ELI5: non euclydian geometry
// explanation
What is non-Euclidean geometry?
Non-Euclidean geometry is geometry that doesn't happen on a flat, flat surface like a piece of paper [3]. Instead, it's geometry on curved surfaces, like drawing shapes on a ball or a saddle [3]. In regular geometry you learn in school, the rules are one way, but on curved surfaces, the rules change in fun ways!
Why is it different from regular geometry?
In regular geometry, parallel lines never meet, and the angles in a triangle always add up to 180 degrees [2]. In non-Euclidean geometry, these rules don't work the same way because the surface itself is curved [3]. It's like trying to use flat-paper rules on a basketball — the rules have to bend too!
What happens in non-Euclidean worlds?
If you were walking around in a non-Euclidean world, things would feel very strange and confusing [4]. Lines that look straight might curve in unexpected ways, and distances wouldn't work like you'd expect [4].
Why do people study it?
Mathematicians discovered non-Euclidean geometry by imagining geometry that doesn't follow the old rules [2]. This opened up entirely new ways of thinking about space and shapes!
// sources
Jul 15, 2019 ... Firstly, non-Euclidean geometry pretty much means it isn't on a flat plane. A simple way to do that might be to plot the whole dungeon onto a ...
"Non-Euclidean Geometry is a history of the alternate geometries that have emerged since the rejection of Euclid¿s parallel postulate.
May 25, 2024 ... Non-euclidean geometry is just geometry on a curved surface. Usual examples are a sphere or a horse saddle shaped plane. For example you can ...
Jan 29, 2021 ... Lovecraft's description gives a rather impressive and accurate description of how an Euclidean would feel in a non-Euclidean world.
Feb 18, 2013 ... After the discovery of non-Euclidean geometry, Kant's claims for the synthetic a priori status of Euclid's geometry as a description of physical space came ...
Video by CodeParade
Video by Extra History
Video by 2 Minute Educational
