Regular heptagon - Method # 1 - Paul Courbis


   

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Home > Various (and summer) > Geometry > Regular heptagon - Method # 1

Regular heptagon - Method # 1

Sunday 25 June 2006, by Paul Courbis

Regular heptagon - Method # 1: 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 vertical segment of any length.

Step 2: any point of the vertical segment, draw a circle of arbitrary radius, then see its diameter by a new circle that is itself delayed, thus constructing a sequence 1, 2, 4.

Step 3: the top of the larger circle, draw a tangent (perpandiculaire the vertical segment) of any length.

Step 4: Taking down the center of the figure, draw a circle with radius equal to the diameter of the first circle drawn, then, with its center at the intersection of two lines, draw a circle passing through the bottom of the circle drawn.

Step 5: draw a circle whose center is lower and smaller circle drawn through the last two intersections with the horizontal line formed at the previous step.

Step 6: Beginning of the intersections used in the previous step, draw circles, crosses the intersection of the previous circle with the vertical.

Step 7: See these diameters as a center with new intersections and formed.

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 is the contruction of the report 5 / 4 (in steps 1 through 4), 1.25, knowing that the tangent of 2.PI / 7 is actually 1.254 ... The mistake in the construction of the angle is 0.0884 ° with respect to the actual angle, a total error of 0.62 °, or less than 0.2% error ...

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