MSUB Math Circle Activity: Paper Cutting with a Twist
September 11, 2019
Sunday, September 29, 2019
6:00 PM— 9:00 PMUTC
MSUB Math Circle is making their first appearance at the 2019 SteamFest, held at Billings Depot on September 29, has two activities ready to engage the minds and imaginations of their young attendees. Kids will be able to discover how a matching card game can teach us about alternative geometries, modular arithmetic, and 4-dimensional space. The other activity, “Rational Tangles” is a game that will see math embedded in the midst of a knot in a most surprising way!
Before we dive into MSUB Math Circle’s activity for families to do at home together, let’s get their perspective on the value of STEAM. Tien Chih, Ph.D., Assistant Professor of Mathematics points out that what is often the case with STEM subjects (mathematics in particular), they are framed as dry, technical subjects, a set of archaic procedures to be memorized. To the contrary, Tien notes that Science and Mathematics are driven by human curiosity, engagement, creativity, and wonder. The MSUB Math Circle was founded, in part, to reframe this narrative, giving a presentation to mathematics that centers collaboration and independent discovery. Finally, the presentation of Mathematics as a part of STEAM with the inclusion of the Arts is a vital one, as it emphasizes the human and imagination-motivated facet of these disciplines.
MSUB Math Circle’s Paper Cutting with a Twist
- Paper (printer paper works!)
- Pen, pencil, or marker
- A pair of scissors
1. Make a cylindrical band by cutting a strip of paper, wrapping it into a band, and taping the ends:
2. Make a Mobius band by cutting a strip of paper, giving it one twist before wrapping it into a band, and taping the ends:
3. Make a second Mobius band.
4. Mark a point halfway through the cylindrical band. What do you think will happen if you draw a line through the band until you reach the starting point?
5. Draw this line. What happened? Were you right? (You probably won’t be surprised).
6. What would happen if you cut along this line?
7. Go ahead and cut along this line. What happened, were you right?
8. Mark a point halfway through the Mobius band. What do you think will happen if you draw a line through the band until you reach the starting point?
9. Draw this line. What happened? Were you right?
10. What would happen if you cut along this line?
11. Go ahead and cut along this line. What happened, were you right? (You may be surprised!)
12. Repeat steps 8 through 11, but instead mark your point one third of the way up the band. Do you think the same thing would happen as halfway? What something diﬀerent happened? How about when you cut? (You may be surprised again!)
Bonus: What if you repeated these steps, but made a band with 2 twists? 3 twists? Is there a pattern you can see?