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MathGroup Archive 2007

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Re: Curvature calculations

  • To: mathgroup at smc.vnet.net
  • Subject: [mg76315] Re: Curvature calculations
  • From: CKWong <CKWong.P at gmail.com>
  • Date: Sat, 19 May 2007 04:47:43 -0400 (EDT)
  • References: <f2eltq$2mt$1@smc.vnet.net>

Since I'm not on the design team of Mathematica, I'm hardly in the
position to comment on the presence or absence of any particular
algorithm in the software.

On the other hand, I think you may want to know that there is a huge
difference in geometric significance between the ArcLengthFactor and
the curvature of a curve.  This is because, THE line element (not A
line integral) defines the metric tensor of the underlying space in
terms of the chosen coordinate system.  Thus, all geometric properties
of the space can be derived from the ArcLengthFactors.

In contrast, the curvature of a line is just that:  a local property
of a specific object.  It goes without saying that anyone interested
in such things may expect to do some leg-work himself.



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