How to Build a Regular Heptagon with a Compass and a Straightedge   Leave a comment

The heptagon can be drawn but it is considered that it cannot be constructed with just a compas and a straightedge. I tried this construction by using as the lenght of the sides a combination of the rational and irrational symmetry, the segment from the point R1 to i2 (in green color).

I linked to picture on the math section of Reddit website and a kind person told me that “The length of each side of the regular heptagon should be |e2𝜋i/7-1| ≈ 0.867767 times the radius of the circle. The line inside which it appears to be constructed from is √3/2 ≈ 0.866025 times the radius. Therefore, the constructed heptagon is not regular.”

As the segment is built on the root square of 0,25 (for the 0 to R1 leg on Y ) and the root square of 0,50 (for the 0 to i2 leg on X), because of the pytagorean theorem a^2 + b ^2 = c ^2, the segment that is the hypotenuse of that triangle will be the root square of 0,75 = 0.86600254

So the figure is an aaproximation to th eregular heptagon.

But if for calculating the sides of the heptagon it’s necessary to use Pi and Pi has infinite decimals, if it comes to being exact I suposse it would be necessary to say as well that the regular heptagon properly does not exist at all. It will be always an endless aproximation even having limited segments, which to me is quite contradictory.

If you read this blog you will know what I think about the irrational numbers and what I proposued as way to solve the problem of irrationality, the infinite decimals in a limited segment.

Have a nice day.

Publicado mayo 16, 2018 por also65 en Uncategorized

Escribe tu comentario

Introduce tus datos o haz clic en un icono para iniciar sesión:

Logo de

Estás comentando usando tu cuenta de Cerrar sesión /  Cambiar )

Google photo

Estás comentando usando tu cuenta de Google. Cerrar sesión /  Cambiar )

Imagen de Twitter

Estás comentando usando tu cuenta de Twitter. Cerrar sesión /  Cambiar )

Foto de Facebook

Estás comentando usando tu cuenta de Facebook. Cerrar sesión /  Cambiar )

Conectando a %s

Este sitio usa Akismet para reducir el spam. Aprende cómo se procesan los datos de tus comentarios .

A %d blogueros les gusta esto: