In this session , the problems consists the uses of symmectries of the polygon . Here , we illustrate this with the following fasciating facts of the construction of the regular petagons .Of cource there exists a classical ruler and compass construction , but there is an easierway to do it . At first , make the simplest knot, the trefoil knot, on a ribbon of paper , then flattern it as the following knot .After cutting of the two ends of the ribbon , one obtains a regular pentagons .

Problems :

1.Let be a regular polygons inscribed in the circle of the centre and the radius . On the half line cnoose such that is between and .Prove that

= .

2.Let be a regular heptagon .Prove that

If the above relation holds then prove that the polygon is a heptagon , that is ( ).

Problems :

1.Let be a regular polygons inscribed in the circle of the centre and the radius . On the half line cnoose such that is between and .Prove that

= .

2.Let be a regular heptagon .Prove that

If the above relation holds then prove that the polygon is a heptagon , that is ( ).

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