Sequence, symmetry and pattern formation

The main capability of symmetry groups in pattern formation is the invariance of the object under the group action. Proper identification of sequential symmetries may lead to a better understanding of global patterns generated by local constructions. The objective of the present paper is to show the fruitfulness of this approach in presenting innovative proofs for two classical geometric theorems; i.e.; concurrence of bisectors in a triangle and Morley’s theorem.