Dissections, cuts and triangulations

: H F R Q V LG H U W ZR S U R E OH P V R Q G LV V H F W LR Q V R I S R O\J R Q V ,Q W K H p U V W S U R E OH P ZH F R Q V LG H U W K H P LQ LP X P Q X P E H U R I S LH F H V LQ G LV V H F W LQ J ZLW K U H F W LOLQ H D U J OD V V F X W V D Q P Q d P Q U H F W D Q J OH LQ W R D X Q LW V TX D U H $ U H F W D Q J OH LV F D OOH G V H P L LQ W H J H U LI H LW K H U LW V E D V H R U LW V K H LJ K W LV D Q LQ W H J H U ,Q W K H V H F R Q G S U R E OH P ZH V K R Z W K D W Q R W U LD Q J X OD W LR Q R I D U H J X OD U S R O\J R Q F D Q E H D G LV V H F W LR Q R I D Q R W K H U U H J X OD U S R O\J R Q R I W K H V D P H D U H D