Re: 4-dimensional Integral


A N Niel wrote:
> In article <1125085061.811875.156520@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
> Randy Poe <poespam-trap@xxxxxxxxx> wrote:
>
> > Hsuan-Yeh Chang wrote:
> > > Dear All,
> > >
> > > Anyone wants to try this simple integral in four dimension:
> > >
> > > \int dx dy dz dt (x^2 + y^2 + z^2 + t^2)
> > >
> > > where the integration is restricted to the space:
> > >
> > > { (x, y, z, t) | 1 >= x^2 + y^2 + z^2 + t^2 }
> >
> > Volume of the unit 4-sphere.
> >
> > http://mathworld.wolfram.com/Hypersphere.html
> > http://www.mathreference.com/ca-int,hsp.html
> >
> > - Randy
> >
>
> without the integrand, that would be it

You're right, I answered too fast.

Another poster's suggestion sounds like the right way
to go. Convert to hyperspherical coordinates with
r^2 = x^2 + y^2 + z^2 + t^2, integrated from r=0 to 1.
The trick will be figuring out the correct transformation
of the volume element dx dy dz dt.

- Randy

.

Relevant Pages

  • Re: filtering feedback
    ... Aaah I see, got it now. ... hand side of the summary bar. ... Niel H ... Prev by Date: ...
    (uk.people.consumers.ebay)
  • Re: why do people take paypal?
    ... 99.9% of the PayPal whiners are a victim of ... their own stupidity. ... Niel H ... Prev by Date: ...
    (uk.people.consumers.ebay)
  • Re: Help with Fibonacci & Co
    ... A N Niel wrote: ... (Sadly, it's no longer taught.) ... --- Christopher Heckman ... Prev by Date: ...
    (sci.math)
  • Re: Sellers
    ... > It seems most common when they are selling a link or some shitty ebook. ... Because they're silly twats? ... Niel H ... Prev by Date: ...
    (uk.people.consumers.ebay)
  • Re: How much do ebay charge?
    ... > So why are you even considering selling on Ebay if that is the case? ... Alan ... > Niel H ... Prev by Date: ...
    (uk.people.consumers.ebay)