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 [url=http://www.fi.uu.nl/wiskrant/artikelen/artikelen11-20/162/162_hogendijk.pdf]Wiskrant[/url]. In one of them a square is divided into four kites and a smaller square. [list][*]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.[/*][/list]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 [url=https://nl.wikipedia.org/wiki/Koefisch_schrift]Kufic writing[/url]. You can find more on Kufic calligraphy at [url=https://design.tutsplus.com/tutorials/creative-arabic-calligraphy-square-kufic--cms-23012]Arabic Callygraphy[/url] and [url=http://www.kufic.info/design.htm]Square Kufic Design[/url].

Information: Filling in a square