bad news, euclid fans! i just disproved his assertation that parallel lines don't intersect for their entire infinite length. i walked along them for approximately 8.6 x 10⁸ km and you know what i found? that's right, a tangle.
they don't touch for the rest of their infinite length though, i did check. in both directions.
i'm sorry that's my fault i was walking along that stretch earlier and accidentally tripped and tangled them up and i couldn't get them untangled and i thought no one would notice i'm so sorry