NON-EUCLIDEAN GEOMETRY
LOBACHEVSKY (HYBERBOLIC) GEOMETRY
RIEMANN (ELLIPTIC) GEOMETRY
(I)
Triangle: A+B+C < 180 degree
(II)
Parallel (//) lines did not meet but the distance between them become smaller.
(III)
(III.1)
Only 2 triangles which have the same area have the same 3 angles.
If 2 triangles which have different area, they are not similar (~).
(III.2)
Whenever a triangle's area increase (+), the total angles decrease (-).
(IV)
Given a point outside a line, can draw only one perpendicular line to that line.
(V)
(V.1)
(V.2)
Circle: C/d > π
The ratio is larger when the area increases (+).
(I)
Triangle: A+B+C > 180 degree
(II)
Each line in a surface must intersect each other.
(III)
Whenever a triangle's area increase (+), the total angles increase (+).
(IV)
Can draw numberless lines from a point to a given line.
(V)
(V.1)
Circle: C/d < π
(V.2)
The ratio is smaller when the area increase (+).