What is the differences and what are the uses of non Euclidean geometry in the real world if there are any?
In: Mathematics
All math is based on a few rules, that are combined to make new rules.
If you don’t use all of those rules, you’re doing a different kind of math.
Euclid set 5 rules.
1. You can draw a line from any point to any point.
2. You can make a line longer as far as you like
3. You can draw a circle.
4. All right angles are the same.
5. That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which the angles are less than two right angles. IE parallel lines never meet and they never get further apart either.
Number 5 was much more complicated than the other 4, and this really bugged Euclid and math guys for thousands of years. They kept thinking it could be derived from rules 1-4 if put in the right order.
Turns out they couldn’t.
Most of non-Euclidean geometry decides to mess with rule 5.
So say instead of parallel lines never meeting either they meet eventually, or they split apart.
So how is this useful?
We’ll say you’re at a spot on Earth, and head straight north and just keep going, you’ll eventually cross the north pole.
Say another person at a different spot also heads north and just keeps going, he’ll eventually cross the north pole as well.
So the two of you had parallel paths, and yet your paths met, because the Earth is a globe, and not flat.
And that’s where non-euclidean geometry works. Euclidean geometry describes what geometry is on a flat surface. Non-euclidean geometry describes what geometry is on a not flat surface, for example: the globe we live on.
Latest Answers