26 March 2011
Here's a small vector diagram I made to illustrate Varignon parallelograms (paler blue central quadrilateral in image). [I posted this because it relates to the Equinox comp above.] It demonstrates a fascinating connection between regular and irregular 4-sided shapes (proved by Varignon in 1731, and known as Varignon parallelograms). Essentially his theorem states that you can draw up any irregular quadrilateral you like (i.e. side-lengths can be random, you simply connect any 4 dots with straight lines to make a random quadrilateral). Then, (and here's the surprise), you halve each side and then join each of those mid-points to make another quadrilateral inside that. It turns out remarkably that the inner quadrilateral is always a parallelogram! The 'regular' within the 'irregular'. 'Symmetry' within asymmetry: perfectly apt as a syntactical rationale for a visual composition, a geometric collage-composition (Equinox post above).