7-Pointed Star: Approximate Construction 1

Steven Dutch, Natural and Applied Sciences, University of Wisconsin - Green BayXbr> First-time Visitors: Please visit Site Map and Disclaimer. Use "Back" to return here.

180/7 = 25.7 degrees, and tan (180/7) = 0.481. Arctan(0.5) = 26.6 degrees, less than a degree difference. This fact suggests a simple approximation.

Start with a square sheet folded diagonally in half.
Fold the two bottom corners together
Unfold the paper.
Fold the paper lengthwise in half
Unfold the paper.
A diagonal of one quarter of the paper is a good approximation to 180/7 degrees.
Fold the paper up along the diagonal
Then fold the corner flat again.
Fold the paper so the left half of the base coincides with the diagonal crease. The upfolded left edge makes an angle of 4(180/7) with the base. Bisect this angle twice to get 180/7 degrees.
Here the angle is bisected once
The final bisection
Cut the wedge as desired and unfold it as shown below.
A somewhat better approximation is to start the diagonal crease 1/4 of the way from the vertical center crease as shown.
Below is the process animated

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Created 22 March 2006, Last Update 14 December 2009