What are the key differences between Euclidean and plane geometry?

In summary, Euclidean geometry is the geometry of a flat plane while simple plane geometry is the geometry of a plane that is not flat.
  • #1
yungman
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What is the difference between the Euclidean Geometry and the simple plane geometry? They seems to work with flat planes.
 
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  • #2
hi yungman! :smile:

i'm confused :redface:

aren't they the same thing? :confused:
 
  • #3
I don't necessarily associate "plane geometry" with Euclidean geometry. Something like [itex]\mathbb{R}^3[/itex] or [itex]\mathbb{R}^n[/itex] are also Euclidean geometries (to me).
 
  • #4
Thanks for the reply, I just gone on the Youtube to take a crash course into spherical trigonometry. The lectures review the basic of Euclidean geometry as an introduction to spherical geometry. Everything about Euclidean geometry sounds like just simple plane geometry I learned long time ago, but I never learn the name Euclidean geometry. I really don't know the detail, that's the reason I asked.

Thanks

Alan
 
  • #5
Hi Alan!
yungman said:
Everything about Euclidean geometry sounds like just simple plane geometry I learned long time ago …

Yes it is … different name, same thing! :smile:
 
  • #6
tiny-tim said:
Hi Alan!


Yes it is … different name, same thing! :smile:

Hi Tiny-Tim

Thanks for the reply. That's all I want to know.

Alan
 
  • #7
to me plane geometry means two dimensional geometry, either euclidean or hyperbolic, while euclidean geometry means essentially the geometry of R^n, i.e. a geometry of any finite dimension in which triangles have angle sum 180 degrees.

to people who have not studied hyperbolic plane geometry, the term plane geometry probably means the more familiar euclidean plane geometry. i do not consider the hyperbolic plane to be flat however.
 
  • #8
I guess I consider plane geometry can be extended to 3D as long as all the surfaces are flat. Just like a cube composes of six planes. All the trig functions apply.

The spherical surface is totally different where circumference is not 2[itex]\pi[/itex]R as the surface is not flat.
 
  • #9
I believe geometries (2D or 3D) are referred to as Euclidean if the parallel postulate holds. In Euclidean geometry, a 2D triangle has a total internal angle of 180 degrees or pi radians. In non-Euclidean geometries, there is no parallel postulate, and the total internal angle of a 2D triangle is not equal to 180 degrees.
 

1. What is the difference between Euclidean and plane geometry?

Euclidean geometry is a type of geometry that studies the properties of objects in a flat, two-dimensional space. Plane geometry, on the other hand, is a type of geometry that studies the properties of objects in a three-dimensional space.

2. What are the basic principles of Euclidean geometry?

The basic principles of Euclidean geometry include the concepts of points, lines, and planes, as well as the postulates of equality, symmetry, and parallelism. It also involves the use of axioms and theorems to prove geometric relationships.

3. What is the importance of Euclidean geometry in real life?

Euclidean geometry has many practical applications in fields such as architecture, engineering, and design. It is used to create accurate measurements and designs for structures and objects in the physical world.

4. Can Euclidean geometry be applied to non-flat surfaces?

No, Euclidean geometry is limited to studying objects in a flat, two-dimensional space. It cannot be applied to non-flat surfaces, such as spheres or curved surfaces.

5. What are some famous examples of Euclidean geometry in history?

One famous example is the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. Another example is Euclid's Elements, a mathematical treatise that is considered the foundational work of Euclidean geometry.

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