Questions tagged [noneuclidean-geometry]

For general questions about non-Euclidean Geometry. Consider using more specific tags, like (projective-geometry), (hyperbolic-geometry), (spherical-geometry), etc.

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35 views

Can Euclidean and non Euclidean geometry be tied together? [closed]

Is there a field of math that contains operations(i.e. tensors/ matrices) which mediate the smooth transition between Euclidean and non Euclidean geometry?
39 views

If $\ell_1$ is a hyperbolic line, show there exists a perpendicular line $\ell_2$ such that $p\in \ell_2$ where $p \in \mathbb{H}\setminus\ell_1$

I am working within the upper half plane. I broke this question into three categories: $\ell_1$ is a vertical line. $\ell_1$ is a semi-circle and $p$ is directly above the center of $\ell_1$. $\ell_1$...
43 views

Is spherical geometry "infinite" in the same sense that a Euclidean plane is?

This seems like a pretty straightforward question (assuming I worded it well), but I've never been able to find an answer anywhere. So, in Euclidean geometry, a plane extends infinitely in all ...
38 views

Projecting a band of a sphere onto a 2D surface

For a craft project, I want to take a "band" of a sphere (i.e. the area between two latitudes) and project it onto a plane, so that I can fold the 2d shape onto the sphere and recreate the ...
54 views

Spherical Pythagorean Theorem

In class, we came across the following relation for a right triangle on the surface of the sphere. $cos(\frac{c}{R})=cos(\frac{a}{R})cos(\frac{b}{R})$ where R is the radius of the sphere. Here a, b, c ...
60 views

The smallest codimension for isometric immersions

I just read Azov's article in the considered two classes of Riemannian metrics, \begin{align*} ds^2&=du_1^2+f(u_1)\sum_{i=2}^ldu_i,&f>0\\ ds^2&=g^2(u_1)\sum_{i=2}^ldu_i^2 ,&g>0\...
28 views

Textbook Suggestions for Teaching Senior Level Geometry

I will be teaching a senior-level class on geometry next semester. The class consists of both Euclidean and non-Euclidean geometry with an axiomatic approach. Right now, it appears I have the liberty ...
10 views

Need to calculate the 3D volume of a growing 4D hypersphere in Minkowski space

4D geometry and Minkowski space are areas of expertise which I fundamentally lack, so I'm hoping people are able to help me with this. The problem is this, if you had a hypersphere in Minkowski space ...
117 views

Real numbers vs. the real number line

I don't know how to formulate this question precisely, so let me explain where I am coming from, noting that I know little about nonEuclidean geometry. I was thinking about how to explain how ...
24 views

Newton's Shell Theorem in non-Euclidean spaces

Newton's Shell Theorem for gravity states, in two parts, that The gravitational field of a sphere outside the sphere is equal to the gravitational field of a point mass at the sphere's center. (This ...
41 views

Confusion regarding composition of two spatial rotations of a sphere.

I am currently studying Complex analysis from the book "Visual Complex Analysis" by Tristan Needham. In the chapter "Non-Euclidian Geometry" on page 282 the author says that the ...
48 views

Does classical mathematical logic consider Euclidean Geometry and Non-euclidean Geometry to be distinct object languages?

From the basis of mathematical logic (specifically classical logic), would we consider Euclidean Geometry and Non-euclidean Geometry as distinct object languages? Is that what it means to be an object ...
37 views

Coordinate transformation that would transform an doughnut inside out (in 2D)

Sorry for the non-precise lingo, but not really a mathematician here. I am looking for a transformation that given a set of points in a carthesian plane, would move the outermosts points closer to the ...