Regular heptagon - Method # 2 - Paul Courbis


   

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Home > Various (and summer) > Geometry > Regular heptagon - Method # 2

Regular heptagon - Method # 2

Sunday 25 June 2006, by Paul Courbis

Regular heptagon - Method # 2: there is no exact construction of this figure with a ruler and compass. This is also the smallest regular polygon with this property. However, it is possible to construct an approximate version in which errors are based in the thickness of the line ...

Step 1: draw a horizontal segment of any length.

Step 2: Please enter this segment with two circles centered on the ends and radius equal to its length.

Step 3: Draw the equilateral triangle formed.

Step 4: Using the bracket, determine the center of this triangle.

Step 5: Draw a circle in which the triangle is entered, taking the center point determined in the previous step and diameter as the distance between the center and one of the vertices of the triangle.

Step 6: Taking the center of the triangle, draw the circle through the midpoint of the triangle.

Step 7: the circle drawn in step 5, see the points thus formed in step 6.

Step 8: Attach the sides of the polygon, the figure is complete.

This construction is only approximate, but the error is in the thickness of the line ...

The general principle the construction of an equilateral triangle whose half-side is very close to the side of the heptagon inscribed in the same circle. The error is less than 0.12% over the length of the segment and built, and 0.22% in terms of angle. This method is somewhat less efficient than its predecessor, but has the advantage of building around the figure of an equilateral triangle, which allows for easier design (to make a massive example) ...

The 1 / 2 side of the inscribed equilateral triangle is a very approximate value on the side of the heptagon inscribed in the same circle.

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