Given an arrangement of n not all coincident lines on the Riemann Sphere we show that there can be no more than [4n/3] two-edged faces and give explicit examples to show that this bound is tight. We describe the connection this problem has to the problem of obtaining lower bounds on the number of ordinary points in arrangements of not all coincident, not all parallel lines (the sharpened dual to Sylvester's Problem).
By: Jonathan Lenchner
Published in: RC23412 in 2004
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