Results 1 to 7 of 7
Like Tree3Thanks
  • 1 Post By topsquark
  • 1 Post By topsquark
  • 1 Post By topsquark

Thread: Other Geometries

  1. #1
    Super Member harpazo's Avatar
    Joined
    Sep 2014
    From
    NYC
    Posts
    995
    Thanks
    42

    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?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    11,425
    Thanks
    871
    Awards
    1

    Re: Other Geometries

    Quote Originally Posted by harpazo View Post
    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
    Thanks from harpazo
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member harpazo's Avatar
    Joined
    Sep 2014
    From
    NYC
    Posts
    995
    Thanks
    42

    Re: Other Geometries

    Quote Originally Posted by topsquark View Post
    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?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    11,425
    Thanks
    871
    Awards
    1

    Re: Other Geometries

    Quote Originally Posted by harpazo View Post
    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
    Thanks from harpazo
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member harpazo's Avatar
    Joined
    Sep 2014
    From
    NYC
    Posts
    995
    Thanks
    42

    Re: Other Geometries

    Quote Originally Posted by topsquark View Post
    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.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    11,425
    Thanks
    871
    Awards
    1

    Re: Other Geometries

    Quote Originally Posted by harpazo View Post
    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
    Thanks from harpazo
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Super Member harpazo's Avatar
    Joined
    Sep 2014
    From
    NYC
    Posts
    995
    Thanks
    42

    Re: Other Geometries

    Quote Originally Posted by topsquark View Post
    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.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. World of Geometries
    Posted in the Geometry Forum
    Replies: 2
    Last Post: Feb 5th 2017, 01:33 PM
  2. Non-Euclidean Geometries
    Posted in the Math Topics Forum
    Replies: 2
    Last Post: Aug 20th 2014, 09:53 PM
  3. Applications of Non-Euclidean Geometries
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: Jan 30th 2010, 01:50 AM
  4. Geometries Beyond Plane Geometry
    Posted in the Geometry Forum
    Replies: 2
    Last Post: Dec 3rd 2008, 05:38 PM

/mathhelpforum @mathhelpforum