Sure, you can choose your camp; I think I'm in the two legs good, three legs bad one.
Your example of the triangle was based on the premise that a chord is defined as at least 3 notes (a triad), and was thereby self-fulfilling; in contrast, mine of two eyes says you can see how far away something is without having to actually walk there.
Interestingly, further regarding the triangle and maths, the mathematical definition of a chord is a line which passes through two points...
Going back to written definitons of a musical chord, I can see that the number "three" in definitions of a chord is often preceded by the qualifier "usually", thereby hinting that it is not a hard rule.
Is there anything else in chord definitions, other than the number of notes which define its characteristics?
For instance, if you were to take any definition and replace the words "two" or "three" with "multiple", what else does it say about what makes a chord? eg. Does it have to uniquely identify the key you are playing in?