ELI5- How does non euclidean geometry work?

Question

ELI5- How does non euclidean geometry work?

In: 4

Answer 1

At the very simplest –

In Euclidean Geometry two parallel lines will never intersect and the reason for this is because “Euclidean space is flat.”

Ok whatever that means.

In Non-Euclidean Geometry, two parallel lines ***can*** intersect and this is because “non-Euclidean space is curved”.

WTF?

Take a piece of paper and draw two parallel lines – they don’t cross, right? Because paper is flat.

Take a tennis ball and draw two vertical parallel lines at the middle, the lines will connect at the top and bottom of the ball, because the surface of a sphere is curved.

Another example – draw a triangle on paper and add up the degrees in all the corners, you’ll get 180 degrees. If you do the same on a tennis ball you can actually make a triangle with (3) 90-degree corners because it’s actually a wonky-triangle with curved sides.

Long story short – Euclidean geometry is the geometry of shapes drawn on a flat plane. Non-Euclidean geometry is the geometry of shapes drawn in curved space.