Math-e-Magician

The great Math-e-Magician Mr.Hegde Jadugar performed some magic tricks in a television show and at last did this. He took a paper strip and joined the ends of the strip to form a loop as shown in fig 1. He cut the strip along the center line which yielded two separate simple loops. He took another paper strip, gave it half a twist and joined the ends of the strip to form a loop as shown in fig 2. He cut the strip along the center line. This time he got one long strip with two full twists in it. Then he asked the television show viewers to find out the different types of shapes we would obtain if for the above process, we gave 1, 1.5, 2 so on ... number of twists before joining the ends of the strip.












fig 1: A simple loop. Has 0 twists. fig 2: A mobius loop. Has 0.5 twists.

Little Bozo was amazed by the trick and he immediately followed the things said by Mr.Hegde Jadugar and got many interesting results.

Find out the results of the said process for 1, 1.5, 2 and more twists. Also research on the properties of the resulting shapes.