HSC 2016 MX2 Integration Marathon (archive) (3 Viewers)

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seanieg89

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Re: MX2 2016 Integration Marathon

Are there any useful sufficient conditions that'd make the arc length of the limit curve equal the limit of the arc lengths?
For sure if you just want sufficient. Prepping for a meeting right now so will work one out later, but basically you just want to use a stronger norm than the uniform norm (to avoid wiggly approximations that are uniformly close but have massive arc length), such as looking at the C^1 norm. (Such a criterion would not quite be directly applicable here because the limit curve is not everywhere smooth and the obvious parametrisation of the curves have velocity blowing up near the x=1 endpoint, but you could most likely get a limit result with some trickery.)

Working with general rectifiable curves is pretty gross though, there would be a lot of old school papers on things like this.
 
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leehuan

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Re: MX2 2016 Integration Marathon

This forums so dead...
I came to realise that learning new maths > doing more integrals (at least for now)


I have other excuses for this holiday period though
 
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