Those in favor of “traditional triangles” insisted that to be a triangle was to have three sides and three angles Those in favor of “square triangles” insisted that it was exclusionary (and “side-ist”) to not include squares as triangles, with all of the rights and privileges thereof. They pointed to the fact that squares who identified as triangles were likely to be ostracized by their peers (especially traditional triangle-ists). They pointed out that the same critical features that occurred in triangles also occurred in squares: they have straight sides, a definite number of angles, the sum of their interior angles was always a multiple of 180 degrees, they were closed planar figures. Some traditional triangle-ists pointed out that the square didn’t have the same structural integrity as the triangle in construction or that including squares would undermine the sanctity of triangularity, but the square triangle-ists pointed to a few squares that seemed to have born some structural loads (so the squares said). They also pointed to the fact that many triangles made of flimsy materials had collapsed under pressure, and that such triangles already undermined the sanctity of triangularity, so how could including square triangles be wrong? Besides, wasn’t it hypocritical of the traditional triangle-ists to only complain about squares undermining the sanctity of triangularity, while they ignored the flimsy triangles that had broken?
Still other traditional triangle-ists insisted that Euclid had defined triangularity in his book Elements thousands of years ago, and that what was good enough for Euclid was good enough for them. But the square-triangleists mocked Euclid and Elements as old-fashioned, bigoted and contradictory. They pointed to contradictions in grade-school textbooks about geometry and insisted that, had Euclid known of today’s committed square triangles, he would never have excluded squares from being triangles.
A few polygons tried to point out the absurdity of the arguments used by the square-triangle-ists. “How can you square-triangle-ists insist that the number of sides and number of angles of a polygon doesn’t matter, and not realize that you are only campaigning to include squares in the definition of triangle? Don’t you realize that the same logic applies to pentagons?”
“Don’t be absurd,” the square triangle-ists replied, “no one is trying to include pentagons in the definition of triangle. That is a slippery-slope argument. Anyway, everyone realizes that pentagons aren’t triangles, and we are offended that you would even bother comparing us to pentagons. Bigot.”
Eventually, after harassing or demonizing every mathematician and geometer who dared to disagree, and calling them “bigots” and “side-ists” whose backward reasoning no longer applied now that the goal of polygons had changed, the square-triangle-ists won the day. After a few artists and bakers were included on the polygon committee, it was decided that, although there was no geometrical or mathematical reason to do so, redefining triangles to include squares was a “good idea”. Facebook went wild with a new app designed to make everyone’s faces into a square, and square-triangle-ists everywhere celebrated.
Meanwhile, a few polygons continued to insist that the very nature of triangles excluded squares from being triangles, and that calling a square “triangle” would no more make it a triangle than calling a same-sex couple “married” would make them so. But the squares and the polygons who supported them immediately denounced the comparison as absurd. “No one could possibly doubt that marriage is between a man and a woman! Don’t be ridiculous!”