Fig. 5. The geometrical construction referred to by Tons Brunés, a Danish engineer and student of ancient geometry, as the Sacred Cut. When the point of a compass is placed at one vertex of a square and an arc is swept out, the edge of the square is cut by a factor of 1/Ö2, the sacred cut. Four sacred cuts mark the vertices of a regular octagon and lead to a subdivision of the square into three species of rectangles: a square of proportion 1:1; a square root rectangle of proportion 1:Ö2; and a rectangle of proportion 1: q, referred to as a Roman rectangle.  top of page  back to text 
