7-Pointed Star: Approximate Construction 1
Steven Dutch, Professor Emeritus, Natural and Applied Sciences, Universityof Wisconsin - Green Bay
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 |
 |
Return to Recreational Mathematics Topics
Return to Paper-Folding
Return to Symmetry Index
Return to Professor Dutch's home page
Created 22 March 2006, Last Update20 January 2020