Moebius strip essay

take a rectangle (it is easier to visualize this when the rectangle is a longer strip), and twist the shorter side 180 degress and then glue it to the other shorter side. What you get is called a Moebius strip. What is the boundary of the Moebius strip? Explain why it is only one circle (abstractly a circle, in space it is somewhat twisted). Now you can make two new surfaces: glue a disk (which has a circle boundary) to the boundary of the Moebius strip. Describe this surface, make drawings, try to understand what you get this way. Can all loops be reeled back in---the famous rope reeling in test. You can also glue two Moebius strips together along their respective circle boundaries. What surface do you get this way? Draw pictures,  make a model (if you are so inclinded), describe in words,  and answer the question whether all loops can be reeled in. Write at least 2-3 pages with a general audience in mind.