As Professor mentioned in class, this is called triangle inequality. "Pentagon inequality" reminds us of thinking while reading notes.
Animagus
Say if we have a, b and c satisfy a triangle.
a + b > c
|a - b| < c
geminish
What's the meaning of |a-b|<c? I think a transform of first inequality should be |c-a|<b?
PPCC
@geminishActually we have some symmetricity of the triangle inequality. That is to say, we have |c-a|<b, |a-b|<c and |b-c|<a. Basically we should think that all edges have equal role and none of them are special and singular. For @Animagus, I guess he/she just wants to point out the relationship between (a,b) and c. The second inequality does not directly come from the first one.
As Professor mentioned in class, this is called triangle inequality. "Pentagon inequality" reminds us of thinking while reading notes.
Say if we have a, b and c satisfy a triangle.
What's the meaning of |a-b|<c? I think a transform of first inequality should be |c-a|<b?
@geminishActually we have some symmetricity of the triangle inequality. That is to say, we have |c-a|<b, |a-b|<c and |b-c|<a. Basically we should think that all edges have equal role and none of them are special and singular. For @Animagus, I guess he/she just wants to point out the relationship between (a,b) and c. The second inequality does not directly come from the first one.