Formulas relating the number of lines, sections, and intersection points
$$ (Error compiling LaTeX. Unknown error_msg)\text{1) The maximum number of intersection points of n lines is .}\text{2) The maximum number of planar sections (assuming the plane is bound at some point) created by n lines is \frac{n^2+n+2}{2}}\text{3)The number of lines + number of intersection points = number of sections -1 assuming that no three lines intersect at one point.}\text{4) The number of curved lines (enclosed circles)+ number of lines+ number of intersection points -1= number of sections created, provided that no three curved or straight lines intersect at the same point.}$$ (Error compiling LaTeX. Unknown error_msg) Proof: Almost the same, note however that two curved lines and intersect at two points, same for one curved and one straight line.