Triangle equality:
for vectors a, b,

(Note here || is "norm", not or.)

Angle between two vectors:
The angle theta between two vectors a, b satisfies

(That the second theorem implies the first is left as an exercise for the reader. :-)

For one dimensional vectors ("numbers") the norm is the absolute value, and there are only two "directions" -- out along the positive axis and out along the negative axis. So syphilis is applying the triangle equality, while lodin is computing the cosine directly (note cos 0 = 1 -> "same sign" while cos 180 degrees = -1 -> "opposite sign").
</obsMathRef>

We now return to our regular interpretation of line noise as script.

--woody

lodin is computing the cosine directly (note cos 0 = 1 -> "same sign" while cos 180 degrees = -1 -> "opposite sign").

Maybe this is what you mean, but I don't actually calculate the angle (or cosine) between $_[0] and $_[1]. I calculate the respective angles of $_[0] and $_[1] against the positive axis, and compare them.

Equivalently, you could also view it as I'm taking the norm of the two 1D vectors $_[0] and $_[1], which gives me two unit vectors pointing in the direction of $_[0] and $_[1], which I then test for equality. If they're equal, they point in the same direction, and in 1D that means they have the same sign.

lodin

arg, eyes are getting old. You are absolutely right. I was thinking of the "trick" people had described about taking the product and checking if positive; you are indeed normalizing the vectors and checking for equality.