Particpants used a long thin strip of paper, gave it one twist, and taped the ends together to create a Mobius strip. We drew a design on just "one side" of the strip and noticed that there is only "one side".
We hypothesized what would happen when we cut strip down the center, then we made the cut and found that we had just one strip that was half as wide, but twice as long. We hypothesized what would happen when we cut the new strip down the center, then we made the cut and found that we had two strips that were interlocked.
After dinner, we conducted experiments with directional designs on various strips. Each time we conjectured and explored. We also explored creating strips with multiple twists that were sliced. We created a table to record results. Brie introduced notations to track our results. Mark showed a proof of his findings.
Brie suggested that we explore "Vi Hart's webpage" and view the video titled "Mobius Story: Wind and Mr. Ug" There are numerous incredibly creative items on that webpage, including a link to see Möbius strip music boxes like the one Brie showed us.
Brie's son, Arlo Gideon Zvi Foote, was born September 11, 2011. That was just three days after this presentation!
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| Brie introduced the ideas of topology | To create a Möbius strip, give the strip one twist. | Pondering what will happen when we cut down the center. |
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Some of the AIMS Standards addressed include:
4.1.2 (Grade 8) Predict results of combining , subdividing, and changing shapes of plane figures and solids.
4.1.2 (HS) Visualize solids and surfaces in 3-dimensional space when given 2-dimensional representations and create 2-dimensional representations for the surfaces of 3-dimensional objects.
5.2.2 (Grades 7 & 8) . Analyze and compare mathematical strategies for efficient problem solving; select and use one or more strategies to solve a problem.
5.2.2 (HS) . Solve problems by formulating one or more strategies, applying the strategies, verifying the solution(s), and communicating the reasoning used to obtain the solution(s).