Plate XIXApproximate
The construction in 23 steps

Seven will not close

No compass and straightedge can draw a true seven sided figure: Gauss stated it in 1801 and Wantzel proved it in 1837. The workshop booklet Geometria deutsch prints this answer and calls it a true heptagon; Dürer printed it again in 1525. Take half the side of the inscribed triangle as the side. It is 0.20 percent short, so seven steps leave 0.8 degrees open, ringed here in red. So every seven fold rose window rests on an approximation, whether this one or a careful trial with the dividers.

Sources

  • Carl Friedrich Gauss, Disquisitiones arithmeticae, 1801
  • Pierre Wantzel, 1837
  • Albrecht Dürer, Underweysung der Messung, 1525