DIAGRAM OF A HEPTAGON

Approximate method – 7 angles of 51°,42 (companions)

The angle at the heptagon’s centre is equal to
360°/7 = 51°,42

The heptagon side GH is equal to the radius OH * 2 sin (51°,42/2)

If the radius =1, sin (51°,42/2) = 0,4338 -> GH = 0,867

On the same circle create the equilateral triangle ABC

We notice that BD = radius * cos 30°, or, radius * sin 60°, or sin 60° = cos 30° = 0,866 = BD

The half side of the inscribed equilateral triangle is a very approximate value of the side of the inscribed heptagon in the same circle.

Following page : the angle trisection