Origami is the ancient Japanese art of folding paper and it has well known algebraic and geometrical properties, but it also has unexpected relations with partial differential equations. A motivation comes from the properties of origami. Many mathematicians interested in geometry or algebra (for example in group theory, Galois theory, graph theory) studied origami constructions.In some aspect origami turns out to be more powerful than the classical rule and compass construction. In fact, in order to determine what can be constructed through origami, it is important to formalize the rules.

Here few details about this geometric approach to origami Here are the seven axioms. • Axiom 1: given two points P 1 and P 2, there is a unique fold passing through both of them; • Axiom 2: given two points P 1 and P 2, there is a unique fold placing P 1 onto P 2; • Axiom 3: given two lines L 1 and L 2, there is a fold placing L 1 onto L 2; • Axiom 4: given a point P and a line L, there is a unique fold perpendicular to L passing through P; • Axiom 5: given two points P 1 and P 2 and a line L, there is a fold placing P 1 onto L and passing through P 2; • Axiom 6: given two points P 1 and P 2 and two lines L 1 and L 2, there is a fold placing P 1onto L 1 and P 2 onto L 2; • Axiom 7: given a point P and two lines L 1 and L 2, there is a fold placing P onto L 1 and perpendicular to L 2.

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