Construction of a Polygon with “N” sides

Geometric constructions with ruler and compass

Architect Francesca Ferraro

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Geometric constructions

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29th June 2023

 

Geometric construction with ruler and compass

Starting from side AB, the axis of the segment is constructed and with radius AB, pointing first at A and then at 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 reversed and, for convenience, the numbers 7, 8, 9, 10, 11, 12 are assigned to the intersections with said axis.
 





Heptagon (7 sides)

Aiming at 7, with radius 7 a circle is constructed.

On the circumference, starting from A and B, we draw arcs of circumference with radius AB until we obtain a heptagon.
 





Octagon (8 sides)

Aiming at 8, with radius 8-A, a circle is constructed.

On the circumference, starting from A and B, we draw arcs of circumference with radius AB until we obtain an octagon.
 



Nonagon (9 sides)

Aiming at 9, with radius 9-A, a circle is constructed.

On the circumference, starting from A and B, we draw arcs of circumference with radius AB, until we obtain a non-gon.
 


Decagon (10 sides)

Aiming at 10, with radius 10-A, a circle is constructed.

On the circumference, starting from A and B, we draw arcs of circumference with radius AB, until we obtain a decagon.
 

Hendecagon (11 sides)

Aiming at 11, with radius 11-A, a circle is constructed.

On the circumference, starting from A and B, we draw arcs of circumference with radius AB, until we obtain a hendecagon.
 

Dodecagon (12 sides)

Aiming at 12, with radius 12-A, a circle is constructed.

On the circumference, starting from A and B, we draw arcs of circumference with radius AB, until we obtain a dodecagon.

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