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Message: [QUOTE="Matthew Moss, post: 4502864"] I think (offhand, didn't actually run your code) your problem is not math but pass-by-reference vs. pass-by-value issues. Look at your Vector.normalize function: [i] v is not a copy of the parameter passed in but a reference to it. And you are changing the elements of v directly. In these two cases here, you don't notice the destructive behaviour, since you assign the result to the parameter. But here: You are assigning the result to a different variable, but you've actually changed b1 as well because it's not pass-by-value. I would write a Vector normalize like such: class Vector def normalize div =3D inner_product(self) if div.zero? self else self * (1 / Math.sqrt(div)) end end def Vector.normalize(v) v.normalize end end[/i] [/QUOTE]