Instruct the participant to use the safety scissors to cut the Mobius strip lengthwise in the middle and to observe the result and compare it to their hypothesis. Now ask the participant what they think will happen when the Mobius strip is cut lengthwise. Two loops should be formed as the result. Give the participant a pair of safety scissors and ask them to cut the normal loop of paper lengthwise and observe what happens when it is cut. Explain that as long as they can continue to draw a continuous line along a surface or edge, they are travelling along the same surface or edge.Īsk the participant whether their initial hypothese about the number of faces and edges in the Mobius strip were were supported or not by their experimental results. As a hint, you may point out the fact that they were able to trace the entire face with one single stroke, and the entire edge with one single stroke. Ask the participant to draw on the edge of the strip, all the way round until they reach the end.Īsk the participant again how many faces and edges they think the Mobius strip has. The participant then tests their hypothesis about the number of edges. The line should travel through the centre of the width of the strip. Give them a marker and instruct them to draw a line all the way around the strip. The participant will first test their hypothesis about the number of faces. Explain that they will now test these ideas (hypothese). Ask the participant how many faces and edges they think the Mobius strip has. Afterwards, summarise this step of the experiment by explaining that the normal loop of paper has two separate edges – emphasize how the two edges are distinct because they do not touch- and two faces because the outside face and the inside face are separated by an edge. If needs be, point out one of the faces and edges of the loop and let the participant identify the others. Encourage the participant to create their own Mobius strip.Īsk the participant how many faces and edges the normal loop has. Contrast the Mobius strip with the a normal loop of paper that was made beforehand. Show the participant the Mobius strip and explain how it was made by making another one in front of them. To create a normal loop just directly connect the two ends of a strip of paper using tape. Add a half-twist to the strip in either the clockwise or anti-clockwise sense by flipping one of the ends and then taping the ends together. To make a Mobius strip, cut out a strip of paper with a width-to-length ratio of 1:4 – for example, a strip 3cm wide and 12cm long. ![]() Create 3 Mobius strips and a single normal loop. Prepare the Mobius strips prior to the demonstration. It is not necessarily flat, it can be curved. Examples of orientable surfaces are a sphere and a flat surface.Īn area that is contained within the edges of an object. A Möbius band is an example of such an object that is non-orientable.Ī surface is orientable if you can walk along some path and come back to where you started with the same orientation as you started with. It is not necessarily straight, it can be curved.Ī proposed explanation based on limited evidence, used as a starting point for further investigation.Īn object which has one edge and one side.Ī surface is nonorientable if you can walk along some path and come back to where you started but reflected in such a way as left becomes right and right becomes left. Introduction to objects with a unique number of sides and edges.Ī sharp boundary which outlines a face. Understanding what a hypothesis is and how to test it through experimentation. Created using tape and paper, these objects are a great way of introducing surfaces and edges. These are demonstrated using papers, ropes and other materials, so we will use less mathematical formulas.Meta Description Mobius strips are truly fascinating. We will give different definitions of the spin structure on a band and see how they are related to each other. In other words, we can distinguish amounts of half-twisting mod 4 by considering the band (surface) with the spin structure on it. ![]() In the talk we introduce the so called spin structure on the band, which recognizes this parity of twisting. In fact, any band with integer twists is considered the same as the non-twisted one, even though they look different in reality. ![]() If we perform a full twist and then glue the edges, we get a “more” twisted band, which as a surface, is still considered to be the same as the “non-twisted” band. If we twist by a half turn before gluing, we get the famous Mobius band. Gluing two edges of a strip, we can make a closed band in a ring form. The talk will focus on examples and make use of clever visual aids. We’ll hear from our own co-organizer Tetsuya Nakamura about a concept important to geometry, topology, and physics: spin structure. Please join us in LGRT 1528 on Wednesday, 2/1/17 from 5 pm to 6 pm for the first talk of the Spring semester.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |