By Bhavya shah
When we were kids we were taught different geometric shapes in our school and at our colleges. First we learnt about a line,then about squares,rectangles and circles,then came 3D cubes,cuboids and cones.But our teachers never taught us about the most interesting geometric shape in today’s world.A Möbius strip
What is a Möbius strip?
A Möbius strip(also known as Möbius band or Möbius loop) is a unique surface with only one side and only one edge.This shape cannot be drawn on a piece of paper. This shape is named after a German mathematician August Ferdinand Möbius,who discovered this in September 1858.Another mathematician Benedict Listing also independently discovered the Möbius band.
Möbius Strip and Their Magic
Take a paper strip(about 3cm wide and 12cm long).How many sides and edges does that paper have?If answered two sides and two edges,you are correct.
Now give the strip of paper a half twist and connecting the ends to make a strip. The final output would look like the below image.
The new shape you have just made has only 1 side and 1 edge and is in fact a Möbius strip.To prove that there is only one side ,take a pencil and start drawing a line over the strip and you will have drawn across the entire strip before you reach the starting point.Similarly ,you could check if the strip now has only one edge.
Where will you find Möbius Strips?
The symbol for INFINITY is a Möbius strip.
Giant Möbius strips have been used as conveyor belts on airports as Möbius conveyor belts last longer and require less wear and tear.Scarfs and other clothing items have also been designed as a Möbius strip.
A Möbius resistor was patented by Nikola Tesla in 1894.
Various other applications of Möbius loops are fount in electro-technology and nano-technology.
Adding Möbius Strips Together
When we glue together 2 cubes it makes a cuboid,when you cuboids are glues,it still makes a cuboid,but what would happen if two Möbius Strips would be glued together along their edges?
Turns out,gluing two interesting shapes,creates a new and more complex shape named Klein Bottle ,discovered by Felix Klein in 1882.
Fun Fact:Even though Möbius strips are named after August Möbius,Benedict Listing discovered them first in July 1858.Plus Möbius loops have been in Roman mosaics dated circa 200-250 AD.
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