# Christopher Bartlett

Professor Emeritus of Art

Art Department, Towson University

Baltimore, Maryland, USA

My meta-golden Chi ratio is a unique mathematical constant related to the golden or phi ratio.

I discovered this meta-golden Chi ratio came after nearly a decade of analyzing the geometry of composition in master paintings. Dirk Huylebrouck detailed the mathematical properties of it in Bridges Proceedings 2014.

The Chi (χ) ratio, 1+√(4phi+5)/(2phi) or approximately 1.355... is a pleasing mathematical number with remarkable geometric properties similar to the golden ratio. However, instead of partitioning into a phi rectangle and a square, as in a golden rectangle, a rectangle of width 1 and a length of Chi, sub-divides into a phi rectangle and another smaller Chi rectangle.

I discovered this meta-golden Chi ratio came after nearly a decade of analyzing the geometry of composition in master paintings. Dirk Huylebrouck detailed the mathematical properties of it in Bridges Proceedings 2014.

The Chi (χ) ratio, 1+√(4phi+5)/(2phi) or approximately 1.355... is a pleasing mathematical number with remarkable geometric properties similar to the golden ratio. However, instead of partitioning into a phi rectangle and a square, as in a golden rectangle, a rectangle of width 1 and a length of Chi, sub-divides into a phi rectangle and another smaller Chi rectangle.

Ambergris, Belize

40 x 54 cm

acrylic on canvas

2016

I have used the generative qualities of the meta-golden Chi ratio proportions to format the geometric design of this painting. The architecture of the design grid forms an analogous correlation between the proportions of the picture plane and the partitions of the areas defined inside it. The composition thus achieves an aesthetically harmonious coherence: a structure where the verticals, horizontals and divisions at edges are mathematically aligned to marshal all the elements into a unified organizational plan. It generates a geometric progression of asymmetric parts each integrally related by Chi and Phi rectangles, and squares.