Möbius Strip

Jul 14, 2020 | Hinsdale

The other day, we learned a new vocabulary word to describe an infinity symbol (a lemniscate). But a lemniscape comes in another shape beyond the traditional figure eight! This is what we call a möbius strip.

Wolfram Mathworld gives us a helpful image and description:

The Möbius strip, also called the twisted cylinder (Henle 1994, p. 110), is a one-sided nonorientable surface obtained by cutting a closed band into a single strip, giving one of the two ends thus produced a half twist, and then reattaching the two ends (right figure; Gray 1997, pp. 322-323). The strip bearing his name was invented by Möbius in 1858, although it was independently discovered by Listing, who published it, while Möbius did not (Derbyshire 2004, p. 381). Like the cylinder, it is not a true surface, but rather a surface with boundary (Henle 1994, p. 110).

MobiusStrip               MobiusStripSquare

MobiusStripArcLength

Even more interesting is this gif that shows the Strip in motion!

Moebius gears

The illustration above shows interlocked turning gears along the length of a Möbius strip (M. Trott, pers. comm., 2001).