# The Effects of Half Twists and Cuts on the Geometry of Mobius Strips

## School Name

Heathwood Hall Episcopal School

Mathematics

Non-Mentored

## Abstract

Discovered in 1858 by August Mobius, the mobius strip is a geometric figure that falls under the study of topology, which is the study or surfaces. This object is considered one of the few one sides or surfaced objects. The purpose of this project was to explore those interesting properties by researching any effects that varying numbers of cuts down the center of the mobius strip and half twists have on the geometry of the mobius strip. In order to perform this experiment, 20 mobius strips were constructed in total. Each strip was cut once, twice, and three times down the center. The results were recorded and there were 2 observable patterns. Firstly, the new strips were always interlocked with each other when split into halves. Secondly, the strips with an odd number of twists were mobius strips whereas the strips with an even number of twists were not mobius strips. Lastly, every trial kept the original number of half twists after being cut once, twice, and three times down the center. The only exceptions were when the strip kept its form and wasn't split at all. These trials were different from the rest, as the mobius strip did not separate, which caused the number of half twists to go up by a factor of 2. In conclusion, the results did support the hypothesis, as the results did show a change in geometry with the mobius strips.

Furman Hall 121

## Start Date

3-28-2020 11:30 AM

Oral and Written

## Group Project

No

COinS

Mar 28th, 11:30 AM

The Effects of Half Twists and Cuts on the Geometry of Mobius Strips

Furman Hall 121

Discovered in 1858 by August Mobius, the mobius strip is a geometric figure that falls under the study of topology, which is the study or surfaces. This object is considered one of the few one sides or surfaced objects. The purpose of this project was to explore those interesting properties by researching any effects that varying numbers of cuts down the center of the mobius strip and half twists have on the geometry of the mobius strip. In order to perform this experiment, 20 mobius strips were constructed in total. Each strip was cut once, twice, and three times down the center. The results were recorded and there were 2 observable patterns. Firstly, the new strips were always interlocked with each other when split into halves. Secondly, the strips with an odd number of twists were mobius strips whereas the strips with an even number of twists were not mobius strips. Lastly, every trial kept the original number of half twists after being cut once, twice, and three times down the center. The only exceptions were when the strip kept its form and wasn't split at all. These trials were different from the rest, as the mobius strip did not separate, which caused the number of half twists to go up by a factor of 2. In conclusion, the results did support the hypothesis, as the results did show a change in geometry with the mobius strips.