What does this shirt represent?
The picture is a depiction of Euclid's 5th postulate, which is equivalent to the statement "given a line and a point not on that line, there's only one line you can draw through the point (and lying in the same plane as the other line) so that it never crosses the other line". People thought it was just 'true' (it seems so!) and provable from the first 4 axioms of geometry for a long long time, but could never prove it--because it's not. You can negate the 5th postulate and get perfectly good other weird geometries (spherical, hyperbolic). But once you throw in the 5th you get 'Euclidean' geometry, which is the kind of geometry everyone is used to.
Anyway the picture shows that if the angles alpha and beta pictured sum to less than pi radians (180 degrees), then those two lines will eventually cross somewhere on the same side as the two angles.
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