<obsMathRef>
lodin's observation and syphilis' cantrip come from the same underlying mathematical principles.

Triangle equality:
for vectors a, b,

||a+b|| <= ||a|| + ||b||, with equality iff a is a positive scalar multiple of b

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

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

cos theta = (a dot b) / (||a|| ||b||)

(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

In reply to Re^2: Seeing if two numbers have the same sign ($x / abs $x) by WoodyWeaver
in thread Seeing if two numbers have the same sign by grinder

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