Saturday, August 13

Tag: Euclidean

Orbital Explains: The Line At Infinity
Science & Technology

Orbital Explains: The Line At Infinity

You’ve probably never stood on a train track, and looked as it disappeared off into the distance. But let’s imagine you have. The two mutually parallel tracks seem to meet just as they venture over the crest of the horizon - a strange illusion. You know that the two tracks can never meet, because a train has to be able to move over them, with a fixed distance between its wheels. Perhaps it is just an illusion, created by the optical receptors in your eye - or perhaps it isn’t. In Euclidean mathematics, two parallel lines will exist along side each other at a fixed length and never meet. Euclid also explained that two lines will meet at exactly one point, unless they are parallel. This idea upsets modern day mathematicians, who don’t like the word ‘unless’; they believe it’s not elegant....