
#1
Feb513, 03:02 PM

P: 3,843

What is the difference between the Euclidean Geometry and the simple plane geometry? They seems to work with flat planes.




#2
Feb513, 04:55 PM

Sci Advisor
HW Helper
Thanks
P: 26,167

hi yungman!
i'm confused … aren't they the same thing? 



#3
Feb513, 05:02 PM

Mentor
P: 16,565

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
Feb513, 05:17 PM

P: 3,843

Euclidean and plane geometry.
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
Feb513, 05:33 PM

Sci Advisor
HW Helper
Thanks
P: 26,167

Hi Alan!




#6
Feb513, 06:22 PM

P: 3,843

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



#7
Feb613, 09:15 AM

Sci Advisor
HW Helper
P: 9,421

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
Feb613, 12:22 PM

P: 3,843

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
Feb613, 02:16 PM

HW Helper
Thanks
P: 5,542

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 nonEuclidean geometries, there is no parallel postulate, and the total internal angle of a 2D triangle is not equal to 180 degrees.



Register to reply 
Related Discussions  
Euclidean geometry and complex plane  Differential Geometry  4  
Euclidean Geometry  Special & General Relativity  9  
Euclidean Geometry  Precalculus Mathematics Homework  1  
euclidean geometry  General Math  3  
Euclidean Geometry  General Math  8 