What is Klein's bottle?
Klein bottle is a type of un orientable surface, which is often displayed so that it looks like a long -throat flask with a bent neck passing in itself to open like a base. The unique shape of the klein bottle means it has only one surface - its inside is the same as outdoors. Klein bottle cannot really exist in a three-dimensional, Euclidean space, but blown glass-presentations can give us an interesting view. It is not a real Klein bottle, but it helps to imagine what German mathematician Felix Klein imagined when he came up with the idea of Klein's bottles. If you connect the symbol to an orientable surface, such as the outer side of the ball, no matter how you move the symbol, it will maintain the same orientation. The special shape of the klein bottle allows you to slide in a symboltak way that it takes a different orientation - it can appear as its own mirror image on the same surface. This feature of Klein's bottle is what makes her im oriented.
Klein bottle is named after German mathematicians Felix Klein. Felix Klein's work in mathematics was very familiar with Möbi's belt. Möbius strip is a piece of paper given by Haltta-Twist and joined the ends. This reversal turns a regular piece of paper into an unrimental surface. Felix Klein justified that if you should connect two möbius belts together along the edges, you would create a new type of surface with equally strange properties - Klein surface or Klein Bottle.
Unfortunately, for those of us who would like to see the real Klein bottle, they cannot be built in the 3-D, Euclidean space in which we live. Join the edges of the two Möbius strips to the Kleinalihai position creates an intersection that cannot be present in the theoretical model. The model of the real life of the Klein bottle must be interspersed as the neck of the bottle passes sideways. It gives us something that is not a real, functional klein bottle, but whichIt is still quite interesting.
Because the Klein bottle shares many of their strange qualities with the Möbius belt, those of us who do not have a deep understanding of mathematics necessary to truly understand the complexity of the Klein bottles, can experiment with the Möbius belt to gain some insight into the fascinating discovery of the Felixeins.