How to continuously deform a mobius strip into a cross-cap (homeomorphism)

The Mobius band is topologically equivalent (homeomorphic) to a cross-cap, and in this video we give a physical demonstration why. The Mobius band (also known as the Mobius strip) is the famous non-orientable surface obtained by taking a rectangular strip, giving it half a twist and then gluing the ends. The mobius band is one-sided, and its boundary is a circle. If one glues a disk to that circle then one gets the projective plane -a highly important and interesting surface. However, it looks hard to change the mobius strip so that its boundary is a simple circle. To do this we must change the mobius strip into a cross cap. The cross-cap is a self-intersecting surface with a simple circular boundary. I show my own method of continuously deforming the mobius strip into the cross-cap using white-tack. Basically the method roughly can be described as follows: 1 Flatten the mobius band so the twist only takes up a small amount of the band. 2 Stretch out and twist up a loop from flat part of the band (to make something roughly like a figure 8) 3 Intersect the twist within the newly formed loop with the original twist to make a true figure 8 4 Pinch together the holes (this can be done as a homoemorphism because center of the figure 8 is the intersection of two twists. 5 enjoy!