directed length, angle, and area

[pkerichang]

I first found the idea of directed length, angle, and area in a MOP note on geometry. but I'm still confuse on its defintion and use (like, when will a segment\angle\area have negative value, and how to apply it on proofs). cansomeone explain it to me? thank you (because this is important in proving collinearity and concurrency)

[darij grinberg]

This is a fairly old topic, but I am currently writing a note called "The Neuberg-Mineur circle" which will contain, on its first 5 pages, a brief introduction into some prerequirisites - including directed angles and lengths. A PDF of these pages is attached to this post. Feedback is greatly appreciated - feel free to tell me what can be improved, what is missing and what is plain wrong. Note that I am just itemizing the main properties, not proving them - in particular, I am not proving that the notions I define are indeed well-defined.

Darij