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Re: Re: Gray's Differential Geometry error?

• To: mathgroup at smc.vnet.net
• Subject: [mg63238] Re: [mg63215] Re: Gray's Differential Geometry error?
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Tue, 20 Dec 2005 04:19:37 -0500 (EST)
• References: <dnv48c$och$1@smc.vnet.net> <200512191201.HAA10976@smc.vnet.net> <7F9B8DFC-F317-4A5E-8341-457A8F7BBCC0@mimuw.edu.pl> <200512191618.57147.hattons@globalsymmetry.com>
• Sender: owner-wri-mathgroup at wolfram.com

Andrzej KOzlowskiOn 20 Dec 2005, at 06:18, Steven T. Hatton wrote:

> On Monday 19 December 2005 10:11, Andrzej Kozlowski wrote:
>
>> I do not have Gray's book here (I do own it but tend to  keep it on a
>> different continent than the one I am on now ;-)) but it is trivial
>> to show that the above can't possibly be correct.  Just put b = -a.
>> Then obviously s is 0 so the expression for the derivative is 0.
>> However, the function z[t] has a non zero derivative, unless a = b  
>> = 0.
>
> I don't believe b=-a is legal in this context.  My assumption is a  
> > b > 0.
> Or, at a minimum, |a|==a && |b|==b.  Your reasoning may be correct  
> in so much
> as an inverted ellipse would still be an ellipse.

It does not matter at all what the geometric interpretation is. The  
concept of derivative of this function is completley independent of  
whatever meaning you won't to assign to the formula and it could not  
possibly be true that the derivative of the funciton is given by the  
formula. There is nothing at all here to argue about.

Andrzej Kozlowski

• References:
  • Re: Gray's Differential Geometry error?
    • From: "Steven T. Hatton" <hattons@globalsymmetry.com>