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

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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.

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Written by also65

mayo 16, 2018 a 8:01 pm

Publicado en Uncategorized

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