Okay so i wanna do this project on finding a volume of the klein bottle (while it is said that volume of a klein bottle is 0 as it technically is not an enclosed shape, however i'll be using the water method and using motors to completely fill up the bottle, then equating the volume of water to another method and trying to derive a volume for the bottle) What mathematical way can I try to use to find the volume of the klein bottle and what all will that require me to do?
Volume of klein bottle project
- Thread starter sparky01
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Dr.Peterson
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You'd have to show the details of your particular Klein bottle. The Klein bottle is not defined as a specific shape, but as a particular topological configuration, which could have many different shapes. (Here, for example, you will see several different models of the Klein bottle, each a somewhat different shape.) Some would be easier to calculate than others; I've seen a polyhedral version that would be easy.
Of course, you also have to define what it means to fill it up.
And since all models of the Klein bottle are inaccurate, since it can't actually be embedded in 3-space, you don't really have one at all ...