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

>