Analysis / Triang Relations

This blog post from April 2012 uses The Hunger Games to make the point that of the 13 listed, only the ones with at least one double-headed arrow (i.e. Types 4 and 6-12) are really love triangles.

The Triang Relational Same-sex Attraction Theorem:

"If we assume strict sexual dichotomy, any love triangle where all three characters are connected by three separate arrows requires some form of same-sex attraction."

Such triangles include types 2, 6, 8, 9, and 11-13. Refer to the following proof:

There are three characters required for there to be a love triangle.

Assume that these three characters either have one sex or another.

Combinatorics tells us that there are two ways to arrange them: either three of the same sex, or two of one sex and one of another.

Assume characters A and B are of the same gender, and C is the other.

Regardless of the arrows pointing between A and C and B and C, if an arrow points between A and B, then some form of same-sex attraction is happening, regardless of its direction.

If we have three arrows, then a line between A and B would be required.

Therefore, if we have three arrows, then some form of same-sex attraction must be happening.

Q.E.D.
http://tvtropes.org/pmwiki/pmwiki.php/Analysis/TriangRelations