## Re: Interesting Math Error

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• I think I found the answer, Pete. http://imgs.xkcd.com/xk3d//(_frame.png Larry
Message 1 of 25 , Apr 1, 2011
I think I found the answer, Pete.

http://imgs.xkcd.com/xk3d//(_frame.png

Larry

--- In SeattleRobotics@yahoogroups.com, "Pete Miles" <robots@...> wrote:
>
> x^n and -x^n and (-x)^n are considered unary operations
>
> (x-y)^n, -(x-y)^n, and (sin(theta)-cos(theta))^n are not unary operatations
>
> This is the root of the Math Error:
> Forcing -(x-y)^n TO BE EQUAL to (-x+y)^n
>
> These two relationships are NOT equal
>
> The systems that are calculating this incorrectly, are incorrectly passing the -
> sign inside all operators inside the parentheses when the contents of the
> parentheses are raised to a power.
>
> There are 2 schools of thought here:
> -(3-5)^2 = will equal either -4 or +4 Only one answer is correct
>
> Now what would the following answer be to this relationship?
> 0-(3-5)^2
> is it -4 ??
> or is it +4 ??
>
> -(3-5)^2 IS EQUAL to 0-(3-5)^2
>
> Yet most of the the systems that incorrectly calculate -(3-5)^2
> will correctly calculate 0-(3-5)^2
>
> For you trig people:
> if sin(30) = 0.5 then -sin(30) = -0.5
>
> Now (sin(30))^2 + (cos(30))^2 = 1
>
> Solving for sin(30)
> (sin(30))^2 = 1-(cos(30))^2
>
> sin(30) = +(1-(cos(30))^2)^0.5 or -(1-(cos(30))^2)^0.5
>
> if you believe that -(5-3)^2 = +2
>
> then you must believe that
>
> sin(30) = +0.5 or i/2
>
> This math error has far reaching implications
>
> Pete
>
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