What is Non-Euclidean Geometry?
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Imagine a really large sheet of paper and we’re like ants, standing on the same spot. You go North 3 miles, I go East 4 miles, so now we’re 5 miles apart. That’s Euclidean.
Or we’re standing 1 mile apart (doesn’t matter which way). You go to the North 100 miles, I go to the North 100 miles, we’re still 1 mile apart.
Also there’s no boundary to the paper, it can extend as far North / South / West / East as you need it to be. Those are properties of Euclidean geometry.
But you can imagine in a different world, if you’re standing here, and I start from your position but keep going North, I’ll suddenly come back from the South and go back to your same spot. That’s not Euclidean. In fact, the Earth is like that (because Earth is round).
Or in a yet stranger world, I might come back to the same spot again but also from the North, and suddenly the whole world is mirror-imaged. So if you had a pimple in your left cheek, now I’ll see your pimple to be in your right cheek. This is definitely not Euclidean.
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