What is Non-Euclidean Geometry?
In: 408
Its hard to truely ELI5 but the simplest way I could describe it is “phyiscally impossible geometry” For example, you could have a tunnel that is ten meters long. You enter from one side, go through that 10 meter tunnel but you actually have moved 100 meters from the entrance.
Such a feat is not possible in the physical world, but is very much possible in the world of non euclidean geometry.
Extra history did a small segment on non-euclidean geometry.
However, like alot of their segments they do make some videos padded with story then facts in some cases, but in regards to this subject they give a nice history/reactions/outcome to this idea through the years.
It’ll obviously take longer then reading some of the minor posts below, but imo like myself when I discovered it, it was just on autoplay and I just listened to it while playing a game. It is very easy to follow however, and stay usually under 9 minutes for each of the 5 videos.
You know how when you take 3 right turns you’re now facing left from where you started it’d be like taking 3 right turns and you’re still facing right somehow.
Imagine drawing a triangle on a straight piece of paper . This is Euclidean geometry. Now wrap that same piece of paper over an orange and draw a triangle if you look at this in 2d you are now in non-Euclidean geometry. Because the angles of your triangle no longer add up like they normally do.
Euclidean Geometry can be drawn on a flat piece of paper with straight lines, circles and curves. There are a couple rules that you can count on to make predictions that will always hold, eg if you have four equal line segments with four 90 degree turns, you must end up where you started and you’re now looking at a square.
Non-Euclidean geometry is done on a surface or in a space where these simple rules dont hold. If you’re drawing on a ball, you only need three equal line segments with three 90 degree corners to end up where you started, and you’re now looking at a 3D bendy triangle with three right angles. This violates the rules of Euclidean space, hence a spherical surface is a non-Euclidean space. It just means it operates outside the normal standard rules like the example above.
Latest Answers