# Thread: Other Geometries

1. ## Other Geometries

Correct me if I'm wrong but Euclidean geometry is the geometry taught in grades 6 to 12 in USA public schools.
There are other geometries that exceed Euclidean geometry, right?

Questions:

1. What is the difference between Euclidean and Plane Geometry?

2. How many OTHER geometries are taught in colleges worldwide?

2. ## Re: Other Geometries Originally Posted by harpazo Correct me if I'm wrong but Euclidean geometry is the geometry taught in grades 6 to 12 in USA public schools.
There are other geometries that exceed Euclidean geometry, right?

Questions:

1. What is the difference between Euclidean and Plane Geometry?

2. How many OTHER geometries are taught in colleges worldwide?
1. These are essentially the same. I'll let the Mathematicians describe any differences.

2. Many. Euclidean geometry is "flat" in the sense that there is no curvature. (The surface of a sphere is an example of a curved space but the surface of a cylinder is not.) There are a group of geometries which are called Riemannian and non-Riemannian which deal with curved spaces. I have been studying a type of non-Riemannian geometry: the spaces described in Special and General Relativity are of this type.

-Dan

3. ## Re: Other Geometries Originally Posted by topsquark 1. These are essentially the same. I'll let the Mathematicians describe any differences.

2. Many. Euclidean geometry is "flat" in the sense that there is no curvature. (The surface of a sphere is an example of a curved space but the surface of a cylinder is not.) There are a group of geometries which are called Riemannian and non-Riemannian which deal with curved spaces. I have been studying a type of non-Riemannian geometry: the spaces described in Special and General Relativity are of this type.

-Dan
All non-Euclidean geometries are taught in graduate school, right? It is considered advanced geometry, right?

4. ## Re: Other Geometries Originally Posted by harpazo All non-Euclidean geometries are taught in graduate school, right? It is considered advanced geometry, right?
It's called "Differential Geometry" and any college that offers a doctorate program will have this, yes.

-Dan

5. ## Re: Other Geometries Originally Posted by topsquark It's called "Differential Geometry" and any college that offers a doctorate program will have this, yes.

-Dan
I see no need to study this level of geometry at 53 going to be 54. My goal is to learn and revisit high school math. I have nephews and nieces that will need math help once they enter middle school and high school shortly there after.

6. ## Re: Other Geometries Originally Posted by harpazo I see no need to study this level of geometry at 53 going to be 54. My goal is to learn and revisit high school math. I have nephews and nieces that will need math help once they enter middle school and high school shortly there after.
Yes, Differential Geometry requires a lot of background material. Which is why I normally tend to study particular geometries rather than general ones. Though that might change with time. It getting to be more fun as I increase in my understanding. But I doubt I'll need the more general theorems as I study Physics. (I don't study Cosmology which does use the more general theorems. I just try to keep up with the results.)

-Dan

7. ## Re: Other Geometries Originally Posted by topsquark Yes, Differential Geometry requires a lot of background material. Which is why I normally tend to study particular geometries rather than general ones. Though that might change with time. It getting to be more fun as I increase in my understanding. But I doubt I'll need the more general theorems as I study Physics. (I don't study Cosmology which does use the more general theorems. I just try to keep up with the results.)

-Dan
Learning takes hard work and time. If I can "master" the middle school and high school geometry material, I will be totally satisfied. BTW, I know the basics of middle school and high school geometry apart from direct and indirect proofs.