Word of the Month: Mobius strip

David Zapatka

I take our grandsons to a special conference every year the day after Thanksgiving. It’s a regional gathering of people from Arizona and neighboring states who attend outstanding lectures on a wide variety of topics, play games, do puzzles, eat meals, enjoy entertainers and generally just have a good time with each other. Our grandsons love the Kids’ Track brain-stretching activities, seeing special friends once per year and enjoying all the creativity.

One particularly interesting lecture was on Mobius strips, this month’s word of the month.

Mobius strip – noun. Mo·bi·us strip ˈmœ-bē-əs-, ˈmər-, ˈmə-, ˈmō-:  a one-sided surface that is constructed from a rectangle by holding one end fixed, rotating the opposite end through 180 degrees and joining it to the first end.

Etymology – discovered independently by the German mathematicians August Ferdinand Möbius and Johann Benedict Listing in 1858. First known use in English, 1904.

We learned in the lecture through illustration that the Mobius strip has several curious properties. A line drawn starting from the seam down the middle meets back at the seam, but at the other side. If continued, the line meets the starting point and is double the length of the original strip. This single continuous curve demonstrates the Möbius strip has only one boundary.

Cutting a Mobius strip along the center line with a pair of scissors yields one long strip with two full twists rather than two separate strips. The result is not a Mobius strip. This happens because the original strip only has one edge that is twice as long as the original strip. Cutting creates a second independent edge, half of which was on each side of the scissors. Cutting this new, longer, strip down the middle creates two strips wound around each other each with two full twists.

If the strip is cut along about a third of the way in from the edge, it creates two strips: One is a thinner Mobius strip – it is the center third of the original strip, comprising one-third of the width and the same length as the original strip. The other is a longer but thin strip with two full twists in it – this is a neighborhood of the edge of the original strip, and it comprises one-third of the width and twice the length of the original strip.

Mobius strip used in sentences – Stale words and images looped together in a comforting Mobius strip of infinite repeatability is what network television is after all. In an upended Mobius strip version of the book, Andersen’s media fishbowl of a novel was being celebrated by, well, the media fishbowl.

Ever feel like your path in life is like a Mobius strip bringing you right back to where you started but with a different twist? Please submit any thoughts on this month’s column or any word you may like to share along with your insights and comments to dzapatka@wbhsi.net.