This topic is created for the purpose of discussing Euclidean, spherical and hyperbolic geometry for all who fancy. It is created in order to stop people from endless discussions on the validity of a certain comparison that has to do with sets and subsets.

For instance:


Okay, now let's all look at the beauty of a spherical triangle first (a triangle with 180° + top angle, thus the sum of angles > 180°)

http://en.wikipedia.org/wiki/Spherical_triangle

Argh! I want to at least escape this kind of hardcore math in Uni but to have it show up on MLG too?

I don't understand this, but I get the feeling that if I did, it would cause headaches.

I implore you to slow down.

Do you mean geometry is difficult, or just non-Euclidean geometry?

I like strange spacetime, though. ):

Snoble, to get it, think of it like this. If you draw a line from the North Pole to the South Pole (a meridian) and you look at the intersection with the equator, you'll notice that the equator is positioned orthogonal to the meridian. This is true for all meridians. Thus the sum of the angles at the equator is 180°. However, those meridians wil intersect as well (at the North or South Pole) and the total will be larger than 180°.

Just get a globe and measure it, if you don't believe it.

A hyperbolic triangle is more nightmarish.

i'll come back to this topic in a few years

So basically it just breaks the rules?

I can understand at least this since it doesn't involve radians. It just makes me think like it was math class.

Geometry is a**.

It is non-Euclidean, it does not follow Euclidean rules. However, it is very useful for describing our reality.

Let's see here.
Judging by the diagram on Wikipedia, the triangle itself is formed by the placement of the meridians on the sphere. Since the meridians intersect perpendicular to the equator and themselves, each angle in the triangle would therefore logically equal 90°.
From what I can see, the things that form the triangles are adding up to over 180, but not the triangle itself.

Math is unnatural.

No, you agree that the angles of the spherical triangle add up to more than 180°. A triangle is composed of those three angles. How can the triangle not add up to more than 180° if the angles that form it do? Then I could just as well say that the total of the angles that form a Euclidean triangle might be 180°, but that the triangle itself never consists of 180°. However, it is evident from observations that the total of the angles in a Euclidean triangle add up to 180°. Why would observations in non-Euclidean geometry be less valid? Observations are observations.

Hmm. Alright. I'll take your word for it.

It was perhaps not the wisest idea to try to introduce this topic without stating the axioms of spherical, hyperbolic, or whatever geometry you wish to talk about.

A line in spherical geometry, for example, needs redefining. As it is, it turns out that it is the portion of a great circle between the two points.

Just geometry?
Pffft.