanced high school students.

R. E. Schwartz The Optimal Paper Moebius Band: A More Elementary Account
Preprint (2024)

Here are 3 sequel papers

R. E. Schwartz, The Optimal Twisted Paper Cylinder
preprint (2023) arXiv 2309:14033
B.E. Brown and R. E. Schwartz, The Crisscross and the Cup: Two Short 3-Twist Paper Moebius Bands
preprint (2023) arXiv 2310:10000
R. E. Schwartz, On Nearly Optimal Paper Moebius Bands
Advances in Geometry, 2025, to appear

Some public accounts of the main paper:

Scientific American
Science News
Popular Mechanics
quanta
Kyne Santos' instagram video and tiktok video
Thomas Alexander's youtube video gives a complete and nicely animated proof in French.