In any triangle two sides taken together in any manner are greater than the remaining one.My old textbook (which my wife has been hounding me to throw out) a footnote remarks that Proclus (another ancient geometer) reported that it was the habit of the Epicureans to ridicule this theorem because:
"Even an ass knows that. If fodder is placed at one angular point and the ass at another, the ass won't walk the two sides of the triangle but just the one side. Booyah."Proclus would respond,
"Oh no you didn't! Mere perception of the truth is different from a scientific proof of it and a knowledge of the reason why it is true."It was even more devastating in Greek.
I mention this because the assertion that even the ass knows to walk a straightline shows five year olds in an interesting light. Everyday I pick-up my son and carpool buddy and struggle with their inability to walk in a straight line. For example, when I drop carpool buddy off, rather than making a beeline from my car to his front door he takes an elliptical approach that occasionally takes him into neighbors' yards. So, are five year-olds dumber than asses? "What," Proclus would no doubt ask, "Does this say about the human capacity to reason, about logos?"
Or, are five-year olds brilliant? Just as Einstein shattered Newtonian physics showing that space curves, Euclidean geometry also withered before the assault of modernity. Lobchevsky (yes, the one from the Tom Lehrer song) argued that a line lying perpendicular across two parallel lines does not intersect them at exactly 90 degrees because space curves. So perhaps, when my charges are wandering in what to my, aged eyes are parabolic routes they are in fact simply perceiving the curves in space and navigating them.
Or they could just be a pair of dumbasses.