How to Create a Regular Heptagon

Accurately construct a heptagon with our simple guide

A regular heptagon (also called septagon) is a polygon with seven equal sides and seven equal angles. Accurately constructing polygons is an important part of geometry, and for regular heptagons there are multiple ways to draw one. Here is the easiest method if you are using a straight edge and compass.

Steps

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1
Draw an arbitrary circle, centred at a point $X$ . Keep in mind that you will need some extra space around the circle for construction lines.^{[1]XResearch source}
2
Draw the radius $AX$ .^{[2]XResearch source}
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3
Draw a circle with radius $AX$ , centred at $A$ . This circle intersects the first circle at points $B$ and $C$ .^{[3]XResearch source}
4
Connect $B$ and $C$ . $BC$ bisects $AX$ in $E$ .^{[4]XResearch source}
5
Draw a third circle with radius $BE$ , centred at $B$ . This circle intersects circle a in $D$ .^{[5]XResearch source}
6
Use your compass to trace the distance BD around the circle. You should end up exactly where you started. There is an error of about .2% for this method, which is negligible for any heptagon that fits on a regular A4 piece of paper. If you don't end up exactly where you started, there were probably some inaccuracies with the construction tools (e.g. the thickness of the pencil).^{[6]XResearch source}
7
Connect adjacent vertices.
8
Erase the construction lines if needed.

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How do I build a pentagon?
Donagan
Top Answerer
See Construct a Regular Pentagon.
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Tips

Put a piece of cardboard or a book under your paper so your compass doesn't slip.
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Sharpen your pencils before beginning, for increased precision.
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Trace over with a pen so it is easier to see.
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Warnings

Since 7 cannot be written as the product of a power of two and a Fermat prime, it is impossible to do an exact compass and straightedge construction of a heptagon. However, the above method has an error of less than 0.2%. When the circumscribed circle of the heptagon has a radius of 1 meter, there will be an error of approx. 1.7 mm.
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