Klein bottletopological spacenamed for the German mathematician Felix Kleinobtained by identifying two ends of a cylindrical surface in the direction opposite that is necessary to obtain a torus. Klein bottle. Article Media.
If you like a drink, then a Klein bottle is not a recommended receptacle. It may look vaguely like a bottle, but it doesn't enclose any volume, which means that it can't actually hold any liquid. Whatever you pour "in" will just come back out again.
Informally, it is a one-sided surface which, if traveled upon, could be followed back to the point of origin while flipping the traveler upside down. The Klein bottle was first described in by the German mathematician Felix Klein. The following square is a fundamental polygon of the Klein bottle.
Specifically, they have only one side although it seems to be two sides. But the interesting thing about it is that it has only one side. Locally, it seems to have two sides. For example, if you draw a line down the middle, you will never lift your pencil up yet the line will be on both sides.
Look carefully at the M. Escher picture to the left. If an ant keeps moving forward, he will end up on both sides of the strip he is walking on.
I have realised the last time I published a post was way back in November and that maintaining a blog is, in fact, tremendously difficult during preliminary exams period, which very fortunately just ended. I have always enjoyed mathematics in school, whether it was the logic behind exam problems or solving tricky little mathematical puzzles. I had first become aware of the field of topology research after the announcement of the Nobel Prize in Physicswhere pretzels, doughnuts and mugs were used to demonstrate topological properties considering the different number of holes each contains.
Click to get a printable template for five Mobius strips. Print this with as small margins as your printer will allow, and cut along the solid lines to get basic Mobius strip shapes. Do the Mobius twist! What kinds of things could you do?
It locally looks like any other surface. Close-up we see a 2-dimensional object. The surface becomes more interesting when we try to decide how many sides this surface has.