Filling in a square

A Persian handwriting, kept in the Paris Bibliothèque Nationale contains a number of drawings with written instructions, to be used for decorations. Prof. Jan Hogendijk writes about it in the magazine Wiskrant. In one of them a square is divided into four kites and a smaller square.
  • Mark on every edge of a square with edge a distance b < a/2.
  • Connect these points by segments.
  • Fold de the four triangles on these segments to form a smaller square in the middle with an edge of x.
Drag in the applet below the green point so that the ratios of the square change.
You can find this division of a square in many places e.g. in this picture on the Al Hakim Mosque in Isfahan. Kites and the square in the middle are filled in with Kufic writing. You can find more on Kufic calligraphy at Arabic Callygraphy and Square Kufic Design.