Just seen an episode of the Simpsons in which Homer states:
"The sum of the square roots of any two sides of an isosceles triangle is equal to the square root of the remaining side."
Someone in the toilet cubicle corrects him and says it's a right triangle.
Obviously they're both wrong because any two sides of any triangle add up to more than the other side, although what Homer said sounds like Pythagoras except he said square roots instead of squares and it was the wrong kind of triangle. The character in the cubicle also missed that it should have been squares not square roots.
But I'm wondering... did the writer also get Pythagoras wrong, i.e. does the writer agree with the character in the cubicle, or is the writer just nerd-hunting?
Then I thought about the algebraic expression of what Homer said: √a + √b = √c
The simplest whole number solution is 1, 4, 9 which features in 2001: A Space Odyssey. Or there's 9, 16, 49. Or 25, 36, 121. Whatever you like, there are infinitely many solutions, it just doesn't have anything to do with triangles.
Or does it? It certainly doesn't work in a flat plane nor on a sphere, but is there some geometry in which it does work, or is there a physical object or process that satisfies the equation (apart from the Monolith alluded to above)?
The Simpsons often makes vague cultural references and allusions, and I can't help thinking there must be some reason why that specific mistake was written in, some 'in' joke that I've missed?