bilius2007
New member
- Joined
- Dec 9, 2020
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- 20
Yes. The non-collinear requirement is wrong.So is the definition I got from my notes incorrect?
In Euclidean geometry,In my school notes, they defined an angle as two noncollinear rays called sides. But can't collinear rays form 180 degree angles?
Actually, it really depends upon who is writing the definitions. Most advanced courses is axiomatic geometry textbooks define an angle as the union of two rays with a common end point. However, one of the most important mathematicians of the late century, RL Moore, used the definition that you posted. So it is not correct to say that your notes are wrong as two others have done. You must follow the definitions in your own text material. Just be aware that there are disagreements as to definitions.In my school notes, they defined an angle as two noncollinear rays called sides. But can't collinear rays form 180 degree angles?
One reason they would use their definition (in their context) is that for a 180 degree angle you can't distinguish interior and exterior! Also, probably some theorems they state would not apply.In my school notes, they defined an angle as two noncollinear rays called sides. But can't collinear rays form 180 degree angles?