Non-Euclidean Geometry Unit
... along them. Therefore, lines in spherical geometry are Great Circles. A Great Circle is the largest circle that can be drawn on a sphere. The longitude lines and the equator are Great Circles of the Earth. Latitude lines, except for the equator, are not Great Circles. Great Circles are lines that di ...
... along them. Therefore, lines in spherical geometry are Great Circles. A Great Circle is the largest circle that can be drawn on a sphere. The longitude lines and the equator are Great Circles of the Earth. Latitude lines, except for the equator, are not Great Circles. Great Circles are lines that di ...
More on Neutral Geometry I (Including Section 3.3) ( "NIB" means
... Theorem 3.3.3 (Angle-Angle-Side Congruence Condition): If, in two triangles, the vertices of one triangle can be put into one-to-one correspondence with the vertices of the other triangle such that: Two angles and the side opposite one of them in one triangle are congruent to the corresponding angle ...
... Theorem 3.3.3 (Angle-Angle-Side Congruence Condition): If, in two triangles, the vertices of one triangle can be put into one-to-one correspondence with the vertices of the other triangle such that: Two angles and the side opposite one of them in one triangle are congruent to the corresponding angle ...
3-manifold
In mathematics, a 3-manifold is a space that locally looks like Euclidean 3-dimensional space. Intuitively, a 3-manifold can be thought of as a possible shape of the universe. Just like a sphere looks like a plane to a small enough observer, all 3-manifolds look like our universe does to a small enough observer. This is made more precise in the definition below.