Christopher James Huff wrote:
> In article <402### [at] hotmailcom>,
>  andrel <a_l### [at] hotmailcom> wrote:
> 
> 
>>Are you sure? I have used this myself and when I used it
>>the tangents were correct. Note also the symmetries in the
>>coefficient, the binomial coeeficients and the nice alternating
>>signs. I think the original error may be in the line:
>> > P2*3*(2*(1 - t)*(-1)*t + (1 - t)2) -
>>In my deriviation the final '-' is a '+'. BTW, I derived the
>>equations in the same way as you did. Well, of course, we both
>>have the same sort of math training I suspect :).
> 
> 
> The one at the very end? That was in the original equation:
> P1*(1 - t)^3 +
> P2*3*(1 - t)^2*t -
> P3*3*t^2*(1 - t) +
> P4*t^3
> 
> If that's wrong, than the original equation is too. 
Sorry, I did not check all your equations, I should have.
You are absolutely right here, your original equation
is wrong. There should not be a minus there either ;)

> If you're talking 
> about something in that term, the Maxima result is: 
I had never heard of Maxima, just googled it.
Perhaps I give it a try someday.
off-topic: Mostly I do the math required for POV by hand.
For years I did not do as much math as I do now. Sometimes
I even try to convince people that POV is an interesting
kind of application for learning math at a highschool level.
You often want to achieve some goal and the only way to do
it is sit down and do the equations. Along the same line,
if someone asked me why that should learn math at highschool
one of my answers is: to be able to create realworld
objects in POV!
	Andrel

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