
#1
Jan2413, 06:47 AM

P: 162

Is it possible that a triangle with angles totaling over 180 degrees could exist without being embedded in a 3rd dimension?




#2
Jan2413, 07:04 AM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 38,879

If you are talking about Euclidean geometry then, no. Of course, you can have a hyperbolic two dimensional geometry without it being imbedded in a three dimensional Euclidean geometry.




#3
Jan2413, 07:28 AM

P: 162

a hyperbolic two dimensional geometry without it being imbedded
Does this have something to do with it being "intrinsic"? 



#4
Jan2413, 04:15 PM

Sci Advisor
HW Helper
P: 9,421

triangle angles >180 embedded
to speak of the sum of angles in a triangle in a geometry you just need some way to compare angles, AND ADD THEM AND THEN TO SAY THAT THE SUM OF ANGLES IN A TRIANGLE IS MORE THAN (oops) a straight angle.
if you want to prove such examples exist, it depends what your standards of belief are. if you are someone who believes only in euclidean space, then for you it is necessary to find every other example embedded there. it is quite consistent to imagine spherical or hyperbolic geometries, where triangles add to other than a straight angle, but to produce examples of them, we often look in euclidean space of higher dimension. i think Halls meant that for a triangle with angle sum more than a straight angle, we probably look in a spherical geometry, and for less, in a hyperbolic geometry. 



#5
Jan2513, 09:33 AM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 38,879

I always get "hyperbolic" and "elliptic" geometries confused! Of course, I should just associate "ellipsoid" with "spherical".



Register to reply 
Related Discussions  
Triangle angles?  General Math  9  
Angles within a spherical triangle  Calculus & Beyond Homework  15  
Calculate the angles in the triangle  Precalculus Mathematics Homework  4  
Angles of a Triangle  Precalculus Mathematics Homework  1  
Triangle and angles...  General Math  13 