I bet most of you guys didn't know about this equation, a famous one mind you, which comes from Topology: A Doughnut = A Coffee mug. Strange, isn't it? I wouldn't blame you as that is exactly how I felt the first time I read it.
Topology is a branch of geometry which deals with the properties of figures that remain unchanged even when the shape is altered. By altering I mean moulding without tearing, glueing or creating holes! For example, lets take clay. You can make a ball, then deform the same clay to make a cube and remould the same lump of it to make a pyramid! Similarly, a circle, rectangle and triangle are all topologically equal!
Coming back to our doughnut, can you guess why it is topologically equal to a mug now? If you think about it a bit further, you will realise it is also equal to a needle or a straw!
One of the objective of topology is the classification of surfaces. We have all heard of 2D and 3D. These days we even have people selling tickets to 7D films (I wonder what 7D actually means!). But let's take a step back and think about 1D (NOT One Direction - One Dimension).
I suggest you grab a sheet of paper and scissors and try this our yourself while reading this. Take a peice of paper and tear a strip of paper about 8-12 inches long and 1 inch wide. Give it a half twist and tape the edges. The fascinating part of this pretty humdrum looking figure is that it has only one side. One edge. And hence one dimension. Discovered by Mathematicians August Mobius and Johann Listing independently, the MOBIUS BAND has become legendry! ;)
The mobius band is an interesting figure,
You can make it by twisting a strip of paper!
To find the end of the edge, you'll go on looking till eternity,
In fact, IT is the symbol of infinity!
Go ahead and slit it from in between,
Before you is a sight you wouldn't have believed,
The mobius band which should have divded into two,
Has now turned into a large single loop!
If you cut the band with two twists from the middle,
You will end up shocked,
Instead of getting two of them separately..
You will get two bands, with each other, locked!
Anyways, thinking of doughnuts and coffee has made me hungry! But you guys carry on exploring Topology and Mobius band! Tell me if you discover anything!
Kanksha :)
Topology is a branch of geometry which deals with the properties of figures that remain unchanged even when the shape is altered. By altering I mean moulding without tearing, glueing or creating holes! For example, lets take clay. You can make a ball, then deform the same clay to make a cube and remould the same lump of it to make a pyramid! Similarly, a circle, rectangle and triangle are all topologically equal!
Coming back to our doughnut, can you guess why it is topologically equal to a mug now? If you think about it a bit further, you will realise it is also equal to a needle or a straw!
One of the objective of topology is the classification of surfaces. We have all heard of 2D and 3D. These days we even have people selling tickets to 7D films (I wonder what 7D actually means!). But let's take a step back and think about 1D (NOT One Direction - One Dimension).
I suggest you grab a sheet of paper and scissors and try this our yourself while reading this. Take a peice of paper and tear a strip of paper about 8-12 inches long and 1 inch wide. Give it a half twist and tape the edges. The fascinating part of this pretty humdrum looking figure is that it has only one side. One edge. And hence one dimension. Discovered by Mathematicians August Mobius and Johann Listing independently, the MOBIUS BAND has become legendry! ;)
The mobius band is an interesting figure,
You can make it by twisting a strip of paper!
To find the end of the edge, you'll go on looking till eternity,
In fact, IT is the symbol of infinity!
Go ahead and slit it from in between,
Before you is a sight you wouldn't have believed,
The mobius band which should have divded into two,
Has now turned into a large single loop!
If you cut the band with two twists from the middle,
You will end up shocked,
Instead of getting two of them separately..
You will get two bands, with each other, locked!
Anyways, thinking of doughnuts and coffee has made me hungry! But you guys carry on exploring Topology and Mobius band! Tell me if you discover anything!
Kanksha :)
No comments:
Post a Comment