Home⇨circularsaw3⇨

circularsaw3 with line 0 projected to infinity

This pseudoline arrangement is a uniform variation of Ceva's theorem, which has an easy to prove slope constraint (as a line arrangement, with line 0 projected to infinity). Carroll, [2000d] shows: 

   sin(θF-θE)sin(θD-θC)sin(θB-θA) < sin(θF-θA)sin(θE-θD)sin(θC-θB)

Line Order At Infinity

A< B< C< D< E< F

Bases

Positively Oriented

AEF, BEF, CDE, CDF, CEF, DEF,

Negatively Oriented

ABC, ABD, ABE, ABF, ACD, ACE, ACF, ADE, ADF, BCD, BCE, BCF, BDE, BDF,

Not Bases

The Pseudolines