Help me visualize Non-Euclidian geometry

[Zanix]

I've been looking at this site.

It's easy for me to see the step from "flatland" to the third dimension, but I can't see it from the third to the fourth.

Here the author is talking about the Pseudosphere, which looks like a circular asymptote to me. He mentions how it "turns in on itself", which I guess is where I loose him. What does he mean?

In another section he talks about spherical geometry. For that he used the planet as an example, and how sailors and pilots use spherical geometry to plot shortest routes, etc... That one was easy enough. I just thought of a euclidian triangle molded to the planet, like the curved triangle that has the points NY, LA, and Miami. At least, I think I understand that part correctly.

 

[Zanix]

Have I missed something stupid with my post? Is NonEuclidian geometry like horoscopes? 😕

 

[Woodchuck2000]

You havn't missed anything stupid, it's just that life gets very hard to visualise once you leave behind our everyday experience.

As I understand it (which isn't very well!), a pseudosphere differs from a normal sphere in that it has constant negative curvature, rather than the constant positive curvature of a normal sphere.

As to how best to visualise that one, I'm not entirely sure to be honest! It's a construction which is useful in maths but not easily applicable in real life.

 

[DrPizza]

for the 2nd part of your question, no, it's not like horoscopes.
Horoscopes = one of the stupidest things someone could believe in.
Non-euclidian geometry of the universe = better than euclidian geometry for explaning our observations

 

[Zanix]

Originally posted by: DrPizza
for the 2nd part of your question, no, it's not like horoscopes.
Horoscopes = one of the stupidest things someone could believe in.
Non-euclidian geometry of the universe = better than euclidian geometry for explaning our observations

Excellent. I was hoping that was the case, but I didn't know. Some things that I think are interesting are laughed at in the scientific circles. Like epistemology. People think you do alot of drugs when you start asking questions like, "Do we really know anything?"


And to WoodChuck2000, So could a pseudosphere be like a sphere inverse? I keep thinking about being on the inside of a ball vs. being on the outside, but I think that idea is to simple.

 

[Xyo II]

Pseudosphere

Curved Spacetime

 

[Woodchuck2000]

That picture takes a little explanation.

If we create an axis through the centre of the pseudosphere as pictured there (through the centre of both thin ends) it has the following property.

If you choose any point on the interior surface and create a tangent such that the tangent intersects our axis, the distance between that point and our axis will remain constant.

Hence constant negative curvature.

 

[Zanix]

Originally posted by: Einstein Element
Pseudosphere

Curved Spacetime

Awesome, thanks for the links.

 

[Xyo II]

Originally posted by: Zanix

Originally posted by: Einstein Element
Pseudosphere

Curved Spacetime

Awesome, thanks for the links.

that's what google's there for 😉

 

[Mday]

visually, we can only go as high as 3d. there are ways to represent a 4th dimension, by using color. this is typically used for heat\temperature purposes

 

[Zanix]

Originally posted by: Einstein Element

Originally posted by: Zanix

Originally posted by: Einstein Element
Pseudosphere

Curved Spacetime

Awesome, thanks for the links.

that's what google's there for 😉

😱🙁

 

[Zanix]

Originally posted by: Mday
visually, we can only go as high as 3d. there are ways to represent a 4th dimension, by using color. this is typically used for heat\temperature purposes

As in this pic: Pseudosphere?

I don't think I really understand yet, but I'm not sure what questions to ask. 😱

I like trying though. :thumbsup:

 

[Xyo II]

Originally posted by: Mday
visually, we can only go as high as 3d. there are ways to represent a 4th dimension, by using color. this is typically used for heat\temperature purposes

heat/temp? no, i think he/she's asking for the real-life 4th dimension, the one we move around in every day. heat is just a characteristic of a 3-d object, unless you are graphing it, and using it as a new vantage point.