Construction of a Polygon of “N” sides

Geometric constructions with ruler and compass

Article by

Francesca Ferraro

Category

Geometric Constructions

Published on

29 June 2023

		Geometric construction with ruler and compass Starting from the AB side, the axis of the segment is constructed and with radius AB, pointing first to A and then to B, two arcs are drawn that meet at point 6. 6B is divided into six equal parts, which are called 0, the one coinciding with B, and, subsequently, 1,2,3,4,5, up to the 6 already found previously (in blue: construction of “Thales”). The points obtained on the axis of the segment are overturned and the numbers 7, 8, 9, 10, 11, 12 are attributed, for convenience, to the intersections with said axis.
		Heptagon (7 sides) By aiming at 7, with radius 7 a circle is built. On the circumference, starting from A and B, some arcs of circumference of radius AB are reported, until a heptagon is obtained.
		Octagon (8 sides) By aiming at 8, with radius 8-A a circumference is constructed. On the circumference, starting from A and B, some arcs of circumference with radius AB are reported, until an octagon is obtained.
		Ennagon (9 sides) By aiming at 9, with radius 9-A a circle is built. On the circumference, starting from A and B, some arcs of circumference of radius AB are reported, until an ennagon is obtained.
		Decagon (10 sides) Aiming at 10, with radius 10-A, a circumference is constructed. On the circumference, starting from A and B, some arcs of circumference with radius AB are reported, until a decagon is obtained.
		Hendecagon (11 sides) Pointing at 11, with radius 11-A, a circle is built. On the circumference, starting from A and B, some arcs of circumference with radius AB are reported, until a hendecagon is obtained.
		Dodecagon (12 sides) By aiming at 12, with radius 12-A, a circle is built. On the circumference, starting from A and B, some arcs of circumference of radius AB are reported, until a dodecagon is obtained.

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