▁can ▁be ▁imag ined ▁as ▁the ▁project ive ▁closure ▁of ▁the ▁real ▁plane ▁( by ▁a ▁line ▁at ▁infinity ), ▁where ▁the ▁real ▁numbers ▁are ▁replaced ▁by ▁a ▁finite ▁field ▁. ▁O dd ▁order ▁means ▁that ▁ ▁is ▁odd . ▁An ▁o val ▁is ▁a ▁curve ▁similar ▁to ▁a ▁circle ▁( see ▁definition ▁below ): ▁any ▁line ▁meets ▁it ▁in ▁at ▁most ▁ 2 ▁points ▁and ▁through ▁any ▁point ▁of ▁it ▁there ▁is ▁exactly ▁one ▁tang ent . ▁The ▁standard ▁examples ▁are ▁the ▁non de generate ▁project ive ▁con ic ▁sections . ▁ ▁In ▁p app ian ▁project ive ▁plan es ▁of ▁even ▁order ▁greater ▁than ▁four ▁there ▁are ▁o val s ▁which ▁are ▁not ▁con ics . ▁In ▁an ▁infinite ▁plane ▁there ▁exist ▁o val s , ▁which ▁are ▁not ▁con ics . ▁In ▁the ▁real ▁plane ▁one ▁just ▁gl ues ▁a ▁half ▁of ▁a ▁circle ▁and ▁a ▁suitable ▁el lipse ▁smooth ly . ▁ ▁The ▁proof ▁of ▁Seg re ' s ▁theorem , ▁shown ▁below , ▁uses ▁the ▁ 3 - point ▁version ▁of ▁Pascal ' s ▁theorem ▁and ▁a ▁property ▁of ▁a ▁finite ▁field ▁of ▁odd ▁order , ▁namely , ▁that ▁the ▁product ▁of ▁all ▁the ▁non zero ▁elements ▁equals ▁- 1 . ▁ ▁Definition ▁of ▁an ▁o val ▁▁ ▁In ▁a ▁project ive ▁plane ▁a ▁set ▁ ▁of ▁points ▁is ▁called ▁o val , ▁if : ▁( 1 ) ▁Any ▁line ▁ ▁meets ▁ ▁in ▁at ▁most ▁two ▁points . ▁If ▁ ▁the ▁line ▁ ▁is ▁an ▁exterior ▁(